fin

Equity Valuation and Portfolio Management

The Frank J. Fabozzi Series Fixed Income Securities, Second Edition by Frank J. Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi Real Options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi The Exchange-Traded Funds Manual by Gary L. Gastineau Professional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J. Fabozzi Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia Pilarinu Handbook of Alternative Assets by Mark J. P. Anson The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry The Handbook of Financial Instruments edited by Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and Frank J. Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. Fabozzi Foundations of Economic Value Added, Second Edition by James L. Grant Financial Management and Analysis, Second Edition by Frank J. Fabozzi and Pamela P. Peterson Measuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J. Fabozzi,

Steven V. Mann, and Moorad Choudhry Professional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J. Fabozzi The Handbook of European Fixed Income Securities edited by Frank J. Fabozzi and Moorad Choudhry The Handbook of European Structured Financial Products edited by Frank J. Fabozzi and Moorad Choudhry The Mathematics of Financial Modeling and Investment Management by Sergio M. Focardi and

Frank J. Fabozzi Short Selling: Strategies, Risks, and Rewards edited by Frank J. Fabozzi The Real Estate Investment Handbook by G. Timothy Haight and Daniel Singer Market Neutral Strategies edited by Bruce I. Jacobs and Kenneth N. Levy Securities Finance: Securities Lending and Repurchase Agreements edited by Frank J. Fabozzi and Steven V. Mann Fat-Tailed and Skewed Asset Return Distributions by Svetlozar T. Rachev, Christian Menn, and

Frank J. Fabozzi Financial Modeling of the Equity Market: From CAPM to Cointegration by Frank J. Fabozzi, Sergio M.

Focardi, and Petter N. Kolm Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by

Frank J. Fabozzi, Lionel Martellini, and Philippe Priaulet Analysis of Financial Statements, Second Edition by Pamela P. Peterson and Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas, Laurie S.

Goodman, and Frank J. Fabozzi Handbook of Alternative Assets, Second Edition by Mark J. P. Anson Introduction to Structured Finance by Frank J. Fabozzi, Henry A. Davis, and Moorad Choudhry Financial Econometrics by Svetlozar T. Rachev, Stefan Mittnik, Frank J. Fabozzi, Sergio M. Focardi, and

Teo Jasic Developments in Collateralized Debt Obligations: New Products and Insights by Douglas J. Lucas,

Laurie S. Goodman, Frank J. Fabozzi, and Rebecca J. Manning Robust Portfolio Optimization and Management by Frank J. Fabozzi, Petter N. Kolm,

Dessislava A. Pachamanova, and Sergio M. Focardi Advanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T. Rachev,

Stogan V. Stoyanov, and Frank J. Fabozzi How to Select Investment Managers and Evaluate Performance by G. Timothy Haight,

Stephen O. Morrell, and Glenn E. Ross Bayesian Methods in Finance by Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and

Frank J. Fabozzi Structured Products and Related Credit Derivatives by Brian P. Lancaster, Glenn M. Schultz, and Frank J. Fabozzi Quantitative Equity Investing: Techniques and Strategies by Frank J. Fabozzi, Sergio M. Focardi, and

Petter N. Kolm Introduction to Fixed Income Analytics, Second Edition by Frank J. Fabozzi and Steven V. Mann The Handbook of Traditional and Alternative Investment Vehicles by Mark J. P. Anson, Frank J. Fabozzi,

and Frank J. Jones The Theory and Practice of Investment Management, Second Edition edited by Frank J. Fabozzi and

Harry M. Markowitz

John Wiley & Sons, Inc.

Equity Valuation and Portfolio Management

FRANK J. FABOZZI HARRY M. MARKOWITZ

EDITORS

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.

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Contents

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Preface xiii About the Editors xxiii Contributing Authors xxv

CHAPTER 1 An Introduction to Quantitative Equity Investing 1 Paul Bukowski

Equity Investing 1 Fundamental vs. Quantitative Investor 2 The Quantitative Stock Selection Model 7 The Overall Quantitative Investment Process 9 Research 9 Portfolio Construction 18 Monitoring 21 Current Trends 22 Key Points 23 Questions 24

CHAPTER 2 Equity Analysis Using Traditional and Value-Based Metrics 25 James L. Grant and Frank J. Fabozzi

Overview of Traditional Metrics 25 Price Multiples 32 Fundamental Stock Return 36 Traditional Caveats 38 Overview of Value-Based Metrics 39 Key Points 58 Appendix: Case Study 60 Questions 69

vi CONTENTS

CHAPTER 3 A Franchise Factor Approach to Modeling P/E Orbits 71 Stanley Kogelman and Martin L. Leibowitz

Background 72 Historical Data Observations 75 Formulation of the Basic Model 81 P/E Myopia: The Fallacy of a Stable P/E 85 Two-Phase P/E Orbits 91 Franchise Valuation under Q-Type Competition 96 Franchise Labor 97 Key Points 101 Questions 102

CHAPTER 4 Relative Valuation Methods for Equity Analysis 105 Glen A. Larsen Jr., Frank J. Fabozzi, and Chris Gowlland

Basic Principles of Relative Valuation 106 Hypothetical Example 115 Key Points 123 Questions 124

CHAPTER 5 Valuation over the Cycle and the Distribution of Returns 125 Anders Ersbak Bang Nielsen and Peter C. Oppenheimer

The Link Between Earnings and Returns 126 The Phases Can Be Interpreted in Relationship to the Economy 132 Asset Class Performance Varies across the Phases 137 Incorporating Cyclicality into Valuations 139 Appendix: Dates and Returns of the Phases 142 Key Points 146 Questions 146

CHAPTER 6 An Architecture for Equity Portfolio Management 147 Bruce I. Jacobs and Kenneth N. Levy

Architectural Building Blocks 148 Traditional Active Management 151 Passive Management 156 Engineered Management 157

Contents vii

Expanding Opportunities 160 The Risk-Return Continuum 163 The Ultimate Objective 167 Key Points 168 Questions 169

CHAPTER 7 Equity Analysis in a Complex Market 171 Bruce I. Jacobs and Kenneth N. Levy

An Integrated Approach to a Segmented Market 172 Disentangling 176 Constructing, Trading, and Evaluating Portfolios 184 Profiting from Complexity 186 Key Points 187 Questions 188

CHAPTER 8 Survey Studies of the Use of Quantitative Equity Management 189 Frank J. Fabozzi, Sergio M. Focardi, and Caroline L. Jonas

2003 Intertek European Study 189 2006 Intertek Study 197 2007 Intertek Study 205 Challenges for Quantitative Equity Investing 224 Modeling After the 2007–2009 Global Financial Crisis 226 Key Points 228 Questions 229

CHAPTER 9 Implementable Quantitative Equity Research 231 Frank J. Fabozzi, Sergio M. Focardi, and K. C. Ma

The Rise of Econophysics 233 A General Framework 235 Select a Sample Free from Survivorship Bias 238 Select a Methodology to Estimate the Model 239 Risk Control 246 Key Points 248 Questions 249

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CHAPTER 10 Tracking Error and Common Stock Portfolio Management 251 Raman Vardharaj, Frank J. Fabozzi, and Frank J. Jones

Definition of Tracking Error 251 Components of Tracking Error 254 Forward-Looking vs. Backward-Looking Tracking Error 255 Information Ratio 256 Determinants of Tracking Error 257 Marginal Contribution to Tracking Error 261 Key Points 262 Questions 263

CHAPTER 11 Factor-Based Equity Portfolio Construction and Analysis 265 Petter N. Kolm, Joseph A. Cerniglia, and Frank J. Fabozzi

Factor-Based Trading 266 Developing Factor-Based Trading Strategies 269 Risk to Trading Strategies 271 Desirable Properties of Factors 273 Sources for Factors 273 Building Factors from Company Characteristics 274 Working with Data 275 Analysis of Factor Data 283 Key Points 287 Questions 289

CHAPTER 12 Cross-Sectional Factor-Based Models and Trading Strategies 291 Joseph A. Cerniglia, Petter N. Kolm, and Frank J. Fabozzi

Cross-Sectional Methods for Evaluation of Factor Premiums 292 Factor Models 300 Performance Evaluation of Factors 310 Model Construction Methodologies for a

Factor-based Trading Strategy 317 Backtesting 328 Backtesting Our Factor Trading Strategy 330 Key Points 331 Appendix: The Compustat Point-in-Time,

IBES Consensus Databases and Factor Definitions 333 Questions 337

Contents ix

CHAPTER 13 Multifactor Equity Risk Models and Their Applications 339 Anthony Lazanas, António Baldaque da Silva, Arne D. Staal, and Cenk Ural

Motivation 340 Equity Risk Factor Models 342 Applications of Equity Risk Models 350 Key Points 370 Questions 371

CHAPTER 14 Dynamic Factor Approaches to Equity Portfolio Management 373 Dorsey D. Farr

Methods of Active Management 376 Modeling 385 Implementation 392 Key Points 395 Questions 395

CHAPTER 15 A Factor Competition Approach to Stock Selection 397 Joseph Mezrich and Junbo Feng

The Problem 397 The Solution 403 Which Factors Get Picked? 407 Does the Alpha Repair Process Work? 408 Key Points 411 Questions 412

CHAPTER 16 Avoiding Unintended Country Bets in Global Equity Portfolios 413 Michele Aghassi, Cliff Asness, Oktay Kurbanov, and Lars N. Nielsen

Country Membership and Individual Stock Returns 414 Ways to Build Active Global Portfolios 416 Studying the Naive Portfolio 419 Empirical Results 420 Why Does the Naive Stock Selection

Portfolio Make Country Noise Bets? 422 Key Points 423 Questions 424

x CONTENTS

CHAPTER 17 Modeling Market Impact Costs 425 Petter N. Kolm and Frank J. Fabozzi

Market Impact Costs 426 Liquidity and Transaction Costs 427 Market Impact Measurements and Empirical Findings 430 Forecasting and Modeling Market Impact 433 Key Points 439 Questions 440

CHAPTER 18 Equity Portfolio Selection in Practice 441 Dessislava A. Pachamanova and Frank J. Fabozzi

Portfolio Constraints Commonly Used in Practice 442 Benchmark Exposure and Tracking Error Minimization 450 Incorporating Transaction Costs 454 Incorporating Taxes 460 Multi-Account Optimization 465 Robust Parameter Estimation 469 Portfolio Resampling 471 Robust Portfolio Optimization 474 Key Points 480 Questions 481

CHAPTER 19 Portfolio Construction and Extreme Risk 483 Jennifer Bender, Jyh-Huei Lee, and Dan Stefek

Measures of Extreme Loss 484 Constraining Shortfall 485 Performance 485 Imposing Benchmark Neutrality 487 Analysis 489 Key Points 493 Appendix: Constructing Out-of-Sample Shortfall Betas 494 Questions 495

CHAPTER 20 Working with High-Frequency Data 497 Irene Aldridge

What is High-Frequency Data? 497

Contents xi

How is High-Frequency Data Recorded? 499 Properties of High-Frequency Data 500 High-Frequency Data are Voluminous 501 High-Frequency Data are Subject to Bid-Ask Bounce 503 High-Frequency Data are Irregularly Spaced in Time 509 Equity Correlations Decay at High Frequencies 517 Key Points 519 Questions 520

CHAPTER 21 Statistical Arbitrage 521 Brian J. Jacobsen

Pairs Trading 523 General Models 532 Key Points 534 Questions 534

About the Website 535 Index 537

Preface

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In an editorial in the Winter 2011 issue of the Journal of Portfolio Man-agement, Mark Kritzman notes the following regarding what is popularly referred to as Markowitz portfolio theory: “Mean-variance optimization is about to begin its 60th year and by all accounts it has aged extremely well.” He goes on to say, “As with many innovations, however, practitioners of the old technology resisted change and defended their resistance with a variety of excuses, which persist even today.” There are several reasons why practi- tioners were reluctant or slow to adopt a more quantitative approach such as that offered by the mean-variance framework. The computing power needed to manipulate the databases used to obtain the required inputs for mean-variance analysis and then efficiently solve for the optimal portfolios was very limited in the years that followed its introduction in 1952. Major advances in computing power have taken care of this obstacle, as well as the availability of commercial software for solving large complex optimization problems.

A second reason for the reluctance or inability to adopt a more quanti- tative approach was simply practitioners’ lack of the mathematical skill set necessary to appreciate the advantages of a quantitative approach. Since the late 1970s, however, university finance programs have armed their gradu- ates with the mathematical and statistical skills needed to deal with quan- titative models. In fact, over the past decade, a good number of universities have augmented their degree offerings beyond the traditional MBA with a specialization in finance to degree programs that bear titles such as “com- putational finance,” “quantitative finance,” “mathematical finance,” and “financial engineering,” in recognition of the need to equip students with strong quantitative skills.

Finally, the classical mean-variance model required refinements and extensions to deal with real-world institutional constraints and market fric- tions and allow it to be effectively implemented in the real world. In this book, the contributors provide the state-of-the-art methods for implement- ing equity valuation models, trading models, and portfolio management strategies. Both traditional equity management and quantitative equity management are covered. All of the contributors to this book have had experience as equity portfolio managers or equity strategists.

xiv PREFACE

In the first chapter, Paul Bukowski reviews the fundamentals of quan- titative equity investing, the core steps in the quantitative equity invest- ment process, and the most common techniques used by quantitative equity managers. He contrasts quantitative equity investing with the traditional approaches and explains how the quantitative and traditional approaches differ in their creation of a repeatable process that utilizes several key crite- ria to find the most attractive companies—the stock selection model.

Chapters 2 and 3 cover relatively new and improved approaches for what would be classified as “traditional” approaches to equity selection. Fundamentals and valuation metrics are used in traditional and value-based approaches to equity valuation. James Grant and Frank Fabozzi explain and illustrate both approaches in Chapter 2 with the goal of showing their joint role in the valuation process. Liquidity, activity, debt (leverage), and profit- ability measures are used in the traditional approach, with growth rates and profitability measures often combined with relative valuation measures (“multiples”) to assess the attractiveness or unattractiveness of a firm’s com- mon stock. Value-based metrics are financial measures that concentrate on metrics for discerning whether a company is pointing in the direction of wealth creation or wealth destruction. In this relatively new approach, the focus is on identifying firms that can consistently earn a return on capital that exceeds their weighted average cost of capital. A financial metric takes on a value-based metric character when there is an explicit recognition of and accounting for the overall cost of capital or the cost of equity. Hence, the most distinctive feature of the value-based metric analysis in contrast to traditional analysis is the formal recognition of the investor’s required rate of return (cost of equity) and the overall cost of capital. The most often used value-based metrics—residual income, economic value added (EVA®), mar- ket value added (MVA), and cash flow return on investment (CFROI®)—are explained in the chapter. In the end, the objective of both the traditional and value-based approaches is to determine a target valuation for a company leading to a potential buy (or “overweight” relative to reference index), sell (“underweight” relative to index) or hold decision (benchmark weight) on a company’s stock. After reviewing the relevant metrics, Grant and Fabozzi illustrate the benefits of using a synthesized approach to assess potential buy and sell (short) opportunities

As Stanley Kogelman and Martin Leibowitz note in Chapter 3, although the standard dividend discount model is still often used as an equity valua- tion model, the model often masks the extreme variations in growth expec- tations, return on equity, and sustainable earnings that drive the change in valuations and move markets. These limitations of the dividend discount model are overcome by the franchise factor model developed by Kogel- man and Leibowitz. This model offers greater clarity on how corporate and

Preface xv

economic events impact the key components of a firm’s value while still maintaining one of the major appeals of the dividend discount model—sim- plicity and intuitive appeal.

Relative valuation methods are a traditional approach for compar- ing several companies by using multiples or ratios (such as price–earnings, price–book, and price–free cash flow), implicitly assuming that the firms being analyzed are similar in their investment attributes and, therefore, on average, likely to trade at similar multiples. If so, relative valuation methods can be used by portfolio managers to identify companies that look “cheap” or “expensive” relative to their peers and thereby provide another tool for equity portfolio selection in long-only and long-short strategies. Relative valuation methods for equity analysis are covered in Chapter 4 by Glen Larsen Jr., Frank Fabozzi, and Chris Gowlland.

Empirical studies have found what intuition would suggest about stock behavior: Valuation is a good predictor of returns over the long run. Although today’s valuations offer investors a good deal of information about future expected returns, they are silent regarding how these returns should be distributed over time. For example, investors would like to know whether future expected returns are evenly distributed over several years or whether returns cluster into short time periods. Moreover, investors want to know whether there is a process that determines how future expected returns are generated. In Chapter 5, Anders Ersbak Bang Nielsen and Peter Oppenheimer address this issue. As they point out, the empirical evidence based on historical observations suggests that there is a relationship between valuation, earnings, and the economic cycle that provides guidance to future expected returns. The practical implication of their findings that valuations and returns shift over the economic cycle is that valuation models should be adjusted to take into account this important relationship.

In Chapter 6, Bruce Jacobs and Kenneth Levy provide an architecture for equity portfolio management, outlining the fundamental relationships between stocks (the raw investment material), investment approaches (port- folio construction techniques), potential rewards, and possible risks. The basic building blocks for constructing portfolios is the equity core and its constituent style subsets that are comprised of stocks with similar price behaviors—large-cap growth, large-cap value, and small-cap stocks. Inves- tors must also decide among possible investment approaches—traditional, passive, and engineered (quantitative) active—each of which can be char- acterized by an underlying investment philosophy and a general level of risk. Because investment performance reflects breadth of inquiry (the sheer number of investment opportunities) and depth of analysis (the strength of investment insights), the three investment approaches can be distinguished on that basis. Although the traditional management approach provides

xvi PREFACE

depth, it is characterized by a lack of breadth, susceptibility to cognitive errors, and lack of portfolio integrity. In contrast, there is no depth at all provided by the passive management approach but it does offer breadth, freedom from cognitive errors, and portfolio integrity. The advantage of the engineered management approach compared to the other two approaches is that it is capable of allowing a manager to construct portfolios that benefit from both breadth and depth of analysis, are free of cognitive errors, and have structural integrity. Breadth can be expanded with the use of short selling, either in market neutral long-short or 130-30 enhanced active long- short strategies.

Bruce Jacobs and Kenneth Levy describe in Chapter 7 their approach to investing and its application to the stock selection, portfolio construc- tion, and performance evaluation problems in a complex system such as the equity market. They discuss the advantages and disadvantages of portfolio managers trying to cover the broadest possible range of stocks or realiz- ing better analytical insights by allocating their limited resources so as to concentrate on a particular subset of the market or a limited number of stocks. They explain how combining the two may offer the best avenue for identifying investment opportunities. They also discuss what Harry Mar- kowitz in his foreword to the 2000 Jacobs-Levy book (Quantitative Analy- sis for Stock Selection) has termed their “seminal work” on disentangling return-predictor relationships. This involves multivariate analysis of numer- ous individual stock fundamental and behavioral variables, industry affili- ations, and macroeconomic conditions, to forecast “pure” returns to each predictor, independent of the effects of other factors. Disentangling return- predictor relationships can reveal hidden opportunities and distinguish real from spurious effects; the resulting return predictions are also additive and generally more persistent than “naive” predictions obtained from simpler analyses using only one or a few factors at a time.

The balance of the book deals primarily with quantitative equity man- agement. A review of three studies based on surveys and interviews of mar- ket participants about their use and experience with quantitative equity techniques is the subject of Chapter 8 coauthored by Frank Fabozzi, Sergio Focardi, and Caroline Jonas. They report that the primary methodology of financial modeling in investment management is factor models, which are used to forecast returns and to compute exposure to risk factors. Quantita- tive techniques that are also widely used are momentum and reversal mod- els, cash flow–based models, and behavioral models. There is increased use of adaptive models capable of dealing with different market conditions and robust optimization models for portfolio optimization along with robust techniques for estimating inputs. It is expected that in the future there will see greater use of models for dealing with nonlinearities and fat-tailed

Preface xvii

distributions, the use of risk measures suitable for nonlinear distributions, and methods to measure the complexity of the financial system.

In the quantitative process, the identification of any persistent pattern in the data is sought and must then be converted it into implementable and profitable investment strategies. As explained by Frank Fabozzi, Ser- gio Focardi, and K. C. Ma in Chapter 9, how this is done requires the development of underlying economic theories, an explanation of actual returns, estimation of expected returns, and construction of corresponding portfolios. In evaluating models for potential implementation of investment strategies, two guiding principles are model simplicity and out-of-sample validation. A portfolio manager can place a higher level of confidence on a simple model validated on data different from those on which it has been built. The selection of a methodology for estimating a model should sat- isfy the same quality tests as developing economic theories and selecting samples. In the absence of strong intuition, the methodology that needs the least amount of human inputs should be employed for estimating a model. Even if the expected return is modeled properly at the individual stock level, the bottom line of implementable investment strategies is evaluated by an acceptable level of risk-adjusted portfolio excess returns. Because most insti- tutional portfolios are benchmarked, the objective is to minimize tracking error given some level of portfolio excess return. For this purpose, risk con- trol becomes technically much more complex than the conventional efficient portfolio concept.

The measure used to control equity portfolio risk relative to a specified benchmark, as well as for risk budgeting (i.e., allocation of risk) and assess- ing performance, is tracking error. This metric, also referred to as tracking error risk, is the dispersion of a portfolio’s active returns (where the active return is the difference between a portfolio’s return and a benchmark’s return). In Chapter 10, Raman Vardharaj, Frank Fabozzi, and Frank Jones review the concepts of backward-looking and forward-looking tracking error and identify the major factors that affect tracking error.

In Chapters 11 and 12, companion chapters coauthored by Petter Kolm, Joseph Cerniglia, and Frank Fabozzi, a demonstration of how to employ factors to build equity forecasting models is provided. These models, also referred to as alpha or stock selection models, serve as mathematical rep- resentations of trading strategies. The eight main steps in the development of a factor-based trading strategy are defining a trading idea or investment strategy, developing factors, acquiring and processing data, analyzing the factors, building the strategy, evaluating the strategy, backtesting the strat- egy, and implementing the strategy. The authors describe and illustrate with real-world examples these steps. In Chapter 11, the development of trad- ing strategies based on factors constructed from common (cross-sectional)

xviii PREFACE

characteristics of stocks is provided. After providing a definition of factors, they examine the major sources of risk associated with trading strategies and demonstrate how factors are constructed from company characteris- tics and market data. Because the quality of the data used in this process is critical, several data scrubbing and adjustment techniques to deal with the problems arising from backfilling and restatements of data, missing data, inconsistently reported data, as well as survivorship and look-ahead biases are explained. Finally, they discuss the analysis of the statistical proper- ties of factors. Basic statistical measures include the time-series and cross- sectional averages of the mean, standard deviations, and key percentiles.

In Chapter 12, Kolm, Cerniglia, and Fabozzi extend the analysis to include multiple factors with the goal of developing a dynamic multifactor trading strategy that incorporates a number of common institutional con- straints, such as turnover, transaction costs, sector allocation, and tracking error. After reviewing several approaches for the evaluation of return premi- ums and risk characteristics to factors (the four most common being portfo- lio sorts, factor models, factor portfolios, and information coefficients), they describe four approaches (data driven, factor model, heuristic, and optimiza- tion) used to combine several factors into a single model—a trading strat- egy. To understand the performance and risk characteristics of a factor-based trading strategy, it is imperative to perform out-of-sample backtests. An out- of-sample methodology is a backtesting methodology where the researcher uses a subset of the sample to specify a model and then evaluates the fore- casting ability of the model on a different subset of data. The authors explain the two approaches for implementing an out-of-sample methodology: the split-sample approach and the recursive out-of-sample test.

While Chapters 11 and 12 describe how to build and test factor–based models so that they can be used as the basis for trading strategies, in Chap- ter 13. Anthony Lazanas, António Baldaque da Silva, Arne Staal, and Cenk Ural present an actual equity factor model—the Barclays Capital Global Risk Model—and demonstrate its applications to portfolio risk manage- ment, portfolio construction, portfolio rebalancing, scenario analysis, and performance attribution. Although the authors describe the structure of multifactor equity risk models, types of factors used in these models, and estimation techniques as in the prior two chapters, the applications are the focal point. In particular, they explain how an equity factor model provides portfolio managers with insight into the major sources of portfolio risk so that managers can control a portfolio’s risk exposures and understand the contributions of different portfolio components to total risk. They also show how a factor model can be used in performance attribution analysis so as to (1) provide ex post insight into how the portfolio manager’s views and corresponding investments can be translated into actual returns and (2)

Preface xix

provide portfolio managers with a powerful tool to perform stress testing of portfolio positions and gain insight into the impact of specific market events on portfolio performance.

Portfolio managers use factor models to construct portfolios based on tactical exposure to factors such as equity style, industry, or geographic loca- tion, macroeconomic factors, or microeconomic factors while attempting to eliminate sources of security-specific risk. Dynamic factor approaches to portfolio management, the subject of Chapter 14, authored by Dorsey Farr, describes portfolio strategies based on dynamic factor methods, explores a variety of the modeling approaches used to govern the implementation of these strategies, reviews the increasing number of tools available for imple- mentation of these strategies, and highlights how security selection is no longer necessary for an efficient implementation in many cases.

A dilemma facing managers employing factor models for stock selection is deciding when to abandon a factor that seems to have lost efficacy, and when to introduce one that appears to have become important. Joseph Mezrich and Junbo Feng describe an approach in Chapter 15, which they refer to as the “Alpha Repair” strategy, which deals with this issue. The objective of the proposed approach is to provide a systematic framework that removes failed strategies from the factor model until they prove worthy, while providing an opportunity for new strategies to be introduced into the factor model. They cast the problem as one of asset allocation for factors, with the important twist that a large set of factors always compete for a place in a small set of factors that are used for stock selection. The history of a factor return, volatility, and correlation with other factor returns in a given month is the criterion used to determine whether a factor remains in the model.

Although a good number of studies have analyzed the relative impor- tance of stock-specific risk, sector risk, and country risk for global portfolios and find that country risk is a key driver of individual stock returns, there has been less focus on the impact of country membership on actively man- aged stock portfolios. For example, there is a question as to whether ignor- ing country membership in constructing global portfolios can hamper accu- rate risk allocation. This issue is addressed by Michele Aghassi, Cliff Asness, Oktay Kurbanov, and Lars Nielsen in Chapter 16, where they demonstrate that ignoring country membership in stock portfolio construction can yield sizeable country bets, which may in fact be dominated by unintended tilts. They show that these issues are especially pronounced in the context of emerging market countries. They then explain how a stock selection man- ager can (within a quantitative or qualitative process) adjust for country membership in order to achieve accurate risk allocation and thereby reduce the likelihood of “noise pollution” of alpha signals.

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The transaction costs associated with trading adversely impact port- folio return. Therefore, efficient equity portfolio management requires a systematic integration of trading costs management, trading execution, and portfolio management. Petter Kolm and Frank Fabozzi address equity transaction costs in Chapter 17, first defining the different types of costs— explicit costs (which include brokerage and taxes) and implicit costs (which include market impact costs, price movement risk, and opportunity cost)— and then introducing several approaches for the modeling of transaction costs, in particular market impact costs. Typical forecasting models for market impact costs are based on a statistical factor approach.

Quantitative formulations of portfolio allocation problems used in equity portfolio management are presented in Chapters 18 and 19. As noted earlier, a quantitative equity portfolio selection often involves extending the classical mean-variance framework formulated by Harry Markowitz or modifying the framework to incorporate more advanced tail-risk portfolio allocation frameworks so as to include different constraints that take specific investment guidelines and institutional features into account. In Chapter 18, Dessislava Pachamanova and Frank Fabozzi discuss extensions—such as index tracking formulations, the incorporation of transaction costs, optimi- zation of trades across multiple client accounts, and tax-aware strategies— and review methods for incorporating robustness into quantitative portfolio allocation procedures by applying robust statistics, simulation, and robust optimization techniques. In Chapter 19, Jennifer Bender, Jyh-Huei Lee, and Dan Stefek adapt mean-variance analysis so as to construct active equity portfolios with less exposure to extreme losses compared to normal opti- mized portfolio. They do so by introducing a measure of the sensitivity of a portfolio to periods of extreme stress that they refer to as shortfall beta and then constrain this measure in the optimization process. Their empirical evidence demonstrates the potential benefits of constraining shortfall beta.

The idiosyncrasies, opportunities, and pitfalls in equity portfolio man- agement arising from the use of high-frequency data (i.e., bid and ask quotes, sizes and latest trade characteristics that are recorded sequentially at irregular time intervals) are covered in Chapter 20 by Irene Alridge. She explains how and when the traditional methods of data analyses employed when low-frequency data (such as daily data) are used by equity managers must to be modified to deal with the unique nature of high-frequency data.

Statistical arbitrage strategies seek to identify mispriced stocks using quantitative models of historical prices and then exploit the mispricings that have been identified. Investors employing such strategies are subject to a myriad of risks. The major risk is model risk, which is the risk that the quantitative model of the price process of stocks employed in the strategy to identify mispricing may not be valid. In Chapter 21, Brian Jacobsen explains

Preface xxi

two simple models of statistical arbitrage—pairs trading and correlation trading—and then presents a more general method based on modeling the long-run relationships and short-run dynamics of the pricing processes.

Frank J. Fabozzi Harry M. Markowitz May 2011

About the Editors

xxiii

Frank J. Fabozzi is Professor of Finance at EDHEC Business School and a member of the EDHEC-Risk Institute. Prior to joining EDHEC in August 2011, he held various professorial positions in finance at Yale University’s School of Management from 1994 to 2011 and from 1986 to 1992 was a visiting professor of finance and accounting at MIT’s Sloan School of Man- agement. Professor Fabozzi is the editor of the Journal of Portfolio Man- agement, as well as an associate editor of the Journal of Fixed Income and on the editorial boards of the Journal of Asset Management, Journal of Structured Finance, Quantitative Finance, and Review of Futures Markets. He earned a doctorate in economics from the City University of New York in 1972. He is a trustee for the BlackRock family of closed-end funds. In 2002, he was inducted into the Fixed Income Analysts Society’s Hall of Fame and is the 2007 recipient of the C. Stewart Sheppard Award given by the CFA Institute. He earned the designation of Chartered Financial Ana- lyst and Certified Public Accountant. He has authored and edited numerous books in finance.

Harry M. Markowitz has applied computer and mathematical techniques to various practical decision making areas. In finance, in an article in 1952 and a book in 1959, he presented what is now referred to as MPT, “modern portfolio theory.” This has become a standard topic in college courses and texts on investments and is widely used by institutional investors for tacti- cal asset allocation, risk control, and attribution analysis. In other areas, Dr. Markowitz developed “sparse matrix” techniques for solving very large mathematical optimization problems. These techniques are now standard in production software for optimization programs. He also designed and supervised the development of the SIMSCRIPT programming language. SIMSCRIPT has been widely used for programming computer simulations of systems like factories, transportation systems, and communication net- works. In 1989, Dr. Markowitz received the John von Neumann Award from the Operations Research Society of America for his work in portfolio theory, sparse matrix techniques, and SIMSCRIPT. In 1990, he shared the Nobel Prize in Economics for his work on portfolio theory.

Contributing Authors

xxv

Michele Aghassi AQR Capital Management

Irene Aldridge ABLE Alpha Trading

Cliff Asness AQR Capital Management

António Baldaque da Silva Barclays Capital

Jennifer Bender MSCI

Paul Bukowski Hartford Investment Management

Joseph A. Cerniglia Courant Institute of Mathematical Sciences, New York University

Frank J. Fabozzi EDHEC School of Business

Dorsey D. Farr French Wolf & Farr

Junbo Feng Nomura Securities International, Inc.

Sergio M. Focardi EDHEC Business School and The Intertek Group

Chris Gowlland Delaware Investments

James L. Grant University of Massachusetts–Boston

Bruce I. Jacobs Jacobs Levy Equity Management

Brian J. Jacobsen Wells Fargo Funds Management and Wisconsin Lutheran College

Caroline L. Jonas The Intertek Group

Frank J. Jones San Jose State University

Stanley Kogelman Delft Strategic Advisors, LLC

Petter N. Kolm Courant Institute of Mathematical Sciences, New York University

Oktay Kurbanov AQR Capital Management

Glen A. Larsen Jr. Indiana University, Kelley School of Business–Indianapolis

Anthony Lazanas Barclays Capital

Jyh-Huei Lee MSCI

Martin L. Leibowitz Morgan Stanley & Co.

xxvi CONTRIBUTING AUTHORS

Kenneth N. Levy Jacobs Levy Equity Management

K. C. Ma KCM Asset Management, Inc. and Stetson University

Joseph Mezrich Nomura Securities International, Inc.

Lars N. Nielsen AQR Capital Management

Anders Ersbak Bang Nielsen Goldman Sachs International

Peter C. Oppenheimer Goldman Sachs International

Dessislava A. Pachamanova Babson College

Arne D. Staal Barclays Capital

Dan Stefek MSCI

Cenk Ural Barclays Capital

Raman Vardharaj OppenheimerFunds

1

CHAPTER 1 An Introduction to

Quantitative Equity Investing Paul Bukowski, CFA

Senior Vice President, Head of Equities Hartford Investment Management

The goal of this chapter is to provide the reader a basic understanding of quantitative equity investing and to explain the quantitative investing process. We focus on the following three questions:

1. How do quantitative and fundamental equity investors differ? 2. What are the core steps in a quantitative equity investment process? 3. What are the basic building blocks used by quantitative equity investors?

In answering these questions, this chapter explores the quantita- tive equity investment process. We see how it is similar to many other approaches, all searching for the best stocks. Where it differs is in the cre- ation of a repeatable process that uses several key criteria to find the most attractive companies—its stock selection model. Additionally, some of the most common techniques used by quantitative equity investors are covered.

It is important to understand that this chapter is dedicated to a tradi- tional quantitative equity investing approach. There are many other types of investing that are quantitative in nature such as high-frequency trading, statistical arbitrage, and the like, however, these are not covered.

EQUITY INVESTING

Investing can take many forms, but it starts with an investor assigning a value to a security. Whether this value exceeds or is less than the current market price usually determines whether the investor will buy or sell the

2 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

security. In the case of equities, the investor often seeks to understand the specific company under consideration, the broader economic environment, and the interplay between the two. This encompasses a wide range of in- formation for the investor to consider as displayed in Exhibit 1.1. How this information is used differentiates the quantitative from the fundamental investor.

FUNDAMENTAL VS. QUANTITATIVE INVESTOR

Let’s start with a basic question. How do portfolio managers select stocks from a broad universe of more than a thousand companies?

Fundamental managers start with a basic company screen. For instance, they may first look for companies that satisfy conditions such as a price-to- earnings (P/E) ratio that is less than 15, earnings growth greater than 10%, and profit margins in excess of 20%. Filtering by those characteristics may result in, say, 200 potential candidates. Next, portfolio managers in consul- tation with their group of stock analysts spend the majority of their time thoroughly reviewing each of the potential candidates to arrive at the best 50 to 100 stocks for their portfolio. A quantitative manager, in contrast, spends the bulk of their time determining the characteristics for the initial stock screen, their stock selection model. They will look for five or more unique characteristics that are good at identifying the most attractive 200

EXHIBIT 1.1 The Value of a Stock Comes from Multiple Information Sources

Brand Name

Press Releases

Mergers & Acquisitions

Analyst Guidance

Lawsuits

Management Changes

P/E Ratio

Federal Legislation

Sales Growth

New Products

Company Guidance

SEC Investigation

Asset Turnover

Distribution Changes

Patents

Research & Development Gross Margins

Advertising Accounting

Rules

An Introduction to Quantitative Equity Investing 3

stocks of the universe. A quantitative manager will then purchase all 200 stocks for their portfolio.

So let’s expand on how these two investors—fundamental and quantitative— differ? Exhibit 1.2 details the main attributes of the following two approaches:

1. Focus: Company vs. characteristic. The fundamental investor’s primary analysis is on a single company at a time, while the quantitative inves- tor’s primary analysis is on a single characteristic at a time. For example, a fundamental investor may analyze a health care company to assess if a company’s sales prospects look strong and whether this stronger sales growth is reflected in the company’s current stock price. A quantitative investor may also invest in a company based on its sales growth, but will start by assessing the sales growth characteristic. The quantitative investor will determine whether stocks within the group, health care companies, with higher sales growth also have higher stock returns. If they do, then the quantitative investor will buy health care stocks with higher sales growth. In the end, both types of investors may buy a stock due to its good sales prospects, but both come at the decision from a different point of view.

2. Narrow vs. broad. Fundamental investors focus their attention nar- rowly on a small group of stocks. They cover fewer companies since

EXHIBIT 1.2 Fundamentals vs. Quantitative Investor: Viewing Information

Primary focus: company

In-depth company analysis

Targeted stock bets

Qualitative assessment—story Forecast future earnings Predict company catalysts

Know company specific risks

Primary focus: characteristics

Drivers of performance across companies Law of Large numbers

Spread stock bets across companies

Analyze company relative to broad peer group Disciplined—specific stock picking criteria (repeatable) Understanding what worked in the past

Know portfolio level risks

Quantitative (Scientist)

Narrow – Future - Story Broad – Past - Disciplined

Fundamental (Journalist)

4 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

they make more in-depth reviews of each company. Fundamental investors immerse themselves in the company studying everything from financial information, to new products, to meeting manage- ment. Ideally, they are searching for exploitable differences between their detailed assessment of the company’s value and the market’s per- ception of that value. In contrast, quantitative investors focus more broadly. Rather than reviewing one company at a time, they look across a large group of companies. Quantitative investors’ focus on what separates companies from one another; they search for pieces of information (characteristics) that they can use to exploit differences between securities. Since they are dealing with a great deal of data from a large number of companies, they employ quantitative tech- niques to quickly sift through the information.

3. Position concentration/size of bets. Another difference in the two approaches is the size of the positions within a portfolio; they tend to be larger for a fundamental investor and smaller for a quantitative investor. A fundamental investor performs in-depth company analy- sis so they will have greater conviction in taking larger positions in their selected stocks. A quantitative investor performs in-depth analy- sis across a group of companies, so they will tend to spread their bets across this larger group of companies.

4. Risk perspective. The fundamental investor sees risk at the company level while the quantitative investor is more focused at the portfolio level. The fundamental investor will review the risk to both their fore- casts and catalysts for the company. They understand how a changing macro picture can impact their valuation of the company. In contrast, the quantitative investor’s broader view relates to understanding the risks across their portfolio. They understand if there are risk character- istics in their portfolio that are different from their chosen stock selec- tion model. For example, a quantitative investor who does not believe growth prospects matter to a company’s stock performance would want to investigate if their model had them buying many very high- or low- growth companies.

5. Past vs. future. Finally, the fundamental investor often places greater emphasis on the future prospects of the company while the quantita- tive investor studies the company’s past. Fundamental investors tend to paint a picture of the company’s future, they will craft a story around the company and its prospects, and they will look for catalysts generat- ing future growth for a company. They rely on their ability to predict

An Introduction to Quantitative Equity Investing 5

changes in a company. In contrast, the quantitative investor places more emphasis on the past, using what is known or has been reported by a company. Quantitative investors rely on historical accounting data as well as historical strategy simulations, or backtests, to search for the best company characteristics to select stocks. For instance, they will look at whether technology companies with stronger profitability have performed better than those without, or whether retail companies with stronger inventory controls have performed better than those without. Quantitative investors are looking for stock picking criteria, which can be tested and incorporated into a stock selection model.

In the end, we have two types of investors viewing information, often the same information, quite differently. The fundamental investor is a jour- nalist focused on crafting a unique story of a company’s future prospects and predicting the potential for gain in the company’s stock. The quantita- tive investor is a scientist, broadly focused, relying on historical informa- tion to differentiate across all companies, testing large amounts of data and using statistical techniques to create a stock selection model.

These two investors can and often do create different portfolios based on their different approaches as shown in Exhibit 1.3. The fundamental investor is more focused, with higher conviction in their stocks resulting in fewer, larger positions in their portfolios. The quantitative investor, review- ing a large group of companies, generally takes a large number of smaller positions in their portfolio. The fundamental investor is investing in a stock (or sector) and therefore is most concerned with how much each of their stocks (or sectors) is contributing to performance. The quantitative investor is investing in a characteristic and how well it differentiates stocks. They want to know how each of their characteristics is contributing to perfor- mance. Finally, the fundamental investor’s detailed view into the company allows them to understand the intrinsic risk of each investment they make— what are potential stumbling blocks for each company. The quantitative investor’s goal is to understand specific characteristics across a broad uni-

EXHIBIT 1.3 Fundamental vs. Quantitative Investor: Process Differences

Fundamental Quantitative

Small portfolio Large portfolio

Larger positions Smaller positions

Performance at sector/company level Performance at characteristic level

Emphasize stock specific risk Diversify stock specific risk

6 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

verse of stocks. They look at risks across their entire portfolio, attempting to diversify away any firm-specific risks ancillary to their strategy.

Now that you understand the basic differences between the two approaches, it might also be clear how using both investment styles can be very appealing. As Exhibit 1.4 shows, the two styles are quite complemen- tary in nature and can provide a robust, well-rounded view of a company or portfolio. Combining the two approaches provides the following benefits:

■ Breadth and depth. In-depth analysis across a large group of stocks selecting the best subset of companies, which is followed by in-depth review of the small subset of attractive companies.

■ Facts balanced with human insight. The scientific approach reviewing large amounts of data across many companies complemented by per- sonal judgment at the company level.

■ Past and future perspective. A detailed historical review of companies combined with a review of future potential prospects of a company.

■ Full risk analysis. A broad look at risk both within each company owned and across the entire portfolio.

■ Clear portfolio performance. A thorough understanding of which com- panies, sectors, and characteristics are driving a portfolio’s performance.

In fact, over the years, the defining line between the two approaches has been blurring. Some have coined the term for this joint process as quanta-

EXHIBIT 1.4 Benefits of a Combined Fundamental and Quantitative Approach

Fundamental Quantitative

“Quantamental” • Broad based analysis followed by in-depth company analysis • Repeatable process (science) followed by qualitative judgment (journalist) • What worked in the past combined with future prospects • Individual stock assessment with overall portfolio assessment • Understanding of performance across company/sector and style

An Introduction to Quantitative Equity Investing 7

mental. Many investment managers are combining both approaches in one investment process, which is why whether you are a fundamental or quanti- tative investor, it is important to understand both perspectives.

Given our preceding discussion, the distinction between the quantita- tive and fundamental approaches should now be better appreciated. In the remainder of this chapter we restrict our focus to the quantitative equity investment process addressing the last two topics listed at the beginning of this chapter: the core steps in a quantitative equity investment process and some of the basic building blocks used by quantitative investors.

THE QUANTITATIVE STOCK SELECTION MODEL

Before diving into the details of the quantitative investment process, let’s look at what is at its core—the stock selection model. As explained in the previous section, the quantitative investment approach is rooted in under- standing what separates strong performing stocks from weak performing stocks.1 The quantitative investor looks for sources of information or com- pany characteristics (often referred to as factors or signals)2 that help to explain why one stock outperforms another stock. They assemble these characteristics into a stock selection model that can be run daily to provide an updated view on every stock in their investment universe.

The stock selection model is at the heart of the quantitative process. To build their model, the quantitative investor will look throughout history and see what characteristics drive performance differences between stocks in a group such as a universe (i.e., small cap, small-cap value, and large-cap growth) or a sector (i.e., technology, financials, materials).

The quantitative investor’s typical stock selection methodology is buy- ing stocks with the most attractive attributes and not investing in (or short- ing if permitted by investment guidelines) stocks with the least attractive attributes. For instance, let’s suppose retail stocks that have the highest profitability tend to have higher stock returns than those with the lowest profitability. In this case, if a retail stock had strong profitability, there is a greater chance a portfolio manager would purchase it. Profitability is just one characteristic of a company. The quantitative investor will look at a

1Throughout the chapter, we discuss whether characteristics can separate a stock with strong future returns from one with weak future returns. Many times reference will be made to a “strong” characteristic that can differentiate the strong- from weak-performing stocks. 2In this chapter, “characteristic” means the attributes that differentiate companies. Quantitative investors often refer to these same characteristics as factors or signals, which they typically use in stock selection models and like models.

8 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

large number of characteristics, from 25 to over 100 to include in their stock selection model. In the end, they will narrow their final model to a few char- acteristics, which are best at locating performance differences among stocks in a particular universe or sector.

Exhibit 1.5 is an example of a stock selection model for the retail sec- tor. If a stock has good margins, positive earnings growth, sell-side analyst like it, solid inventory management, and is attractively valued, especially as it pertains to earnings, then the quantitative investor would buy it. And if it did not have these characteristics, a quantitative investor would not own it, sell it, or short it. This example is for a retail sector; a quantitative investor could also have different models to select stocks in the bank sector or utili- ties sector or amongst small-cap value stocks.

So how does a quantitative investor create and use their stock selection model? A good analogy is a professional golfer. Like a quantitative inves- tor, golfers create a model of their game. First, golfers analyze all elements of their basic swing from backswing to follow through. They then alter their swing to different conditions (high winds, rain, cold), and different courses types (links, woodlands, fast greens). Next golfers put their model into action. While they are golfing, they make mental notes about what is and isn’t working to help enhance their game. Could they tweak their swing? What has been effective under the current weather conditions? How are they playing this type of course?

EXHIBIT 1.5 Sample Stock Selection Model for the Retail Sector

Retail Sector

Gross Margin

Earnings Growth

Analyst Recommendation

Inventory Management

Earnings/Price Ratio

An Introduction to Quantitative Equity Investing 9

Overall, the golfers’ process is much like a quantitative investors’ pro- cess. They create a model, implement it, and then monitor it, assessing their ability to shoot below par. Like professional golfers who go to the driving range for countless hours to perfect their swing, quantitative investors will spend countless hours perfecting their model understanding how it works under many different market (weather/course) conditions.

With that analogy in mind, we now turn to the entire quantitative investment process.

THE OVERALL QUANTITATIVE INVESTMENT PROCESS

The quantitative process can be divided into the following three main phas- es (shown in Exhibit 1.6):

■ Research ■ Portfolio construction ■ Monitoring

During the research phase, the stock selection model is created. During the portfolio construction phase, the quantitative investor “productional- izes” the stock selection model or gets it ready to invest in a live portfolio. Finally, during the monitoring phase, the quantitative investor makes sure the portfolio is performing as expected.

RESEARCH

Let’s start with the research phase since it is the basic building block of the quantitative process. It is where the fact-finding mission begins. This is like when the golfer spends countless hours at the driving range perfecting his (or her) swing. In this phase, the quantitative investor determines what as-

EXHIBIT 1.6 Three Core Phases of the Quantitative Equity Investment Process

Monitoring

–Characteristic Testing –Model Creation

–Data Collection –Create Security Weights –Trade Portfolio

–Risk Analysis –Portfolio Attribution

Portfolio Construction

Research

10 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

pects of a company make its stock attractive or unattractive. The research phase begins by the quantitative investors testing all the characteristics they have at their disposal, and finishes with assembling the chosen characteris- tics into a stock selection model (see Exhibit 1.7).

1. Characteristic testing. First, quantitative investors determine which characteristics are good at differentiating strong performing from weak performing stocks. Initially, the quantitative investor segments the stocks, this could be by sector, such as consumer discretionary, indus- try such as consumer electronics or a universe such as small-cap value stocks. Once the stocks have been grouped, each of the characteristics is tested to see if they can delineate the strong performing stocks from the weak performing stocks.

2. Model creation. Second, quantitative investors select the final charac- teristics that are best at picking the most attractive stocks. Then they weight each characteristic in the stock selection model—determining which characteristics should be more relied upon when picking stocks, or if they all should be treated equally.

During the research phase, the quantitative investor tries to get a broad picture of a characteristic making sure it performs well under a diverse set of conditions and performance measures. For their testing, the quantitative investor looks at historical information over 20 years or more in order to cover multiple market cycles. While testing, many performance metrics are reviewed to get an expansive view of a characteristic’s ability to differentiate stocks. These metrics span the return category, risk category and other met- rics categories as outlined in Exhibit 1.8. Using an array of metrics, quanti- tative investors are better able to confirm a characteristic’s consistency. They make sure that the selected characteristics’ score well on more than a single

EXHIBIT 1.7 Two Core Steps in the Research Phase of the Quantitative Equity Investment Process

Characteristic Testing

–Segment Stocks –Determine Characteristic Strength

–Select Final Characteristics –Weight Characteristics

Model Creation

An Introduction to Quantitative Equity Investing 11

metric. Before continuing with the research process, let’s review a few of the more commonly used metrics by quantitative investors.

Characteristic Testing: Key Quantitative Research Metrics

In this section, we review quintile returns and information coefficient that measure whether a characteristic can differentiate between winning and los- ing stocks. Although profitability was chosen for the examples, other char- acteristics such as sales growth, P/E ratio or asset turnover could have also been chosen.

Quintile Returns

The quintile return is already prevalent across most research publications, but is gaining popularity in more and more mainstream publications such as the Wall Street Journal, Barron’s, and the like. Quintile returns measure how well a characteristic differentiates stocks. In essence, the stocks that are being reviewed are segmented into five groups (quintiles) and then are tested to determine if the companies in the group with the best attributes (top quintile) outperform the group with the least desirable attributes (bot- tom quintile).

Exhibit 1.9 provides an example. In this example, we start with 20 companies that we refer to as A through T. The first step—the left-hand side of the exhibit—is to order the 20 companies by profitability from highest to

EXHIBIT 1.8 Characteristic Testing in the Research Phase

Quintile/Decile Returns

Information Coefficient

Information Ratio

Batting Average

Up/Down Markets

Which characteristics are

best at differentiating stock

performance

Review

Performance

over

20+ years

(multiple market cycles)

Returns

Risk

Other Turnover

Coverage

Skewness/Kurtosis

Tracking Error

Draw Down

Downside Deviation

Sortino Ratio

12 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

lowest. In the second step, this ordered list is divided into five groups, creat- ing a most profitable group (top quintile) down to the least profitable group (bottom quintile). The top and bottom quintile groups are boxed on the right-hand chart of the exhibit. Finally, the performance of the top quintile is compared to the bottom quintile.

As Exhibit 1.9 shows, the stocks with highest profitability (top quin- tile) returned 2.6% on average while the stocks with the lowest profitability (bottom quintile) returned only 0.6% on average. So the top quintile stocks outperformed the bottom quintile stocks by 2.0% meaning for this month, the most profitable companies outperformed the least profitable companies by 2.0%. This is commonly referred to as the characteristic’s quintile return or quintile spread. The higher the quintile spread, the more attractive the characteristic is.

Information Coefficient

Another common metric used for determining if a characteristic is good at separating the strong from the weak performing stocks is the information coefficient (IC). It does so by measuring the correlation between a stock’s characteristic (i.e., profitability) and its return. The major difference be- tween the IC and quintile return is that the IC looks across all of the stocks, while the quintile return only focuses on the best and worst stocks ignoring

EXHIBIT 1.9 Determining the Characteristic’s Quintile Spread

–10.0% 0.0% 10.0% 20.0%

Profit Margin

H M F D T G N I

A J

O B K E P Q R S C L

–5.0% 0.0% 5.0% 10.0%

Monthly Return

H M F D T G N I

A J

O B K E P Q R S C L

C om

pa ni

es (

A t

o T

)

Bottom quintile = 0.6%

Quintile spread = 2.6% – 0.6% = 2.0%

Top quintile = 2.6%

An Introduction to Quantitative Equity Investing 13

those stocks in the middle. The IC is more concerned with differentiating performance across all stocks rather than the extremes.

The calculation of the IC is detailed in Exhibit 1.10. Similar to assessing the quintile return, the sort ordering of the companies based on profitability is done first. However, the next step is different. In the second step, each stock is ranked on both profitability and return. The most profitable com- pany is assigned a rank of 1 all the way down to the least profitable com- pany that is assigned a rank of 20. Likewise for stock returns, the highest returning stock is assigned a rank of 1 down to the lowest returning stock receiving a rank of 20. In the third step, the rank of the company’s profit- ability is correlated with the rank of the company’s return. The correlation of the two ranks is the IC that is 11% as shown in Exhibit 1.10. The higher the correlation (i.e., IC), the more likely companies with higher profitability also have higher returns and the more effective the characteristic.

When is it better to employ an IC over a quintile spread? IC is a better metric when a quantitative investor is considering owning a greater number of stocks in the portfolio. The reason is that the IC looks at the relationships across all of the stocks in the group. The quintile return is better suited for more concentrated bets in fewer stocks as it places a greater emphasis on measuring the few stocks at the extremes.

The last two examples reviewed how a characteristic (profitability) was able to explain the next month’s return for a group of stocks. In both cases,

EXHIBIT 1.10 Determining the Characteristic’s Information Coefficient

–10.0% 0.0% 10.0% 20.0%

Profit Margin

H M F D T G N I

A J

O B K E P Q R S C L

C om

pa ni

es (

A t

o T

)

Company Profit Margin Rank Return Rank

H M F D T G N I A J O B K E P Q R S C L

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

11 2 7 17 8 16 20 1 9 5 12 18 10 15 3 4 13 5 19 14

Information coeeficient = Correlation = 11.0%

14 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

it looked effective—a quintile return of 2.0% and an IC of 11%. However, in practice, it is also necessary to assess whether the characteristic was effec- tive for not only one month, but over decades of investing encompassing multiple market cycles. To that end, during the research process a quan- titative investor will look at the average quintile returns or ICs over an extended period of up to 20 years or more. When looking at these longer time series, quantitative investors use additional metrics to understand the characteristic’s effectiveness.

Characteristic Testing: Key Measures of Consistency

Two commonly used measures of consistency are batting average and infor- mation ratio.

Batting Average

Batting average is a straightforward metric. In baseball a player’s batting av- erage is the number of hits divided by the number of times at bat. A similar metric is used in investing. Batting average is the number of positive perfor- mance months (hits) divided by the number of total months (at bats). The higher the batting average, the more consistently the characteristic generates positive performance.

As Exhibit 1.11 displays, to arrive at the batting average we take the number of months the quintile return was positive divided by the number of months tested. In our example, in 47 of the 72 months the profitability characteristic was effective, resulting in a positive return. This translates to a batting average of 65%, which is quite high. Imagine walking into a casino in Las Vegas where you have a 65% chance of winning every bet. That casino would not be in business very long with you at the table.

Information Ratio

Information ratio is also used to measure consistency. This measure is de- fined as the average return of a characteristic divided by its volatility—basi- cally a measure of return per unit of risk or risk reward ratio. For volatility, quantitative investors use tracking error, which is the standard deviation of excess returns.

Exhibit 1.12 demonstrates the calculation of the information ratio. In this example, there are two characteristics. Which one should be selected? Based only on returns, we would choose Characteristic 2 since it has a higher excess return (3.0%) than Characteristic 1 (2.0%). However, as we can see in the exhibit, Characteristic 2 also has much larger swings in per-

An Introduction to Quantitative Equity Investing 15

EXHIBIT 1.11 Determining the Characteristic’s Batting Average

–10.0%

–5.0%

0.0%

5.0%

10.0%

15.0%

Q u in

ti le

S p re

ad R

et u rn

1 /1

/9 0

5 /1

/9 0

9 /1

/9 0

1 /1

/9 1

5 /1

/9 1

9 /1

/9 1

1 /1

/9 2

5 /1

/9 2

9 /1

/9 2

1 /1

/9 3

5 /1

/9 3

9 /1

/9 3

1 /1

/9 4

5 /1

/9 4

9 /1

/9 4

1 /1

/9 5

5 /1

/9 5

9 /1

/9 5

Positive Months = 47

Total Months = 72 = 65%

EXHIBIT 1.12 Determining the Characteristic’s Information Ratio

Tracking Error Characteristic 1 = 4.0% Characteristic 2 = 12.0%

Excess Return Characteristic 1 = 2.0% Characteristic 2 = 3.0%

Information Ratio Characteristic 1 = 0.50 Characteristic 2 = 0.25

=

8.0% 7.0% 6.0% 5.0% 4.0% 3.0% 2.0% 1.0% 0.0%

–1.0% –2.0%

E xc

es s

R et

ur n

Ja n

Fe b

M ar

A pr

M ay Ju n

Ju l

A ug Se p

O ct

N ov

D ec

Characteristic 1 (profit margin) Characteristic 2 (sales growth)

16 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

formance than Characteristic 1 and therefore more risk. The higher risk of Characteristic 2 is confirmed by its high tracking error of 12.0%, three times greater than Characteristic 1’s tracking error of 4.0%. Characteris- tic 1 looks much better on a risk-adjusted basis with an information ratio of 0.50 (2.0%/4.0%) or twice Characteristic 2’s information ratio of 0.25 (3.0%/12.0%). So even though Characteristic 1 has a lower return than Characteristic 2, it also has much less risk making it preferred since the investor is rewarded more for the risk she (or he) are taking.

Model Creation

After reviewing and selecting the best characteristics, the quantitative inves- tor then needs to assemble them into a stock selection model. This step of the research process is called model creation. It usually involves two main components:

1. Ascertaining whether the characteristics selected are not measuring the same effect (i.e., are not highly correlated).

2. Assigning weights to the selected characteristics and potentially placing greater emphasis on those in which the quantitative investor has stron- ger convictions.

Let us begin by discussing the first component in model creation: mea- suring correlation. When including characteristics into a stock selection model, the quantitative investor does not want to include two characteris- tics that have very similar performance since they may be measuring simi- lar aspects of the company. In these cases, the quantitative manager could be potentially doubling their position in a stock for the same reason. For instance, stocks with a historically high sales growth may perform similarly to stocks with high expected growth in the future or stocks with strong gross margins may perform similarly to stocks with strong profit margins. In either case, we would not include both similar characteristics.

An example is provided in Exhibit 1.13, which shows the cumulative quintile spread return over 10 years for three characteristics (which we have labeled A, B, and C). Characteristic A did the best at differentiating the win- ners from losers—the stocks it liked outperformed the stocks it did not like by almost 10% over the 10-year period. Characteristic B was next with a return slightly greater than 8% and characteristic C was the lowest with an almost 4% cumulative 10-year return. Given that all three characteristics have good performance, which two should the quantitative investor retain in the model?

An Introduction to Quantitative Equity Investing 17

Although characteristic A and B are better at differentiating winners from losers than characteristic C, A’s return pattern looks very similar to B’s. This is confirmed by the table in Exhibit 1.13 where characteristics A and B have a correlation of 0.80. Since a correlation of 1.00 means their returns move in lock step, a correlation of 0.80 indicates they are very simi- lar. Rather than keeping both A and B and potentially doubling our posi- tions from similar characteristics, it would be best to keep either A or B and combine the characteristic retained with C. Even though characteristic C is the worst performing of the three, for the stock selection model C provides a good uncorrelated source of performance.

Once the characteristics to select stocks are identified, the quantitative investor is ready to determine the importance or weight of each character- istic. They must decide whether all characteristics should have the same weight or whether better characteristics should have greater weight in the stock selection model.

There are many ways to determine the weights of the characteristics. We can simply equal weight them or use some other process such as create an algorithm, perform regressions, or optimize. Exhibit 1.14 shows how a typical stock selection model is created. In this step, the selected characteris- tics are combined to determine a target for each stock whether it be a return forecast, rank, or a position size.

EXHIBIT 1.13 Model Creation: Correlation Review

0%

2%

4%

6%

8%

10%

12%

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

C um

ua lt

iv e

E xc

es s

R et

ur n

A B C

Characteristic Correlation Table

A B C

A 1.00 0.80 0.12

B 0.80 1.00 0.04

C 0.12 0.04 1.00

18 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 1.14 Stock Selection Model: Characteristic Weightings

Gross Margins

Sales Growth

Earnings Yield

• Equal Weighted • Algorithm • Optimization • Regression

FINAL MODEL

Security Rank =

WeightGross Margin × ValueGross Margin +

WeightSales Growth × ValueSales Growth +

WeightEarnings Yield × ValueEarnings Yield

Determine Characteristic’s Importance

Once the combination of characteristics for the model is selected, the quantitative investor determines their weights and then reviews the model. Model review is similar to reviewing a single characteristic. The model is looked at from many perspectives, calculating all of the metrics described in Exhibit 1.8. The quantitative investor would look at how the top quintile stocks of the model perform versus the bottom and look at information coefficients of the stock selection model over time. In addition, how much trading or turnover the stock selection model creates is reviewed or if there are any biases in the stock selections (e.g., too many small-cap stocks, or a reliance on high- or low-beta stocks). In practice, the review is much more extensive covering many more metrics. If the stock selection model does not hold up under this final review, then the quantitative investor will need to change her stock selection model to eliminate the undesirable effects.

PORTFOLIO CONSTRUCTION

In the second phase of the investment process, the quantitative investor uses the stock selection model to buy stocks. It is in this phase that the quantita- tive investor puts the model into production. Returning to our golfer anal- ogy, this is when he travels to the course to play a round of golf.

During the portfolio construction phase, the model is ready to create a daily portfolio. This phase consists of three main steps:

EXHIBIT 1.15 Three Main Steps of the Portfolio Construction Phase

TradeCreate Security Weights

Data Collection

An Introduction to Quantitative Equity Investing 19

Step 1: Data collection. Data are collected on a nightly basis, making sure the data are correct and do not contain any errors. Step 2: Create security weights. New, updated nightly, data are used to both select the stocks that should be purchased for the portfolio as well as how large its position should be. Step 3: Trade. The stock selection model that has incorporated the most current information is used for trading.

Data Collection

As Exhibit 1.16 shows, data come from many different sources, such as com- pany fundamental, pricing, economic, and other data (specialized data sourc- es). All of these data are updated nightly so it is important to have robust systems and processes established to handle large amounts of data, clean the data (check for errors), and process it in a timely fashion. The quantitative investor seeks to have everything ready to trade at the market opening.

Creating Security Weights

After the data are collected and verified, the next step is running all of the updated company information through the stock selection model. This will

EXHIBIT 1.16 Data Collection Step of the Portfolio Construction Phase

Fundamental –Income Statement –Balance Sheet –Cash Flow Statement

Core Database

Other Data –Industry Specific –Country Specific –Customer/Supplier –News Feeds/Sentiment –Ownership –Same Store Sales –High Frequency

Pricing –Stocks –Bonds –Derivatives

Economics Data –GDP –Interest Rates –Credit SpreadsOther Considerations

• Data Delivery • Reporting Dates • Survivorship Bias • Frequency

20 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

create final positions for every stock in the screened universe. In this step, each stock is ranked using the stock selection model, with the better scoring companies making it into the portfolio.

Exhibit 1.17 provides a simplified example of this, showing a stock selection model with three characteristics: gross margins, sales growth, and earnings yield (i.e., earnings-to-price ratio, the higher the ratio the more attractively priced the stock is). From the example, Company ABC is in the top 10% of companies based on gross margin, top 30% in sales growth, and average on earnings yield. Company ABC may represent a company finding a profitable market, growing into it, and the rest of the market has not caught on to its prospects so it is still valued like an average stock. In this case, the stock rates favorably by the stock selection model and would be purchased. The other stock, the stock of Company XYZ, is not as favor- able and would either not be held in the portfolio or if permitted could be shorted. Although Company XYZ also has good margins, its growth is slowing and it is relatively expensive compared to its earnings. The com- pany could be one that had a profitable niche, but its niche may be shrink- ing as sales are dwindling. Furthermore, the investment community has not discounted the slowing growth and hence the stock is still expensive.

Trade

The final step in the portfolio construction process is to trade into the new positions chosen by the stock selection model. While many investment

EXHIBIT 1.17 Creating Security Weights Step of the Portfolio Construction Phase

Best Fundamentals

Worst Fundamentals

Underweight Position

Overweight Position Company ABC Company XYZ

Gross margin Top 10% + Top 20% +

Sales growth Top 30% + Bottom 20% –

Earnings yield Median 0 Bottom 10% –

Active weight + –

Overweight Underweight

Buy Sell

An Introduction to Quantitative Equity Investing 21

approaches trade regularly, even daily, quantitative investors tend not to. Quantitative investors tend to trade monthly or longer. They may wait for the views from their stock selection model to change significantly from their current portfolio before trading into the new views.

MONITORING

The third and final phase in the quantitative equity investment process is monitoring performance and risk. This step is important to check if any hid- den biases are embedded in the portfolio and that the portfolio is perform- ing in-line with expectations. Returning one last time to our golfer analogy, this is when the golfer is making mental notes as to what is and isn’t work- ing during the round to improve his game in the future. This step can be broken into two activities: risk management and performance attribution.

Risk Management

In risk management, the main emphasis is to make sure that the quantitative investor is buying companies consistent with her stock selection model. Re- turning to the retail model discussed earlier in this chapter, the model liked companies with good profit margins but had no view on the company’s beta. So the quantitative investor would want to make sure that the com- panies included in her portfolio have high profit margins but average beta. If the portfolio started to include high-beta stocks, the quantitative investor would want to make adjustments to the process to eliminate this high-beta bias. There are many types of risk management software and techniques that can be used to detect any hidden risks embedded in the portfolio and ways to remedy those identified.

Another aspect of risk management is to make sure that the portfolio’s risk level is consistent with the modeling phase. The quantitative investor wants to assure that there is not too high or low tracking error relative to expectations. Again, risk management techniques and software can be used to monitor tracking error, sources of tracking error, and remedy any devia- tions from expectations.

Performance Attribution

Performance attribution is critical in assuring the actual live portfolio’s per- formance is coming from the characteristics in the stock selection model and is in-line with performance expected during the modeling stage. Perfor- mance attribution is like monitoring a car’s gas mileage: If the gas mileage

22 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

begins to dip below what the driver expects, or is known to be, then the driver would want to look under the car’s hood. Similarly, if the stock selec- tion model is not producing the desired results, or the results have changed, then the quantitative investor would need to look under the hood of the stock selection model. If performance is not being generated from the se- lected characteristics, then the quantitative manager would want to check out the model in more detail. One possibility is that another characteristic is cancelling the desired characteristics or perhaps there is something wrong with the model itself. Another possibility is that there are data issues.

The monitoring phase is critical in making sure that the stock selection model is being implemented as expected.

CURRENT TRENDS

Let’s look at some recent trends in the quantitative investment industry. Many quantitative equity investors are looking for additional sources

of alpha by using alternative data sources to help select stocks. One notable source is industry-specific data (e.g., banking, airlines, and retail). Addition- ally, quantitative investors are turning to the Internet to better understand news flows for companies through Web-based search engines. Furthermore, quantitative investors are using more conditioning models. Conditioning occurs when two characteristics are combined together rather than choosing them side by side in a stock selection model. Traditional models would look for companies that have either attractive margins or growth. With condi- tioning models, companies that have both attractive margins and growth are sought.

Dynamic modeling is gaining a renewed popularity. It consists of timing characteristics, determining when they should enter or leave a stock selec- tion model based on business cycle analysis, technical market indicators, or other information. For instance, during recessionary periods, a quantita- tive investor may want companies with strong profitability, while in expan- sionary periods companies with good growth prospects are sought. A stock selection model would contain profitability when the economy is entering a recession, and then include the growth characteristic once it felt that the economy is moving into an expansionary period. This is an example of how quantitative investors may be bringing more personal judgment to the pro- cess, similar to fundamental investors.

Finally, with the advent of high-frequency trading and more advanced trading analytics, many quantitative investors are reviewing how best they implement their stock selection models. Some characteristics such as earn- ings surprise may have short-lived alpha prospects, so quantitative investors

An Introduction to Quantitative Equity Investing 23

would want to trade into these stocks more quickly. Other characteristics are longer-term in nature, such as valuation metrics, so investors would not have to trade into companies with attractive valuations as quickly. Further- more, trading costs are being measured with greater granularity, allowing quantitative investors to measure transaction cost and incorporate these better estimates into their research modeling phase.

KEY POINTS

■ Investing begins with processing many different types of information to find the most attractively priced assets. Fundamental and quantita- tive investors differ in their approach to the available information. The fundamental investor’s primary focus is on a single company at a time, while the quantitative investor’s primary focus is on a single character- istic at a time.

■ Quantitative and fundamental approaches are complementary. By com- bining the two approaches, you can obtain a more well-rounded invest- ment process including breadth and depth in analysis, facts based with human judgment, a past and future perspective of a company, and a more well-rounded view of risk and performance of the portfolio.

■ The quantitative equity investment process is made up of three phases: research, portfolio construction, and monitoring. During the research phase, the stock selection model is created. During the portfolio con- struction phase, the quantitative investor “productionalizes” the stock selection model or gets it ready to invest in a live portfolio. Finally, during the monitoring phase, the quantitative investor makes sure the portfolio is performing as expected.

■ At the heart of the quantitative equity investment process is the stock selection model. The model includes those characteristics that are best at delineating the highest from lowest returning stocks. Models can be created for industries, sectors, or styles.

■ Two common metrics used to judge a characteristic’s effectiveness are quintile returns and information coefficients. Two more metrics used to understand the consistency of a characteristic’s performance over time are batting average and information ratio.

■ During the portfolio construction phase, data is collected from multiple sources and run through the investor’s stock selection model to arrive at a list of buy and sell candidates. The buy candidates will have the strongest characteristic values in the investor’s stock selection model, and the sell candidates the weakest characteristic values.

24 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

■ The monitoring phase is where the investor assures that the perfor- mance in their portfolio is consistent with their expectations. During this phase, investors make sure there are no hidden bets in their port- folio and that the characteristics in their stock selection model are per- forming as expected.

QUESTIONS

1. Identify at least three ways that a quantitative investor’s process may differ from a fundamental investor’s process.

2. What are three ways in which the quantitative and fundamental approaches complement one another?

3. When would a quantitative investor use an information coefficient (IC) over a quintile return?

4. Why do quantitative investors create stock selection models for?

5. What types of data is used in traditional stock selection models?

25

CHAPTER 2 Equity Analysis Using Traditional

and Value-Based Metrics James L. Grant, Ph.D.

JLG Research and Professor of Finance University of Massachusetts–Boston

Frank J. Fabozzi, Ph.D., CFA, CPA Professor of Finance

EDHEC Business School

In this chapter, traditional metrics and value-based metrics are explained with the goal of showing their joint role in equity fundamental analysis and securities valuation. After reviewing the relevant metrics, we apply tra- ditional and value-based metrics analyses to illustrate the benefits of using a synthesized approach to equity analysis in distinguishing “good” com- panies, which can be potential buy opportunities, from “bad,” risky, or troubled companies, which can be potential sell or short-sell opportunities.

OVERVIEW OF TRADITIONAL METRICS

With numerous financial measures available, the investor is often left won- dering which metrics are the most important to focus on. We address this metrics question by examining the information content of two well-known but seemingly distinct types of company and equity analyses—namely, tra- ditional and value-based metrics (VBM) approaches to securities analysis. We begin our financial metrics journey with the traditional approach.

In the traditional approach to company analysis, there are several broad ratio categories. These categories include liquidity, activity, debt (leverage), and profitability measures. Within each category, there are several ratio choices. From the investor’s perspective, growth rates and profitability measures

26 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

are often combined with relative valuation measures (“multiples”) to assess the attractiveness or unattractiveness of a firm’s common stock. As with the value-based metrics approach (discussed later), the end result of a tra- ditional fundamental analysis on a company is a target valuation leading to a potential buy (or “overweight” relative to reference index), sell (“under- weight” relative to index), or hold decision (benchmark weight) on a com- pany’s stock. Some widely used traditional measures of growth and profit- ability include:

■ Revenue growth ■ Earnings and cash flow growth ■ Book value and asset growth ■ Dividend growth ■ Return on equity (reflects profitability) ■ Fundamental stock return

Likewise, some key valuation measures include:

■ Price-to-revenue ratio ■ Price-to-earnings ratio ■ Price-to-cash flow ratio ■ Price-to-book value ratio ■ Dividend yield

While the names of these metrics are descriptive, we provide an over- view of those measures that require formulas. Moreover, it is worth not- ing that some investors and analysts prefer a specific combination of tra- ditional fundamentals and valuation measures when analyzing companies; for example, “tech” analysts may use a combination of revenue growth and price–revenue “multiple” to analyzing software and biotech companies, while other analysts may use an earnings (or book value) growth and price– earnings (or price–book) combination when evaluating the profitability and equity valuation characteristics of financial services companies.

Growth Rates

We begin the formulaic review of traditional metrics with annualized growth rates. Growth rates—variables expressed in terms of revenue, earnings, cash flow, book value, assets, or dividends—are calculated from the basic present value (PV) and future value (FV) relationship:

FV PV= × + ′′( )1 g

Equity Analysis Using Traditional and Value-Based Metrics 27

Solving for the annualized growth rate, one obtains:

g n= −( ) ./FV/PV 1 1 0

This expression is used to calculate growth rates using the variables listed earlier. When growth rates are compared to a benchmark or industry standard, they can be used to distinguish companies having relatively favor- able or unfavorable financial characteristics. Growth rates are also used in equity style analysis (value versus growth stocks) and they are a key input to pro forma forecasts of earnings and cash flows and, notably, in discounted cash flow (DCF) models (along with the required return).

Consider the revenue and earnings data shown in Exhibit 2.1 (among other financial data used later). Upon inserting the revenue figure at 2011 into FV, and the revenue figure at 2006 into PV, one obtains a five-year annualized growth rate, g

r , according to

gr = −

= − =

( ) .

( . / . ) . .

/

.

FV/PV 1 5

0 2

1 0

1 882 0 909 1 0 0 1577 or 15.7%

The five-year earnings per share (EPS) growth rate, g e , can be deter-

mined in a similar manner. At 13.9%, this annualized growth rate is calcu- lated according to

g e = (3.59/1.87)1/5 – 1.0 = 0.139 = 13.9%

Other things the same, if the actual growth rate in either revenue, earn- ings, cash flows, book value, assets, or dividends is higher than benchmark, then based on growth rates alone the company is relatively attractive— meaning the stock is a potential buy opportunity. Otherwise, the company

EXHIBIT 2.1 Income and Balance Sheet Data (all figures USD billions except earnings per share)

Year 2006 2007 2008 2009 2010 2011

Revenue Operating earnings (EBIT) Pre-tax profit

0.909 0.273 0.232

1.052 0.316 0.262

1.212 0.364 0.291

1.423 0.427 0.338

1.575 0.473 0.380

1.882 0.565 0.451

Net income 0.151 0.170 0.189 0.220 0.247 0.293

Earnings per share $1.87 $2.07 $2.30 $2.66 $2.98 $3.59

Equity 0.844 0.970 1.125 1.284 1.483 1.618

Assets 12.194 16.255 18.927 22.795 26.182 29.483

28 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

is relatively unattractive, which points to a potential sell or short-sell oppor- tunity on the stock.

Return on Equity and Extended Dupont Formula

We now look at return on equity (ROE), which is perhaps the best-known traditional measure of corporate success. In accounting terms, ROE is sim- ply net income over stockholders’ equity. The classic Dupont formula (a pioneering formula developed by E. I. duPont de Nemours & Company in the early 1960s) expands this ratio by showing that ROE can be expressed as the product of other important ratios. For example, ROE can be mea- sured by multiplying return on assets (ROA) by a corporate leverage ratio. The leverage ratio is commonly referred to as the “financial leverage multi- plier,” the “equity multiplier,” or just plain “leverage.” The leverage factor is measured by the ratio of total assets to stockholders’ equity, while ROA in the Dupont formula is simply net income (NI) divided by total assets (A).

ROE ROA Leverage NI/A A/E= × = ×

In turn, ROE is related to the net profit margin (NPM) and the asset turnover ratio according to

ROE NPM Asset turnover Leverage

NI/S S/A A/E

= × × = × ×

In this expression, ROA is expressed as the net profit margin (net income over revenue) times the asset turnover ratio—measured by the revenue-to- assets ratio. Investors can use this three-part ROE formula to measure the efficiency of management in generating (1) profit per dollar of sales, (2) sales per dollar of assets (via inventory and asset turns), and (3) assets per dollar of owners’ or stockholders’ equity (implicitly by using debt financing).

Moreover, to better assess the operating and efficiency aspects of a com- pany as well as capital structure and tax issues, the above after-tax version of the Dupont formula can be extended to a five-part, pretax model. In the extended Dupont formula, the firm’s ROE can be expressed as

ROE = Tax burden × Interest burden × Operating profit margin × Asset turnover × Leverage

= NI/PBT × PBT/EBIT × EBIT/S × S/A × A/E

In the extended Dupont formula, the tax burden is measured by the ratio of (or conversion from) net income to pretax profit (PBT), the interest burden is measured by the ratio of profit before tax to operating earnings (EBIT),

Equity Analysis Using Traditional and Value-Based Metrics 29

the pretax operating margin is measured by the ratio of operating earnings to sales, while the asset turnover and leverage ratios are the same as before. The obvious benefit of using the extended Dupont formula is that investors and analysts can focus more clearly on the operating profit and efficiency aspects of a business in the context of the operating profit margin and asset turnover ratio (or pretax ROA) as distinct from financing (capital structure) issues as reflected in the interest burden and leverage ratios, and tax issues as captured by the tax burden. Note that the tax burden in the extended ROE model is simply one minus the effective tax rate.

We use the income statement and balance sheet figures in Exhibit 2.1 to calculate the after-tax (three part) and pretax (five part) versions of the Dupont model for 2011. Based on these figures, the three-part ROE model yields

ROE NI/E 0.293/1.618 0.1811

ROA A/E 0.0099

= = = = × = × 118.22

NPM AT A/E 0.1557 0.0638 18.22

0.181

= × × = × × = 11

In turn, with a 35% tax rate [1 – (0.293/0.451)] and a 30% operating profit margin (0.565/1.882), the extended (five-part) ROE model yields:

ROE = NI/PBT × PBT/EBIT × EBIT/S × S/A × A/E = 0.65 × 0.798 × 0.30 × 0.0638 × 18.22 = 0.1811

With a relatively high operating profit margin (30%), a low asset turn- over ratio (0.0638), and a high equity multiplier (18.22), these are indicative of the ROE characteristics of a firm operating in the financial services sector, such as a profitable bank with a large amount of assets (i.e., creditworthy loans). A company operating in, say, the soft drink industry might have a similar ROE, but the “packaging” of the ROA and leverage components would be reversed. That is, beverage companies have relatively high pretax ROA and asset turnover ratios and are largely financed with equity, such that the values for the interest burden and the equity multiplier would be close to unity.

ROE and Leverage

Investors and analysts alike often look at corporate leverage ratios—such as debt-to-equity, debt-to-capital, and debt-to-asset ratios—when evaluating a firm’s profit versus risk characteristics. In the traditional model, leverage

30 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

can be value increasing because higher levels of corporate debt lead to both higher ROE and earnings per share. However, professional investors are keenly aware that excessive amounts of debt beyond some target level may be wealth destroying for the shareholders (investors). This negative side of debt is generally due to excessive earnings volatility associated with a rising probability of corporate default, leading to bankruptcy.

The traditional view that a larger proportion of debt in the firm’s capital structure leads to higher profitability ratios can be seen in the Dupont for- mula. To emphasize the role of debt, a firm’s ROE can be expressed in terms of its ROA and the inverse of one minus the corporate debt ratio according to

ROE ROA

D/A =

−1

In this expression, ROA is the after-tax return on assets (net income/assets), and D/A is the debt–asset ratio. The debt ratio in this version of the Dupont formula is the ratio of total liabilities (including current liabilities) to total assets, D/A.

Moreover, the “operating assets” approach1 to ROE is yet another way to distinguish operating results from leverage, this time in the context of ROAʹ and the debt-to-equity ratio (D/E) according to

ROE = ROAʹ + (ROAʹ – After-tax debt cost) × D/E

In this ROE expression, ROAʹ is the ratio of net operating profit after tax (NOPAT) to net assets or capital. In practice, NOPAT can be estimated as net income plus the after interest expense, while in a VBM context (shown later) NOPAT is often measured as tax-adjusted operating earnings (EBIT). Based on the previous formulations, it should be clear that with a higher degree of leverage, the Dupont formula shows that ROE goes up because the denominator in the former ROE expression falls as D/A rises; while in the latter or operating assets approach, ROE raises due to an increase in D/E. Conversely, as D/A declines relative to the firm’s ROA, its ROE goes down because the denominator in the Dupont formula now goes up (equivalently, ROE goes down as D/E declines). In effect, when D/A (or D/E) rises rela- tive to ROA, a smaller amount of equity capital is now generating the same amount of profit; thus, the return on shareholder equity goes up. A declin- ing ROE results when a relatively larger equity base is generating the same amount of corporate earnings.

1Paul M. Healy and Krishna G. Palepu, Business Analysis and Valuation: Using Fi- nancial Statements (Mason, OH: Southwestern Thomson, 2007).

Equity Analysis Using Traditional and Value-Based Metrics 31

To illustrate the link between ROE and leverage (debt), assume that a firm’s after-tax profit is $10 and its asset base is $100. Further, assume that the company is financed with all equity such that the D/A is zero. Not surprisingly, with 100% equity financing the firm’s ROE is the same as its ROA, at 10%:

ROE or= −

=0 1 1 0

0 1 10 .

. %

Now assume that the firm engages in financing that effectively swaps the equity shares for more debt, such that D/A rises to 40%. With this pure capital structure change, the firm’s ROE rises from 10% to 16.7%:

ROE or= −

=0 10 1 0 40

0 167 16 7 .

. . . %

As the company moves toward what it perceives to be its “optimal” (or target) capital structure, we see that ROE goes up. Hence, in the traditional view, it is argued that investors should be willing to pay more for the firm’s now seemingly dearer shares as long as the firm does not violate its sup- posed optimal capital structure. We will say more on the firm’s target capital structure as this is a key issue in the value-based metrics approach to equity analysis.

Financial Risk Considerations

The Dupont formula can also be used to illustrate the volatility of ROE at varying corporate debt levels. In this context, Exhibit 2.2 shows the project- ed ROE ratios with corporate debt levels ranging from 0% to 70% in the presence of ROA ratios varying from, say, 10% to –10%. As the economy expands or contracts with a 10% debt load, we see that ROE fluctuates from 11.1% on the high side to –11.1% on the downside.

EXHIBIT 2.2 ROE Impact of Corporate Debt Policy in a Changing Economy

Corporate Debt Ratioa

ROE % 0.0% 10% 20% 30% 40% 50% 60% 70%

Expansion: ROA = 10%

10.0 11.1 12.5 14.3 16.7 20.0 25.0 33.3

Contraction: ROA = −10%

−10.0 −11.1 −12.5 −14.3 −16.7 −20.0 −25.0 −33.3

aThe “debt/cap” ratio for the market (S&P 500 companies) is around 40%.

32 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Exhibit 2.2 also shows that with an economy-wide debt load of 40%, the ROE numbers vary from 16.7% down to –16.7%. Moreover, as the economy expands or contracts with a 60% debt ratio, the ROE is even more volatile, ranging from 25% to –25%. On balance, the table reveals that increasing leverage (or debt) in good times conveys a seemingly positive benefit to the shareholders, while rising corporate debt ratios in bad times are a source of investor concern due to heightened financial risk. If the tra- ditional view of capital structure is correct, then investors may reap windfall capital gains or avoid losses by (1) buying the securities of companies having reasonable amounts of debt in anticipation of an expansionary economy, or (2) trading out of those companies with securities (e.g., the stocks of con- sumer durables and industrial cyclicals) that might be penalized by excessive amounts of debt in a slow-growth to recessionary economy.

PRICE MULTIPLES

Price multiples (or price relatives) are often used by investors and analysts to get a first impression of where a stock should be trading. Price multiples are typically based on the method of comparables or forecasted fundamentals, or may evolve from a statistical analysis of drivers or common factors that are likely to impact the price of a company’s stock. With knowledge of a benchmark multiple of, say, revenue, earnings, cash flow, or book value, a company’s stock price can be estimated by multiplying the appropriate price multiple by the relevant company fundamental (expressed per share). For example, if the selected earnings measure was EBITDA per share (earnings before interest, taxes, depreciation, and amortization), then a company’s stock price could be estimated as

Stock price EBITDA multiple EBITDA

P/EBITDA E

= × = × BBITDA

The estimated stock price would then be compared to the actual price to see if the stock is either potentially undervalued (actual price or mul- tiple is lower than estimated price or multiple) or overvalued (actual price or multiple is higher than estimated price or multiple). This type of equity valuation analysis, albeit simplistic, presumes that a company’s stock price or actual multiple will return to an intrinsic value or target price multiple.

Stock Analysis Using Price Multiples

To illustrate the multiples approach to equity valuation, Exhibit 2.3 shows a graph of the price-to-earnings ratio (P/E) versus the earnings growth rate

Equity Analysis Using Traditional and Value-Based Metrics 33

for U.S. equity “style” portfolios estimated at a point in time. The portfolios range from large- to small-capitalization companies, and they vary from val- ue to growth stocks. The figure suggests a strong linear relationship between the P/E and the earnings growth rate for diversified portfolios of common stocks. In practice, an investor or analyst could plot a set of multiples and earnings growth rates (PEG ratios) around the line to see whether the stocks of individual companies are possibly undervalued or overvalued. Assuming a stationary relationship in Exhibit 2.3, those stocks that plot below the line would be potentially undervalued because for a given growth rate of earn- ings investors would be willing to pay a higher multiple of earnings. For example, if a company had a P/E of 12 and an earnings growth rate of 15%, then the stock would be considered undervalued as investors seem willing to pay a multiple of “20” for that growth rate.

Conversely, stocks falling above the line would be considered overval- ued, as the underlying earnings growth rate is not sufficient to support the higher price multiple. This would happen if the price multiple were, say, 20 and the earnings growth rate were only 10%. In this case, investors will only pay a multiple of 15 for an earnings growth rate of 10%. As a word of cau- tion, the estimated PEG relationship is relevant only within the estimated range of PEG points, and it is relevant only to the extent that the relation- ship is linear and stationary (that is, repeatable). Based on Exhibit 2.3 the estimated model would be relevant only for companies with a P/E range of about 13 to 22 and an earnings growth rate of about 8% to 17%.

In practice, price relatives can be a multiple of any number of account- ing variables and include, the price–sales ratio, the price–cash flow ratio, the price-to-earnings ratio, and the price–book value per share ratio. As noted

EXHIBIT 2.3 P/E vs. Earnings Growth Rate: U.S. Equity Styles

0

10

20

30

0 5 10 15 20

Earnings Growth Rate

P/ E

Y

Predicted Y

34 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

before, the specific price multiple used by investors is often dictated by the type of company or industry. For example, an investor or analyst might use a price–sales multiple to get a sense of where a tech stock should be trading, with high expectation of revenue growth in view of currently low to nega- tive earnings and cash flows. A price–earnings or price–book multiple might be used in the equity valuation process for asset laden companies such as industrial companies as well as banks with a large loan base.

That said, it should be obvious that sole reliance on, say, a price-to-rev- enue multiple can be risky for the obvious reason that revenue is not profit. This simplistic approach to equity analysis was unfortunately commonplace in the valuation of Internet companies during the “dot-com” boom. During the tech bubble, it was thought by some investors and analysts that the mere expansion of sales or market share would ultimately lead to positive earnings and cash flows or rapid growth in these financial variables. If this thinking were correct, then it would have naturally justified higher market prices. Unfortunately, the bursting of the Nasdaq bubble during 2000 and first quar- ter of 2001 revealed the opposite price dynamics. On a more positive note, an investor or equity analyst might use a P/E multiple for consistent earnings growth companies in the health care sector (such as medical device firms as opposed to biotech companies), while, as noted before, another investor might obtain a first impression of a stock by using a price–book value ratio for companies (e.g., financial services and industrials) heavily laden with assets. However, the unadjusted P/E and P/BV approaches have limitations since they depend on accounting accruals as opposed to economic realities.

Price Multiples: Comparables vs. Forecasted Fundamentals

As mentioned previously, price multiples can be based on a method of compa- rables or a method of forecasted fundamentals. In the comparables approach, the investor compares the actual price multiple to a benchmark multiple for the sector or industry. This approach presumes that a high price relative will regress to the mean or median value (meaning that stock price will fall), while low-price-multiple companies would rise to the benchmark (meaning that stock price will go up). By contrast, the forecasted fundamentals approach to estimating a price multiple is a discounted cash flow (DCF) approach. In the DCF model, the investor estimates the fundamental (intrinsic) value of stock as the present value of estimated future cash flow. The investor then forms a ratio of estimated price to the relevant accounting measure-again, sales per share, earnings per share, cash flow per share, or book value per share.

If the actual price relative is higher than the price multiple based on forecasted fundamentals, then the stock is deemed overvalued; conversely, a stock would be considered undervalued if the estimated price relative were

Equity Analysis Using Traditional and Value-Based Metrics 35

higher than the actual price multiple. Notably, the forecasted fundamentals approach to estimating a price relative can be used to show that the multiple is related to the required return (equity discount rate) and the long-term earnings (or cash flow) growth rate. In a simple constant-growth version of the DCF model, the price multiple is related to the inverse of the required return minus the expected growth rate, or the number one over the “equity cap rate.”

Price Multiples Using Drivers or Common Factors

In Exhibit 2.3, we illustrated a single-factor model relationship between the P/E ratio and the earnings growth rate. In practice, investors and analysts might estimate a statistical relationship between a set of drivers or “common factors” that are likely to impact a company’s price multiple. In this section, we illustrate how to interpret the results of a multiple regression approach to measuring a price relative. For example, consider the assumed P/E rela- tionship from a cross-sectional regression of P/E on three well-known com- mon factors, including the dividend payout ratio (DPR), risk (as measured by stock’s beta or systematic risk), and the earnings growth rate (EGR):

Predicted P/E 10 2 DPR 0.5 Beta 20 EGR

Let DP

= + × − × + × RR 0.25, Beta 1.2, and EGR 0.10 such that:

Predic

= = = tted P/E 10 0.50 0.6 2 11.90

Actual P/E (say)1

= + − + = = 00

Given the regression parameters (or sensitivities) and assumed inputs, the regression model produces a predicted price multiple of 11.90. If the actual price multiple is higher than that predicted by the cross-sectional regression model, then the stock would be considered overvalued. In turn, a stock would be considered undervalued if the actual price relative were lower than that predicted by the assumed regression. With an actual price multiple of, say, 10, the common stock would be undervalued relative to the model.

The benefit of using a multifactor approach to measuring a price mul- tiple is that the model can be estimated using readily available market and accounting data, such as size (equity capitalization), beta (a measure of macro risk), ROE components (as explained before), or growth rates in revenue, earnings, cash flow, dividends, and book value. However, a limita- tion of the statistical approach to estimating price multiples is that there is no predefined set of drivers or common factors that go into the model. Moreover, the regression drivers approach is not formally linked to financial

36 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

theory via net present value or economic profit analysis. We describe the value-based metrics (VBM) approach to equity analysis following our dis- cussion of the fundamental stock return (a traditional metric) and its link to the investor’s required return (a key ingredient in the VBM approach).

FUNDAMENTAL STOCK RETURN

Another useful traditional measure of corporate success arises from the re- lationship between the fundamental return on a company’s stock and its ROE. The fundamental stock return (FSR) is equal to the sum of the as- sessed dividend yield (DY) and the internal capital generation rate (ICGR). In formal terms, the FSR can be expressed as

FSR DY ICGR DY (1 DPR) ROE

D/P PBR ROE

= + = + − × = + ×

In this expression, DPR is the firm’s dividend payout ratio, while D/P is the assessed dividend yield on its common stock. In turn, PBR is the “plow- back ratio,” measured by one minus DPR. Since PBR is the fraction of earn- ings that are retained by the firm for investment in real assets, the FSR shows how internal growth is related to financial happenings at the company level.

That is, the firm’s internal capital generation rate (also called the sustain- able growth rate) derives its value from the product of the fraction of earn- ings retained for future investment—which reflects additional equity capital resulting from reinvestment of a firm’s profit—and the estimated return that the firm’s managers can generate on those retained earnings. ROE in the tra- ditional realm of financial analysis measures that likely return on stockhold- ers’ equity. As we argue below, the FSR should be compared to the investor’s required return (or cost of equity) to see if the return that a company can deliver from its underlying fundamentals exceeds or falls short of the required return. Herein begins our first link to the VBM approach to company analy- sis, as a financial metric becomes a value-based metric when there is a formal recognition of and a link thereto the investor’s required rate of return.

Required Return: The Missing Link

Up to this point, we have been long on traditional metrics but short on the notion of the investor’s required rate of return. This observation points to a problem with the traditional model of company analysis—whether it is the extended Dupont model or otherwise. Unfortunately, in the traditional approach to equity analysis there is no direct link between metrics such as

Equity Analysis Using Traditional and Value-Based Metrics 37

ROE and FSR and the investor’s return expectation for undertaking risk. This omission is important because the fundamental stock return is largely based on accounting data—such as the plowback ratio and ROE—while the investor’s required return is (or should be) based on an equilibrium model of expected return and risk.

According to one widely used approach to estimating the required return on common stock, namely, the Capital Asset Pricing Model (CAPM), the required return is equal to

ER = R f + MRP × Beta

In the CAPM, R f is the risk-free rate of interest, MRP is the expected market

risk premium, and beta measures the systematic risk of a firm’s common stock. In a nutshell, beta can be interpreted as a measure of macro risk, although beta also reflects other factors such as leverage via the debt–equity ratio. When beta is greater than unity—as is the case of growth stocks—the expected return on common stock is higher than that projected for the mar- ket portfolio. Conversely, when beta is less than one—typically for value stocks—the required or expected stock return (ER) is lower than the antici- pated return on the market portfolio (M).

Note, too, that the CAPM provides a benchmark for determining whether the FSR on stock is attractive or unattractive. Exhibit 2.4 shows a graph of CAPM as measured by the expected return (as shown on the verti- cal axis) versus the expected risk (beta as shown on the horizontal axis). A plot of the CAPM is formally known as the securities market line (SML).

In principle, companies with FSRs that plot above the SML, such as value stocks B and C, and growth stocks F and G, are attractive because their ROE-induced growth prospects make an abnormally positive contri- bution to their fundamental stock return. Likewise, any company whose FSR falls below the CAPM benchmark, such as low-risk stock A and moder- ate-to-risky growth stocks E and H, would be considered unattractive in this security selection framework. This happens because the sum of the assessed dividend yield and internal capital generation rate is not high enough for the company’s fundamental stock return to lie either above or on the SML.

In other words, the FSR-linked CAPM model indicates that investors should buy securities of firms having a fundamental stock return that lies above the CAPM line, as their prices seem low when evaluated in terms of the firm’s underlying earnings capabilities. In contrast, they should sell or possibly short sell the shares of companies with FSRs that fall below the SML, because stock price appears high when measured relative to the firm’s assessed dividend yield and anticipated growth opportunities. By inference, stocks that lie on the SML, such as market-risk stock D, are priced just right,

38 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

in the sense that their fundamental return could be synthetically replicated with an unlevered or levered index fund in combination with the risk-free asset (appropriate lending or borrowing points along the SML respectively).

TRADITIONAL CAVEATS

The link between FSR and CAPM provides a natural transition to the VBM approach to company analysis. We provide that discussion later in the chap- ter. However, as a cautionary word on the traditional role of corporate debt policy, it may seem odd that investors should somehow feel better off with higher amounts of leverage, even though the firm’s return on assets (or capi- tal) remains constant. This comment points to a hopefully obvious limita- tion of the traditional approach to company analysis. That is, unless the corporate debt change is associated with a rise in real profitability (due to cash-flow benefits received from a higher debt-interest-tax subsidy) or a per- ceived decline in equity risk (when a firm moves from a position of too much debt back to its presumed target level), then nothing of any real significance has changed for the shareholders. Without a meaningful change, investors have little incentive to pay a higher or lower price for the firm’s shares due to corporate leverage changes per se.

EXHIBIT 2.4 FSR vs. CAPM

16

14

12

10

8

6

4

2

0

FS R

, C A

PM

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 Beta

Stock A

Stock E

Stock D Stock C

Stock B

Stock F Stock G

Stock H

SML

Equity Analysis Using Traditional and Value-Based Metrics 39

Moreover, in a special case of the VBM approach to capital structure (namely, the original 1958 capital structure model developed by Modigli- ani and Miller2), the perceived stockholder benefits resulting from higher leverage are offset by a rise in the expected (required) rate of return on the firm’s common stock. We discuss the comparative valuation effects of capi- tal structure in the next section.

OVERVIEW OF VALUE-BASED METRICS

We now provide an overview of VBM. Value-based metrics are financial measures that largely evolve out of corporate finance. The focus here is on metrics that can assist managers and investors in discerning whether a com- pany is pointing in the direction of wealth creation or, unfortunately, wealth destruction. In the VBM approach to fundamental analysis, the focus is on discovering firms that can consistently earn a return on capital (ROC) that exceeds the weighted average cost of capital (WACC).

A financial metric takes on a VBM character when there is an explicit recognition of and accounting for the overall cost of capital (WACC in the economic value added model described below) or the cost of equity (r in the residual income or abnormal earnings model also described below). Hence, the most distinctive feature of VBM analysis (in contrast to traditional anal- ysis) is the formal recognition of the investor’s required rate of return (cost of equity) and the overall cost of capital. Value-based metrics include:

■ Residual income (abnormal earnings) ■ Residual income spread ■ Economic value added (EVA®) ■ Economic value added spread ■ Market value added (MVA) ■ Cash flow return on investment (CFROI®)

Background

We’ll begin the VBM approach to equity analysis with a metric called eco- nomic value added (EVA). EVA was developed commercially in the early 1980s by Joel Stern and G. Bennett Stewart III. This economic profit mea- sure gained early acceptance in the corporate community because of its innovative way of looking at profit net of the overall dollar cost of capital,

2Franco Modigliani and Merton Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review 48, no. 3 (1958): 261– 297.

40 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

including debt and equity capital costs. EVA principles have been used by many companies to design incentive compensation programs that provide value-based incentives for managers (agents) to make wealth-enhancing decisions for the shareholders (principals).

In turn, EVA gained popularity in the investment community with the establishment in 1996 of CS First Boston’s annual conference on economic value added. In 1997, the U.S. Equity Research Group at Goldman Sachs developed an EVA platform to evaluate the performance of companies, industries, and sectors of the economy. On the buy side, Centre Asset Man- agement LLC and EVA Advisors LLC are two examples of today’s invest- ment firms that use an EVA approach to select stocks and build long-short equity portfolios.

The financial significance of using EVA to evaluate company and stock performance is crystal clear: Wealth-creating firms have positive EVA because their NOPAT exceeds the dollar weighted average cost of capital. Wealth destroyers lose market value and incur share price decline because their corporate profitability falls short of the capital costs. This wealth loss can occur even though the firm’s accounting profit is positive. This happens when pretax operating earnings (EBIT) are sufficient enough to cover debt- interest costs, but they are not high enough to cover the combined dollar costs of debt and equity financings. Herein lay a key distinction between accounting-based traditional metrics and value-based metrics.

Basic EVA

Central to the EVA calculation is the concept of levered and unlevered firms. A “levered” firm, like most real-world firms, is one that partly finances its growth opportunities with long-term debt. In contrast, an equivalent-risk “unlevered” firm is financed by 100% equity. This firm-type classification is helpful because EVA is calculated by subtracting the firm’s dollar weighted average cost of debt and equity capital ($WACC) from its unlevered NOPAT.

EVA NOPAT WACC= − $

NOPAT is used in the EVA formulation for two reasons. First, emphasis on this term serves as a reminder that the firm largely receives its profit- ability from the desirability of its products and services. Second, since most firms have some form of debt outstanding, they receive a yearly interest tax subsidy—measured by the corporate tax rate times the interest expense— that is already reflected in the dollar cost of capital.

This second point is important. An incorrect focus by managers or investors on the levered firm’s net operating profit after taxes, LNOPAT,

Equity Analysis Using Traditional and Value-Based Metrics 41

rather than its unlevered profit measure, NOPAT, would lead to an upward bias in the firm’s economic value added. By avoiding the double counting of the firm’s yearly interest tax subsidy, the investor avoids imparting a posi- tive bias in not only the firm’s profitability but also its enterprise value and underlying stock price.

In basic terms, NOPAT can be expressed as (1) tax-adjusted operat- ing earnings (EBIT) or (2) net income (NI) plus after-tax interest expense according to

NOPAT EBIT

CGS SGA

NI

= × − = − − − × − = + −

( )

[ ] ( )

(

1

1

1

t

S D t

tt)*Interest expense

In the first expression, NOPAT is shown as tax-adjusted operating earnings, EBIT × (1 − t). EBIT in the second expression is sales less cost of goods sold, selling, general, and administrative expenses, and depreciation. In principle, depreciation should be a charge that reflects the economic obsolescence of the firm’s operating assets. In the third expression, the analyst or inves- tor begins with accounting net income and adds back the after-tax interest expense to work back to tax-adjusted operating earnings, EBIT × (1 − t).

In turn, the firm’s $WACC can be expressed as

$WACC = [%WACC/100] × C

In this expression, %WACC is the firm’s percentage weighted average cost of debt and equity capital, while the letter C is its operating capital. Note that capital can be expressed in terms of operating assets (such as net short- term operating assets plus net plant, property, and equipment) or financing capital (reflecting debt and equity financings). The cost of capital percentage is given by

%WACC = %After-tax debt cost × Target debt weight + %Equity cost × Target equity weight

With NOPAT expressed as tax-adjusted operating earnings, we see that a firm’s basic EVA can be expressed as

EVA NOPAT WACC

EBIT WACC C

S CGS SG

= − = × − − × = − −

$

( )

[

1 t

AA D WACC C− × − − ×] ( )1 t

42 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

This expression shows that the firm’s EVA is equal to its NOPAT less the dollar cost of all capital employed in the business. Moreover, the EVA for- mula suggests at least five ways to increase a company’s economic earnings. These include:

1. Increase revenue (growth). 2. Reduce operating expenses where prudent. 3. Use less capital to produce the same amount of goods and services

(improved capital turnover ratios). 4. Use more capital in the presence of positive EVA growth opportunities. 5. Reduce WACC (via greater consistency of earnings and cash flows).

Exhibit 2.5 provides a three-part example on how to estimate basic EVA. The table shows how to estimate the three components of EVA, including NOPAT, WACC, and capital. In this illustration, the firm is pointing in the direction of value creation because its economic profit is positive. Likewise, in EVA spread terms, the firm is a potential wealth creator because its after- tax ROC is higher than its cost of capital.

In practice, there are numerous accounting adjustments that investors should be aware of when estimating EVA via NOPAT and capital. We cover some of the more popular ones at the end of our VBM survey. In the next few sections, we’ll discuss related VBM metrics and concepts including (1) how to measure the EVA spread, (2) how to decompose ROC into profit margins and capital turns, (3) WACC issues, (4) cash flow return on invest- ment, (5) residual income (abnormal earnings), and (6) the role of EVA and residual income momentum in discerning “good companies” from “bad” or risky-troubled companies and related stock valuation considerations. Finally, the appendix provides a case study on how to combine traditional and value-based metrics to come up with an integrated, overall stock rating.

EVA Spread

VBM can be expressed in either dollar or ratio terms. One of the more pop- ular ratio (or percentage) forms is the EVA spread. This is also referred to as the residual ROC (or surplus rate of return on capital). The EVA spread is simply the return on capital less WACC. The EVA spread is obtained by dividing EVA by capital to obtain:

EVA/C NOPAT/C $WACC/C

ROC WACC

= − = −

Equity Analysis Using Traditional and Value-Based Metrics 43

EXHIBIT 2.5 Three-Part Calculation of EVA

1. Calculate basic NOPAT.

NOPAT = EBIT × (1 − t) = (S − CGS − SGA − D) × (1− t)

Assume the following:

Sales = S = $140,000 Cost of goods sold = CGS = $80,000 Selling, general, and administrative expenses = SGA = $15,000 Depreciation = D = $2,000 Tax rate = t = 35%

Then,

NOPAT = ($140,000 − $80,000 − $15,000 − $2,000) × (1 − 0.35) = $43,000 × 0.65 = $27,950

Note that, in practice, NOPAT = Basic NOPAT (shown above) + VBM ac- counting adjustments (described later)

2. Calculate the dollar weighted-average cost of capital, $WACC.

WACC = After-tax debt cost × Target debt weight + Equity cost × Target equity weight

$WACC = WACC × C After-tax debt cost = Pre-tax debt cost × (1 − t) Cost of equity (using CAPM) = R

F + MRP × Beta

Assume the following:

Pretax debt cost = 6% Risk-free rate = RF = 3% Market risk premium = MRP = 5% Beta = 0.8 Target debt weight = 30% Capital = $140,000 (Net working capital + Net PP&E; or Long-term debt + Equity)

Note that in practice, Capital = Basic capital (shown above) + Other debt and equity equivalents. Then,

After-tax debt cost = 0.06% × (1 − 0.35) = 0.039 or 3.9% CAPM = 0.03 + 0.05 × 0.80 = 0.07 or 7.0% WACC = 0.039 × 0.3 + 0.07 × 0.70 = 0.0607 or 6.07% $WACC = 0.0607 × $140,000 = $8,498

3. Combine results to calculate economic value added, EVA.

EVA = NOPAT − $WACC = $27,950 − $8,498 = $19,452 > 0 (potential wealth creator)

44 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

With this expression, an investor can assess whether a company is pointing in the direction of wealth creation, wealth neutrality, or wealth destruction. If the EVA spread is positive, the firm is a potential value creator, since ROC exceeds WACC. Conversely, if ROC is less than WACC, the firm points in the direction of value destruction, even though reported accounting earn- ings may be positive. While such a firm may meet its debt interest expense, it is unable to account for the opportunity cost of equity, whether measured in dollar or ratio terms. The EVA spread in the example given in Exhibit 2.5 is 13.89% as shown:

EVA/C $27,950/$140,000 $8,498/$140,000= − = 0 13. 889 13 89or . %

The EVA spread is positive and attractive because the ROC, at 19.96%, is considerably higher than the WACC, at 6.07%.

Return on Capital Decomposition

Like ROA in the Dupont model, ROC can be expressed in terms of an oper- ating profit margin and a capital turnover ratio:

ROC NOPAT/C NOPAT/S S/C= = ×

Moreover, since C (assets perspective) is equal to net short-term operat- ing assets (NWC less short-term debt) plus net plant, property, and equip- ment, we can express ROC in terms of an operating margin and working capital and NPPE turns:

ROC NOPAT/S S/ NWC NPPE= × +[ ]

Not surprisingly, higher operating margins, higher net working capital, and net plant and equipment (including technology) turns lead to higher ROC. Assuming that WACC remains unchanged, the higher ROC leads to a higher EVA spread. This leads to higher EVA and, if sustainable, higher enterprise value—especially with capital expansion (role discussed shortly), assuming that this information is not already reflected in share price.

From Exhibit 2.5, the NOPAT margin (NOPAT/S) is coincidentally the same as ROC, at 19.96%. This happens because the capital turnover ratio (S/C) is unity:

ROC 27,950/ 140,000 140,000/ 140,000= × =

$ $ $ $

.0 19996 19 96or . %

Equity Analysis Using Traditional and Value-Based Metrics 45

WACC Issues

Central to the VBM model is the recognition that a firm is not truly profit- able unless it earns a return on capital that exceeds the opportunity cost of capital. That being said, questions remain about the actual calculation of WACC. We provide an overview of two particular controversies that present real-world challenges to estimating WACC. These issues pertain to (1) the debt weight (and therefore equity weight) used in the EVA formulation and (2) how to estimate the investor’s required rate of return (cost of equity).

Target Capital Structure

One of the major issues in the real-world application of EVA (or residu- al income) analysis is the question of capital structure. For our purposes, capital structure refers to the debt and equity weights that an investor or analyst should use in the EVA formulation. The question of a target capital structure—reflecting a presumed “optimal” mix of debt and equity financ- ings—is a long-standing debate in the theory of corporate finance. Exhibit 2.6 provides a graphical depiction of the capital structure issue in terms of the traditional view of capital structure versus the Modigliani-Miller view (a celebrated theory proposed in 1958 with subsequent variation). The origi- nal theory by Modigliani and Miller (MM) can be interpreted as a special case of the VBM approach to capital structure.

EXHIBIT 2.6 Impact of Capital Structure Change on Enterprise Value

E nt

er pr

is e

V al

ue (

$)

550,000

540,000

530,000

520,000

510,000

500,000

490,000

480,000

470,000

460,000

Traditional Optimal Capital Structure

Miller-Modigliani

Debt/Capital Ratio(%) 0 20 40 60 80

46 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Exhibit 2.6 shows the pricing implications of the traditional versus MM views of capital structure, measured in terms of corporate value (vertical axis) and leverage (horizontal axis). In general, Vu is the market value of the unlevered firm—a firm having no long-term debt—while Vl denotes the market value of a levered firm—a firm with debt. In the traditional view, when the D/C (or D/A) rises from zero to the target level of, say, 40%, the market value of the firm and its outstanding shares goes up. In this debt range, stock price rises as the “good news” to the shareholders—resulting from positive ROE and EPS happenings net of a small change in perceived equity risk—causes investors to pay more for the firm’s seemingly dearer shares.

However, if the D/C exceeds the 40% target (see Exhibit 2.6), then corporate value and stock price fall as the heightened financial risk—due to ever-rising fixed obligations that now place the firm in financial jeopardy— offsets the leverage-induced ROE and EPS benefits. With a 60% debt load, the firms’ managers have pushed debt beyond the presumed optimal level; hence, they should engage in de-levering activities that effectively swap debt for more equity shares. Moreover, if the 40% debt level is in fact an optimal one, then stock price declines with any sizable movement to the left or right of this target capital structure position.

Exhibit 2.6 also illustrates the pricing implications of a special case of the VBM approach to capital structure—namely, the original MM model. In the MM model, the higher ROE and EPS generated by higher corpo- rate leverage are entirely offset by a rise in the investor’s required rate of return. In CAPM, for example, beta is linearly related to the debt–equity ratio. Consequently, in a perfect capital market, the company’s stock price remains unchanged in the presence of the debt-induced rise in EPS and ROE. In their value-based framework, a firm’s corporate value and stock price are impacted only by real investment opportunities (discounted posi- tive EVA or positive NPV opportunities) as opposed to leverage policies (as in traditional realm) that give investors the illusion of value creation.

Investors and analysts alike must deal with the question of capital struc- ture, since debt and equity weights are required inputs in the WACC (and therefore EVA) formulation. While in theory a capital structure controversy exists, we recommend that investors and analysts use a debt weight that is reflective of the target capital structure mix of debt and equity financings that a firm is likely to achieve over the long term. Moreover, we recommend that investors look “everywhere” for the debt when measuring corporate leverage and estimating stock price.

Equity Analysis Using Traditional and Value-Based Metrics 47

Estimating the Cost of Equity

In practice, the CAPM is perhaps the most popular approach to estimating the cost of equity. We used CAPM in the traditional approach to company analysis when we compared the FSR to the SML (see Exhibit 2.4). However, there are numerous empirical challenges to the CAPM that suggest that the model is not reflective of what actually happens in the real world regarding the relationship between average portfolio return and risk as specified by the beta factor. That is, numerous empirical studies suggest that over the long pull low-beta, “value”-style portfolios actually outperform high-beta, “growth”-style portfolios.

Given that there are significant challenges to the CAPM, the investor or analyst may prefer to use (1) an enhanced CAPM with other system- atic, nondiversifiable risk factors (such as firm size to capture potential size effects and/or the price–book ratio to capture differential expected return effects between value and growth styles) or (2) a non-CAPM approach to measuring the cost of equity, that is, absent beta. Exhibit 2.7 illustrates the components of an equity risk buildup approach to estimating the required return on equity. This non-CAPM alternative was proposed by Abate, Grant, and Rowberry.3

EXHIBIT 2.7 Required Return on Equity: Equity-Risk Buildup Model

R eq

ui re

d R

et ur

n

+

+

+

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

Specific Risk Score

Specific Premium

Sector Premium

Base Premium (“least risky” equity)

Risk-free Rate

7.00 9.00 11.00 13.00 15.00 17.00 19.00 21.00

3James A. Abate, James L. Grant, and Chris Rowberry, “Understanding the Re- quired Return Under New Uncertainty,” Journal of Portfolio Management 32, no. 1 (2006): 93–102.

48 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Here, the cost of equity is modeled in the context of four elements: (1) a risk-free rate of interest, (2) a base or nondiversifiable risk premium to the “least risky” equity, (3) a sector-risk premium, and (4) a company-specific risk premium related to (say) abnormal firm size, leverage (debt–equity ratio), and EVA volatility. While we make no specific recommendation, the investor or analyst needs to decide on a particular approach to measuring the cost of equity, as the required ROE is a key component of the WACC used in the EVA formulation. The required return is also a key ingredient in the residual income or abnormal earnings approach, which we describe next.

Cash-Flow Return on Investment

Another widely used VBM is the cash-flow return on investment (CFROI®). CFROI is a commercial metric of Credit Suisse/HOLT. This metric is an in- ternal rate of return (IRR)–based measure of company performance. CFROI takes on an economic profit perspective when it is compared to the cost of capital, WACC. Exhibit 2.8 shows a five-step process to calculate CFROI, although the actual calculation by CS/HOLT is much more complex with several value-based accounting adjustments. The exhibit also shows a sim- ple example of how to estimate this widely known metric.

In Exhibit 2.8, the estimated CFROI is 16.26%. As a stand-alone fig- ure, CFROI does not give the investor or analyst any indication of whether a company is pointing in the direction of wealth creation or destruction. However, CFROI takes on an economic profit perspective when the esti- mated IRR is compared to the cost of capital. Moreover, an economic profit relationship exists between the two VBMs because the spread between CFROI and WACC is similar to the economic profit or EVA spread.

Specifically, we know that EVA can be expressed in two ways:

EVA NOPAT WACC C= − ×

Or, in spread form,

EVA ROC WACC C= − ×[ ]

In principle, ROC is similar to CFROI, which is an IRR or rate of return on capital concept. While in theory the two value-based metrics (EVA and CFROI) are related in concept, there are notable differences in how these met- rics are calculated in practice. A closer look at EVA and CFROI reveals that:

■ EVA is a dollar-based measure of economic profit. CFROI is an IRR- like measure that takes on an economic profit perspective when com- pared to WACC.

Equity Analysis Using Traditional and Value-Based Metrics 49

■ EVA uses NOPAT and net invested capital, while CFROI is based on gross cash flows and gross investment.

■ EVA is measured in nominal terms, while CFROI is measured in real terms.

■ The accounting adjustments used to measure EVA and CFROI may dif- fer in practice.

EXHIBIT 2.8 CFROI: A Five-Step Process to Calculate CFROI

Step 1. Compute the average life of the firm’s assets

Note that average asset life equals gross depreciable assets/depreciation. Gross depreciable assets exclude land and construction in process.

Step 2. Compute gross cash flow

Gross cash flow equals net income adjusted for noncash operating expenses and financing expenses according to:

Net income before extraordinary items + Depreciation and amortization + Interest expense + Operating rental expense + Deferred taxes = Gross cash flow

Step 3. Compute gross cash investment

Note that gross investment equals gross PP&E plus the present value of operat- ing lease payments plus goodwill and accumulated intangibles amortization.

Step 4. Compute the sum of all nondepreciating assets such as land, working capital, and other assets.

Step 5. Solve for the CFROI

Calculator example:

Gross cash investment = PV = −$40,000

Gross cash flow = PMT = $12,000

Nondepreciating assets = FV = $2,000

Average life of assets = N = 5

CFROI = IRR = 16.26%

50 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Residual Income

Another popular value-based metric is residual income (RI) or abnormal earnings. Residual income is simply accounting net income less the dollar cost of equity:

RI Net income $Cost of equity

[ROE

= − = − ×r E]

In this expression, the difference between ROE and the investor’s required return (r) is the residual income (abnormal earnings) spread. While RI is analogous to EVA in that the measure of profit is net of the investor’s dol- lar-based required return, the concept is somewhat less robust than EVA because ROE in the traditional realm of financial analysis reflects a mixing of operating and financing decisions.

Recall that in the Dupont formula ROE can be expressed as ROA times the equity multiplier (A/E). In contrast, in the EVA calculation the firm’s operating and financing decisions are analyzed separately via NOPAT and $WACC. On the other hand, given the different reporting classifications on income and balance sheets for financial services versus nonfinancial services companies (e.g., loans are an asset for a bank while a liability for an indus- trial or technology firm), the RI (abnormal earnings) approach to equity analysis—with its focus on adjusted book value and the residual income spread—is particularly helpful in estimating and valuing the economic earn- ings of financial services companies.

Exhibit 2.9 provides an example of how to calculate expected future values of RI given (1) the current book value, (2) a consensus earnings growth estimate, (3) an assumed dividend payout ratio (or implied plow- back ratio), and (4) the cost of equity.

Since the RI estimates in Exhibit 2.8 are positive, at $0.70 and $0.74 per share, the firm is expected to make a value-added contribution to share- holder equity. This happens because the estimated ROE (EPS/BV) figures for periods 1 and 2, at 22% and 20.58%, are higher than the investor’s assumed required return of 8%.

Role of EVA Momentum

We now describe how the concept of EVA momentum (and, by extension, residual income or abnormal earnings momentum) can be used as a prism to discern good company growth characteristics from bad company growth characteristics. While the level of EVA is important in deciding whether a company is a value creator or value destroyer, this information may already be reflected in share price. Hence, investors need to assess whether the level

Equity Analysis Using Traditional and Value-Based Metrics 51

of EVA is increasing or decreasing. A firm’s EVA momentum can be assessed according to

ΔEVA = EVA Spread × ΔC = [ROC – WACC] × ΔC

With EVA spread constancy, we see that the change in EVA is driven by the change in net invested capital; that is, capital investment beyond depre- ciation. We illustrate the importance of EVA momentum by placing compa- nies into four quadrants. The EVA quadrants (or EVA “style”) approach to equity analysis was developed by Grant and Abate4 and applied in Abate, Grant, and Stewart5 and Grant and Trahan.6 As shown in Exhibit 2.10, the EVA quadrants are defined by the following characteristics:

■ Quadrant 1: Stagnant company—ROC > WACC; ΔC ≤ 0 ■ Quadrant 2: Good company growth—ROC > WACC; ΔC > 0

4James L. Grant and James A. Abate, Focus on Value: A Corporate and Investor’s Guide to Wealth Creation (Hoboken, NJ: John Wiley & Sons, 2001). 5James A. Abate, James L. Grant, and G. Bennett Stewart III, “The EVA Style of Investing,” Journal of Portfolio Management 30, no. 4 (2004): 61–72. 6James L. Grant and Emery Trahan, “Active Investing in Strategic Acquirers using an EVA Style Analysis,” Journal of Alternative Investments 11, no. 4 (2009): 7–23.

EXHIBIT 2.9 Forecasting Residual Income Assume:

Current book value per share = $5 Current earnings = $1.00 Earnings growth rate = 10% Dividend payout ratio = 20% Cost of equity = r = 8%

Period 1 Period 2

Beginning BV per share $5.00 $5.88

Earnings per share 1.10 1.21

Dividends per share 0.22 0.24

Retained earnings (EPS − DPS) 0.88 0.97

Ending BV per share 5.88 6.85

Net income per share (EPS) 1.10 1.21

Less equity charge [r × BV(t − 1)] 0.40a 0.47b

Residual income $0.70 0.74

a0.08 × $5.00 = $0.40 b0.08 × $5.88 = $0.47

52 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

■ Quadrant 3: Bad company growth—ROC < WACC; ΔC > 0 ■ Quadrant 4: Positive Restructure—ROC < WACC; ΔC < 0

We apply this schematic to S&P Industrial stocks. In Exhibit 2.10, Quadrant 2 and 4 companies have positive EVA momentum. In contrast, Quadrant 1 and 3 companies are for differing reasons destroying economic value added. This is because the stagnant/mature companies in Quadrant 1 have limited future growth opportunities, while Quadrant 3 companies are expanding negative EVA spread businesses. Clearly, Quadrant 2 and 4 com- panies represent potential buy opportunities, while companies that populate Quadrants 1 and 3 are potential sell or short-sell candidates, assuming that market implied expectations of future EVA growth are not fully reflected in share price (see EVA valuation considerations in the next section). Grant and Abate emphasize the EVA spread and capital expansion term (or capital catalyst) in the screening of good companies from bad or risky-troubled companies.

Valuation Considerations

We now describe how to use EVA valuation concepts to identify potential buy opportunities (those we refer to as good stocks) and sell or short sell

EXHIBIT 2.10 EVA Spread vs. Capital Growth: S&P Industrials

Q1: Stagnant companies Q2: Growth creates

shareholder value

Q4: Positive restructuring

Q3: Growth destroys shareholder value

–15.0

–10.0

–5.0

0.0

5.0

10.0

15.0

20.0

–10.0 –5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Capital Growth Rate (% before maintenance CapX)

E V

A S

pr ea

d (%

)

Source: Compustat and Centre Asset Management, LLC.

Equity Analysis Using Traditional and Value-Based Metrics 53

opportunities (those we identify as bad stocks). To illustrate the diversity of valuation approaches using VBM concepts, we also show how to estimate the intrinsic value of a share of common stock using the residual income or abnormal earnings valuation model. RI valuation is similar to EVA valu- ation, with the substitution of residual income for EVA, and the residual income (abnormal earnings) spread for the EVA spread.

Identifying Good Stocks

While EVA momentum can be used to distinguish good companies from bad companies, we still must see whether a stock is a potential buy or sell opportunity. That is, if the market is efficient, then market implied expecta- tions of future economic profit growth will be consistent with actual growth expectations that a company can deliver. In this case, the stock would be fairly priced in the marketplace. However, if actual expectations of future economic profit growth are higher than market implied expectations, then a stock would be considered undervalued. In turn, if actual expectations of future EVA growth are lower than that embedded in share price, then a stock would be overvalued.

In theory, it can be shown that a firm’s net present value (NPV) is equal to the present value of all future EVA. With constant growth, the firm’s NPV—a measure of intrinsic value added in current dollars—can be expressed as

NPV EVA/ WACC= −( )g

In this expression, EVA is a one-step-ahead forecast, WACC is the familiar cost of capital, and g is the expected long-run growth in economic earn- ings. Of course, this form of EVA valuation requires that WACC is greater than the growth rate. It follows that the intrinsic value of the firm can be expressed as:

V C NPV= +

From these relationships, we can calculate the value–capital ratio (V/C). This ratio is analogous to the price–book value ratio in the traditional realm of financial analysis:

V/C NPV/C EVA/ WACC /C

ROC WACC

= + = + − = + −

1 1

1

[ ( )]

[ ]

g

// ( )WACC − g

Since NPV (derived from EVA valuation) measures the value that a firm’s management has added (albeit market and industry considerations)

54 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

to the invested capital in their employ, the value–capital ratio is greater than unity if and only if the firm has discounted positive EVA; that is, NPV is positive, signifying a wealth creator. Equivalently, the V/C ratio is greater than one if the firm’s management can sustainably generate a positive EVA spread [ROC > WACC, and WACC > g in the constant growth EVA valua- tion model].

In contrast, a firm’s V/C ratio will be less than unity if discounted EVA is negative [ROC < WACC]; that is, NPV is negative, signifying a wealth destroyer. Note, too, that if the capital market is efficient, then the mar- ket’s assessment of value added, denoted by MVA, will be equal to the firm’s assessed NPV. From these relationships, we can identify the value-based con- ditions for discovering fairly priced stocks, undervalued stocks, and over- valued stocks; whereby MVA is equal to NPV, MVA is less than NPV, or MVA is higher than NPV, respectively. We summarize the security selection implications of these MVA and NPV conditions as:

Relationship Condition

MVA = NPV Stock is fairly priced

MVA < NPV Stock is undervalued

MVA > NPV Stock is overvalued

Exhibit 2.11 provides a graphical display of the EVA spread versus the V/C ratio for S&P Industrial stocks. The graph in this exhibit follows the EVA quadrants graph shown in Exhibit 2.10, and is based on the EVA style of investing approach developed by Grant and Abate.7

In Exhibit 2.11, the EVA spread is the y variable, while the V/C ratio is the x variable. Stocks that plot above the curve are deemed undervalued or good stocks as actual expectations of future economic profit growth, g, are higher than that reflected in share price; hence, the V/C ratio and stock price should rise. Stocks that plot below the curve are deemed overvalued or bad stocks since actual expectations of economic profit growth are lower than that embedded in share price; hence, V/C ratio and stock price should fall. In turn, stocks that plot on the curve are presumed to be efficiently priced as market implied expectations of future economic profit growth are equal to that which a company can realistically deliver. Moreover, a residual income (abnormal earnings) version of this EVA framework would show the residual income spread (ROE minus r) as the y variable and the price/book value ratio as the x variable.

7Grant and Abate, Focus on Value: A Corporate and Investor’s Guide to Wealth Creation.

Equity Analysis Using Traditional and Value-Based Metrics 55

EXHIBIT 2.11 EVA Spread vs. Value/Capital Ratio: S&P Industrials

–15.0

–5.0

5.0

15.0

0.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25 4.75 Market to Replacement Value Ratio

E V

A S

pr ea

d (%

)

Source: Compustat and Centre Asset Management, LLC.

Residual Income (Abnormal Earnings) Valuation

We now illustrate how to calculate the intrinsic value of a share of stock using the residual income or abnormal earnings model. Specifically, Exhibit 2.12 shows how to calculate the intrinsic value of a share of common stock using a two-stage (or multistage) RI model. The valuation analysis assumes a required return (cost of equity) of 8%, along with forecasted EPS over a finite horizon period (we use the two years of RI estimates from Exhibit 2.8) and forecasted continuing residual earnings.

Like EVA, we can explain the relationship between residual income and the justified price–book ratio based on forecasted fundamentals. Since the forecasted fundamentals approach to multiples analysis is a discounted cash flow (DCF) or intrinsic value approach, we have

P BV per share PV of RI per share= +

such that

P/BV PV of RI /BV= +1 [ ]

56 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 2.12 Residual Income Valuation

Horizon Value Period: Years 1–2

RI(1) = $0.70

RI(2) = $0.74

such that

PV of RI per share = $0.70/(1.08) + $0.74/(1.08)2 = $0.65 + $0.63 = $1.28

Continuing Value Period: Years 3 to ∞

PV of RI (multistage) = PV of RI during forecast period + PV of RI during continuing period = $1.28 + PV(8%,2) × [RI(3) / (r − g)]

Assume that long-term growth in RI = 0.02 (or 2%), such that

RI(3) = RI(2) × (1 + g) = 0.74 × (1.02) = 0.75

PV of RI (multistage) = $1.28 + PV(8%,2) × [$0.75/(0.08 − 0.02)] = $1.28 + PV(8%,2) × [$12.50] = $12.00

such that,

Estimated stock price = BV(t − 1) + PV of all future RI = $5.00 + $12.00 = $17.00

Equity Strategy

Compare estimated stock price (intrinsic value) to actual price to see if overval- ued or undervalued.

where P/BV > 1.0 if the present value of residual income (abnormal earn- ings) is positive. In contrast, P/BV is less than unity when a company is perceived to have consistently negative residual income. Equivalently, P/BV ratio is greater than one if ROE is sustainably greater than r, while P/BV is less than unity when the firm is perceived to incur a negative residual income spread [ROE < r].

Moreover, we could calculate the implied growth rate in residual income given the price–book ratio and an estimate of the required rate of return on equity. Using the constant growth assumption yields,

P = BV + PV of RI = BV + [ROE – r] × BV/(r – g)

such that P/BV = 1 + [ROE – r]/(r – g).

Equity Analysis Using Traditional and Value-Based Metrics 57

Hence, the investor or analyst could solve for market-implied growth in residual income, g, with knowledge of P/BV, ROE, and the investor’s required rate of return. The investor could then compare market-implied g with the long-term growth in residual income that the analyst perceives the company could actually deliver to determine whether a stock is a potential buy or sell opportunity.

VBM Caveats

While value-based metrics such as EVA, CFROI, and RI are fundamentally linked to value creation (via NPV), there are numerous accounting adjust- ments that an investor or analyst must consider in practice. Indeed, the firm of Stern Stewart has discovered some 140 accounting adjustments to con- sider when moving from the traditional accounting concept of income to the VBM concept of economic earnings. At a minimum, we recommend that investors and analysts consider the following list of VBM accounting adjust- ments when measuring economic profit:

■ Research and development (capitalized) ■ Strategic investments (temporary suspension of capital charge) ■ Intangibles (capitalized and not amortized) ■ Deferred taxes (conversion to cash taxes) ■ Operating leases (treated as debt equivalent) ■ Last in, first out (LIFO) inventory costing-LIFO reserve add backs

It is important to note that there are income statement and balance sheet consequences for each VBM accounting adjustment. For instance, the year-over-year change in an unamortized research and development (R&D) account (that is, amortization expense) would get added back to NOPAT, while the accumulated unamortized R&D account would get added back to EVA capital. In this way, the capitalized value of each dollar of R&D has a capital cost as long as it remains on the EVA balance sheet. Also, the after-tax implied interest expense on operating leases would get added back to NOPAT, while the present value of operating leases would be treated as a debt equivalent on the EVA balance sheet. VBM accounting conventions apply to several other value-based accounting items.�

Despite the caveats or limitations cited for both traditional and value- based approaches to equity analysis, we conclude this chapter by recom- mending that investors join the two approaches to securities analysis. In the process, investors and analysts must realize that a combination of traditional and VBM analyses will require an extra effort in terms of the acquisition of knowledge and skills in order to understand what these metrics have to say

58 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

about the creation of shareholder value. That being said, we believe that the extra time spent will be worth the effort in terms of both educational value added and economic value added—a doubly winning EVA benefit!

Case Study: JLG Equity Analysis Template

We present in the appendix to this chapter a synthesized traditional and value-based analysis of Coca-Cola using financial software developed by JLG Research. The accompanying equity analysis includes growth rates, margins, multiples, ROE, and FSR on the traditional side and EVA, EVA spread, residual income (abnormal earnings), and EVA momentum on the value-based metrics side. The equity analysis template shown herewith can be used to distinguish good companies (potential buy opportunities) from average to risky-troubled companies (potential sell or short sell opportuni- ties). The data inputs for the JLG Equity Analysis Template are drawn from a Value Line report.

We emphasize that the case study application is not meant to show that traditional metrics are better or worse than VBM, or that our stock recom- mendation is somehow better than that provided by Value Line. Rather, the goal of the case study application of Coca-Cola is to show that traditional and VBM analyses can in fact complement each other; noting that we give Coca-Cola a “Timeliness” rating of “2” and a “Safety” rating of unity. Based on the Value Line scaling of 1 to 5, these fundamental ratings rep- resent high expected performance over the next 6 to 12 months and low expected risk (from the date of the analysis). Incidentally, Value Line gave the soft-drink company a Timeliness rating of “3” for average expected per- formance over the forward 6 to 12 months with their highest safety rating as of the report date. With respect to these comparative ratings, we realize that past performance is no guarantee of future performance and that investors should seek professional advice when buying or selling securities.

KEY POINTS

■ Fundamentals and valuation metrics are used in traditional and value- based approaches to equity securities analysis.

■ In the traditional realm, growth rates, margins, return on equity, mul- tiples, and the fundamental stock return are at the heart of this well- known approach to company analysis.

■ The extended Dupont formula goes a long way in showing how the multiplicative combination of operating margins, asset turns, interest burden, tax burden and the equity multiplier (leverage) at the company

Equity Analysis Using Traditional and Value-Based Metrics 59

level can impact—either positively or negatively—the shareholders’ return on equity.

■ Valuation measures such as price-to-sales, price-to-earnings, and price- to-book ratios can be used by investors and analysts to assess whether a company’s internal growth opportunities are correctly priced in the marketplace.

■ If the fundamental stock return (which includes the sustainable growth rate as measured by times return on equity) falls short of the required return—equivalently if the fundamental stock return lies below the securities market line—then the stock appears to be overvalued. Conse- quently, the investor should consider selling or short selling the presum- ably mispriced shares. In theory, the firm’s common stock is priced “just right” when the fundamental stock return equals the investor’s required return. In turn, a potential buy opportunity is present when the FSR exceeds the required rate. We also examined the traditional (and value- based) role of corporate debt policy.

■ Investors and analysts must determine whether a seemingly favorable change in return on equity is due to changes in a firm’s real growth opportunities, or whether it is due to an illusionary benefit to share- holders resulting from a debt ratio that exceeds the presumed target or optimal level.

■ A value-based metric becomes a VBM when there is a direct recognition of and a formal link to the opportunity cost of capital (via WACC in the EVA formulation) or the investor’s required rate of return (via r in the residual income or abnormal earnings model).

■ In the VBM approach to company and securities analysis, a firm is not truly profitable unless its return on capital is higher than the cost of capital, including the direct cost of debt and the indirect cost of equity financing. Moreover, the VBM approach emphasizes the concept of wealth creators and wealth destroyers. In this approach, the investor or analyst focuses on the fundamental ability of a firm to create share- holder value.

■ EVA momentum is crucial in determining whether or not a company is pointing in the direction of wealth creation or wealth destruction.

■ On balance, VBM and traditional metrics can (and should) be com- bined in a way that provides investors and analysts with a diversity of equity analysis tools to identify potential buy and sell opportunities in the marketplace.

60 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

APPENDIX: CASE STUDY

Coca-Cola: Integrated Traditional and VBM Analyses In the appendix, we provide an integrated fundamental analysis of Coca- Cola Company (KO) using traditional and value-based metrics. Financial data for KO are drawn from the Value Line report shown in Exhibit 2.A1. An overall fundamental evaluation of the soft drink company is provided using the Timeliness (expected performance) and Safety (risk) rankings employed by Value Line. A Timeliness score of 1 means high expected stock performance, while a score of 5 means low expected stock performance over the next 6 to 12 months. A Safety score of 1 means high expected safety (low risk), while a score of 5 means low expected safety (high risk). A comparative rating using this system is also provided for a hypothetical analyst. The accompanying equity analysis of Coca-Cola is conducted using financial software developed by JLG Research and consists of three parts, shown in Exhibit 2.A2:

1. Evaluation of Expected Performance (timeliness) 2. Evaluation of Expected Risk (safety) 3. Equity Fundamental Summary and Rating

The usual caveat applies to the case study: Past performance is no guar- antee of future performance, and investors should seek professional and legal guidance when buying and selling securities.

Equity Analysis Using Traditional and Value-Based Metrics 61

EXHIBIT 2.A1 The Value Line Report

120 100 80 64 48

32 24 20 16 12

8

Percent shares traded

15 10 5

Target Price Range 2013 2014 2015

COCA-COLA NYSE-KO 53.24 15.9 17.521.0 1.03 3.4% TIMELINESS 3 Lowered 3/5/10 SAFETY 1 New 7/27/90 TECHNICAL 3 Lowered 5/28/10 BETA .60 (1.00 = Market)

2013-15 PROJECTIONS Ann’l Total

Price Gain Return High 105 (+95%) 21% Low 85 (+60%) 15% Insider Decisions

S O N D J F M A M to Buy 0 1 1 0 0 0 2 0 0 Options 0 0 0 3 0 0 0 0 1 to Sell 0 2 0 3 0 0 0 0 1 Institutional Decisions

3Q2009 4Q2009 1Q2010 to Buy 545 501 565 to Sell 612 647 601 Hld’s(000)150774914692431439743

High: 70.9 66.9 62.2 57.9 50.9 53.5 45.3 49.3 64.3 65.6 59.4 57.8 Low: 47.3 42.9 42.4 42.9 37.0 38.3 40.3 39.4 45.6 40.3 37.4 49.5

% TOT. RETURN 6/10 THIS VL ARITH. STOCK INDEX

1 yr. 7.8 29.6 3 yr. 4.9 -8.6 5 yr. 38.8 24.0

CAPITAL STRUCTURE as of 7/2/10 Total Debt $11709.0 mill. Due in 5 Yrs. $8616.0 LT Debt $4427.0 mill. Total Int. $265.0 mill. (Total interest coverage: 15x)

(15% of Cap’l)

Pension Assets-12/09 $3.03 bill. Oblig. $3.99 bill.

Pfd Stock None

Common Stock 2,307,050,619 shs. as of 4/26/10 MARKET CAP: $123 billion (Large Cap) CURRENT POSITION 2008 2009 7/2/10

($MILL.) Cash Assets 4979 9151 10099 Receivables 3090 3758 4001 Inventory (Avg Cst) 2187 2354 2363 Other 1920 2288 2111 Current Assets 12176 17551 18574 Accts Payable 6205 6657 6202 Debt Due 6531 6800 7282 Other 252 264 450 Current Liab. 12988 13721 13934 ANNUAL RATES Past Past Est’d ’07-’09 of change (per sh) 10 Yrs. 5 Yrs. to ’13-’15 Sales 5.5% 9.0% 5.5% ‘‘Cash Flow’’ 7.0% 8.5% 7.0% Earnings 7.0% 8.5% 8.0% Dividends 9.5% 11.0% 7.0% Book Value 11.0% 11.0% 12.5%

lluF-laC raeYradne

QUARTERLY SALES ($ mill.) Mar.Per Jun.Per Sep.Per Dec.Per

2007 6103 7733 7690 7331 28857 2008 7379 9046 8393 7126 31944 2009 7169 8267 8044 7510 30990 2010 7525 8674 8460 7716 32375 2011 7925 9500 10000 9075 36500

lluF-laC raeYradne

EARNINGS PER SHARE A Mar.Per Jun.Per Sep.Per Dec.Per

2007 .54 .80 .71 .52 2.57 2008 .64 .98 .81 .59 3.02 2009 .58 .88 .81 .66 2.93 2010 .69 1.02 .90 .74 3.35 2011 .76 1.10 .99 .85 3.70

lluF-laC raeYradne

QUARTERLY DIVIDENDS PAID B ■ Mar.31 Jun.30 Sep.30 Dec.31

2006 - - .31 .31 .62 1.24 2007 - - .34 .34 .68 1.36 2008 - - .38 .38 .76 1.52 2009 - - .41 .41 .82 1.64 2010 - - .44 .44

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003E 2004 2005 2006 2007 6.34 7.19 7.48 7.64 7.63 8.01 8.23 7.06 7.92 8.62 9.12 9.75 10.39 12.45 1.16 1.37 1.60 1.92 1.69 1.63 1.79 1.92 1.99 2.31 2.45 2.59 2.81 3.08 .99 1.19 1.40 1.64 1.42 1.30 1.48 1.60 1.65 1.95 2.06 2.17 2.37 2.57 .39 .44 .50 .56 .60 .64 .68 .72 .80 .88 1.00 1.12 1.24 1.36 .34 .37 .40 .44 .35 .43 .30 .31 .34 .33 .31 .38 .61 .71

2.05 2.15 2.48 2.96 3.41 3.85 3.75 4.57 4.78 5.77 6.61 6.90 7.30 9.38 2551.9 2504.6 2481.0 2470.6 2465.5 2471.6 2484.8 2486.2 2471.0 2441.5 2409.3 2369.0 2318.0 2318.0

22.5 26.8 32.8 38.1 NMF 47.5 37.5 30.5 30.2 22.6 22.6 19.7 18.5 21.0 1.48 1.79 2.05 2.20 NMF 2.71 2.44 1.56 1.65 1.29 1.19 1.05 1.00 1.11

1.7% 1.4% 1.1% .9% .8% 1.0% 1.2% 1.5% 1.6% 2.0% 2.2% 2.6% 2.8% 2.5% 20458 17545 19564 21044 21962 23104 24088 28857 28.9% 35.1% 32.0% 31.6% 32.2% 30.8% 31.3% 30.0% 773.0 803.0 806.0 850.0 893.0 932.0 938.0 1163.0

3669.0 3979.0 4100.0 4790.0 5014.0 5196.0 5568.0 5981.0 27.1% 29.8% 27.0% 21.1% 24.5% 23.5% 22.4% 24.0% 17.9% 22.7% 21.0% 22.8% 22.8% 22.5% 23.1% 20.7% d2701 d1258 11.0 510.0 1123.0 414.0 d449.0 d1120 835.0 1219.0 2701.0 2517.0 1157.0 1154.0 1314.0 3277.0

9316.0 11366 11800 14090 15935 16355 16920 21744 36.4% 31.9% 28.8% 29.2% 29.5% 29.8% 30.7% 24.2% 39.4% 35.0% 34.7% 34.0% 31.5% 31.8% 32.9% 27.5% 21.3% 19.3% 17.9% 18.6% 16.2% 15.4% 15.7% 13.0%

46% 45% 48% 45% 48% 52% 52% 53%

2008 2009 2010 2011 © VALUE LINE PUB., INC. 13-15 13.82 13.46 14.00 15.85 Sales per sh 18.50 3.58 3.55 3.90 4.30 ‘‘Cash Flow’’ per sh 5.10 3.02 2.93 3.35 3.70 Earnings per sh A 4.50 1.52 1.64 1.76 1.88 Div’ds Decl’d per sh B■ 2.24

.85 .87 .85 .90 Cap’l Spending per sh 1.00 8.85 10.77 12.50 14.20 Book Value per sh C 19.80

2312.0 2303.0 2310 2305 Common Shs Outst’g D 2285 17.8 16.3 Bold figures are

Value Line estimates

Avg Ann’l P/E Ratio 21.0 1.07 1.09 Relative P/E Ratio 1.40

2.8% 3.4% Avg Ann’l Div’d Yield 2.4% 31944 30990 32375 36500 Sales ($mill) 42275 30.3% 30.7% 36.0% 35.0% Operating Margin 37.0% 1228.0 1236.0 1240 1250 Depreciation ($mill) 1275 7050.0 6940.0 7825 8625 Net Profit ($mill) 10400 22.2% 22.7% 23.5% 24.0% Income Tax Rate 25.0% 22.1% 22.4% 24.2% 23.6% Net Profit Margin 24.6% d812.0 3830.0 4000 4000 Working Cap’l ($mill) 5000 2781.0 5059.0 5000 4800 Long-Term Debt ($mill) 3500 20472 24799 28900 32800 Shr. Equity ($mill) 45200 30.6% 23.8% 23.5% 23.0% Return on Total Cap’l 21.5% 34.4% 28.0% 27.0% 26.0% Return on Shr. Equity 23.0% 17.2% 12.7% 13.0% 13.0% Retained to Com Eq 11.5%

50% 55% 52% 50% All Div’ds to Net Prof 49%

Company’s Financial Strength A++ Stock’s Price Stability 100 Price Growth Persistence 30 Earnings Predictability 100

(A) Based on primary shs. through ’96, diluted shs. thereafter. Next earnings report due late October. Excls. nonrec. losses: ’99, (32¢); ’00, (60¢); ’01, (2¢); ’02, (43¢); ’03, (18¢); ’04, (6¢);

’05, (13¢); ’06, (21¢) ’08 (53¢). (B) Div’ds historically paid about April 1, July 1, Oct. 1, Dec.1. ■ Div’d reinvestment plan avail. (C) Incl. intangibles. In ’09: $12.8 bill.,

$5.55/sh. (D) In millions. (E) Reflects reclas- sification of sales and expenses.

BUSINESS: The Coca-Cola Company is the world’s largest beverage company. It distributes major brands (Coca-Cola, diet Coke, Sprite, Barq’s, Mr. Pibb Xtra, Fanta, Fresca, Dasani, Evian, Full Throttle, Powerade, Minute Maid, and others) through bottlers around the world. Business outside North America accounted for 74% of net sales in 2009. 2009 depreciation rate: 3.9%. Coca-Cola

Enterprises (CCE) is a 36%-owned soft drink bottler. Advertising expenses, 9.0% of revenues. Has approximately 92,800 employ- ees; Directors and Officers as a group own 5.4% of stock (3/10 Proxy). Chairman and C.E.O. Muhtar Kent. Incorporated: Delaware. Address: One Coca-Cola Plaza, Atlanta, Georgia 30313. Tele- phone: 404-676-2121. Internet: www.coca-cola.com.

Business at The Coca-Cola Company is improving. The beverage behemoth realized top- and bottom-line advances of 5% and 16%, compared to last year’s sec- ond quarter. And we expect full-year sales to advance about 4.5%. The top line ought to stage a recovery, since the economy seems to be on the mend. Although con- sumer spending remains restrained, a more favorable pricing and product mix, and better consumer confidence, should bolster top- line results moving forward. Earnings are set to progress at a faster pace. We expect KO to earn around $3.35 a share this year, represent- ing an increase of some 14% from last year’s tally, with another double-digit ad- vance likely in 2011. An important factor affecting growth is KO’s embarking on several efficiency initiatives at the onset of the recent recession. Perhaps the most sig- nificant shift in operations has been its move to acquire the North American oper- ations of its largest bottler, Coca-Cola En- terprises. Although we have not yet in- corporated this event into our estimates (Value Line policy does not include acquisi- tion figures until a deal is finalized) , the

purchase has significant cost savings potential for The Coca-Cola Company. And KO has not ruled out more small bolt-on acquisitions of other bottlers, as a means of dealing with a challenging operating landscape. Furthermore, hedging policies will likely remain intact. The company has other expansion av- enues. It recently augmented its still- drink lineup with the introduction of Vitaminwater Zero and the relaunch of Dasani flavored waters. As well, energy drinks are now included in its sparkling lineup. These drinks are gaining promi- nence, and KO’s distribution partnership with Hansen Natural to distribute the lat- ter company’s popular Monster energy drink is positive. Too, KO is focused on ge- ographic expansion, especially in emerging markets, like India and China. This neutrally ranked stock may pi- que long-term investors’ interest. Without considering the pending merger, the company still has decent appreciation potential for the 2013-2015 time frame. And a nice dividend payout sweetens in- centives further. Nira Maharaj July 30, 2010

LEGENDS 18.0 x ″Cash Flow″ p sh. . . . Relative Price Strength

Options: Yes Shaded area: prior recession Latest recession began 12/07

© 2010, Value Line Publishing, Inc. All rights reserved. Factual material is obtained from sources believed to be reliable and is provided without warranties of any kind. THE PUBLISHER IS NOT RESPONSIBLE FOR ANY ERRORS OR OMISSIONS HEREIN. This publication is strictly for subscriber’s own, non-commercial, internal use. No part of it may be reproduced, resold, stored or transmitted in any printed, electronic or other form, or used for generating or marketing any printed or electronic publication, service or product.

To subscribe call 1-800-833-0046.

RECENT PRICE

P/E RATIO

RELATIVE P/E RATIO

DIV’D YLD( )Trailing:Median: VALUELINE

Source: Value Line Investment Survey, New York, NY. Reprinted with permission.

62 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 2.A2 JLG Equity Analysis Template*

JLG EQUITY ANALYSIS TEMPLATE

(Note disclaimer)

Description:

This template allows the user to conduct an integrated traditional and value- based metrics analysis of a company and its stock. The equity analysis goal is to rate the company on the basis of expected performance (timeliness) and expected risk (safety); Next, 6 to 12 months, score “1-to-5” each measure. Traditional measures of success and valuation include growth rates, margins, ROE and Du- pont, multiples, PEG, and the fundamental stock return (FSR). Value-based mea- sures include residual income (abnormal earnings), Economic Value Added (1), EVA spread, EVA Dupont, and EVA momentum. Equity risk measures include beta (macro risk), capital structure (leverage), and earnings consistency/predict- ability. Coded fields are shaded; open fields require user input.

FOCUS:

Part I: Evaluation of Expected Performance (timeliness), including:

Traditional metrics: growth rates, profit margins, multiples, 5-factor ROE Dupont analysis, and fundamental stock return.

Value-based metrics: Abnormal earnings (residual income), economic value added (EVA), ROC Dupont, and EVA momentum.

Part II: Evaluation of Expected Risk (safety), including:

Beta (macro risk), price growth persistence, earnings predictability, and capital structure.

Part III: Equity Fundamental Summary, including:

User assigned stock rating.

Comments:

USER NAME: Jane/Joe Analyst User Name

Research Date 10/1/2010 User choice

Company: COCA-COLA User choice

Ticker KO Input ticker symbol

Data Source: Value Line VL or other data source

Date of source report 7/30/2010 Input report date

Ratings: Timeliness Safety

Value Line (or other source) 3 1

Jane/Joe Analyst 2 2

*The equity analysis template applied herewith is a financial product of JLG Research. All rights reserved worldwide. For more information, see www.jlgresearch.com.

Equity Analysis Using Traditional and Value-Based Metrics 63

EXHIBIT 2.A2 (Continued)

PART I: Evaluation of Expected Performance (timeliness)

TRADITIONAL METRICS:

A. Expected Growth Rates

Enter Year:

One-Step Ahead

Year 2010 2011 2014

Year relative 0 1 4

Revenue/share 14.00 15.85 18.5

Cash flow/share 3.90 4.30 5.1

EPS 3.35 3.70 4.50

DPS 1.76 1.88 2.24

CapX/sh 0.85 0.90 1

2010 2011 2014

Rev growth 0.1321 0.0529

CF growth 0.1026 0.0585

EPS growth 0.1045 0.0674

DPS growth 0.0682 0.0601

CapX/sh growth 0.0588 0.0357

Compare prospective growth rates over time/industry/competitor

B. Multiples and PEG

Stock Price (at date of analysis): 53.24 Input Stock Price

2010 2011 2014

Price-to-revenue ratio 3.803 3.359 2.878

Price-to-cash flow ratio 13.651 12.381 10.439

Price-to-earnings ratio 15.893 14.38919 11.831

PEG ratio 1.377 1.755

(P/E-to-EPS growth rate) Compare PEG to comparable company or industry benchmark

64 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 2.A2 (Continued)

C. Projected ROE 2011

Basic Definition:

Net profit (NP) 8625 Input “Net Profit”

Equity 32800 Input “Shareholders’ Equity”

ROE (Net profit/Equity) 0.263

Dupont Analysis: 2011

ROE = ROA × A/E = NPM × AT × EM

Net profit 8625

Assets (= CL + LTD + Equity) 51534 Input “Assets”

ROA (NP/Assets) 0.167

Equity multiplier (Assets/Equity) 1.571

ROE 0.263

Net profit 8625

Sales (S) 36500 Input “Sales (revenue)”

Net profit margin (NP/S) 0.236

Asset turnover (S/A) 0.708

EM (A/E) 1.571

ROE 0.263

ROE: 5-Factor Dupont:

ROE = Tax burden × Interest burden × OPM × AT × EM

Reported income tax 0.24 Input “Income Tax Rate”

Pretax profit [NP/(1 – t)] 11348.68

EBIT (from below) 11525.0

Tax burden [NI/PBT= (1 – t)] 0.76

Interest burdena [PBT/EBIT] 0.98

OPM [EBIT/Sales] 0.316

Asset turnover 0.708

Equity multiplier 1.571

ROE: 5-factor Dupont 0.263

aInterest burden net of nonoperating income/expense items.

Equity Analysis Using Traditional and Value-Based Metrics 65

EXHIBIT 2.A2 (Continued)

D. Fundamental Stock Return 2011

FSR = DY + PBR × ROE

Dividend yield (DPS/stock price) 0.035

Dividend payout ratio (DPS/EPS) 0.508

PRB (plowback ratio) 0.492

FSR 0.1647

CAPM 0.08 See WACC calculation (below)

FSR spread 0.0847

FSR > CAPM (?) Yes Good company if positive

Stock plots above Securities Market Line (SML)

VALUE-BASED METRICS: Residual Income and EVA

A. Residual Income (abnormal earnings)

RI = Net Income – $Cost of Equity = RI Spread × Equity

ROE 0.263

Required return (CAPM, etc.) 0.08

Residual income spread 0.1830 Good company if positive

Residual income (RI) 6001 Good company if positive

RI spread × Equity Since ROE exceeds investor’s required return

EVA = NOPAT – $WACC

B. Estimating NOPAT (basic)

NOPAT = EBIT × (1 – T) = [S – COGS – SGA – Depr] × (1 – t) = [S × OM-Depr] × (1 – t)

where: OM = EBITD/Sales

Year 2011

Sales 36500

Operating margin (EBITD/Sales) 0.35 OM = (Sales – COGS – SGA)/Sales

EBITD 12775

Depreciation 1250

EBIT 11525

Tax rate 0.35 Unlevered tax rate

NOPAT 7491

66 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 2.A2 (Continued)

C. Estimating $WACC (dollar cost of capital)

Note: $WACC = WACC × Capital and

WACC = wd × AT debt cost + we × Cost of equity WACC = wd × Pretax debt cost × (1 – t) + we × CAPM

Debt Cost:

Pretax debt cost = Interest/LT debt

(Assumes bonds trading at “par”)

$Interest 265

LT debt 4427

Pretax debt cost (5% default) 0.0599

AT debt cost = Pretax × (1 – t)

0.0389

Equity Cost:

CAPM = RF + Beta × ERP

RF 0.0500 5-year Treasury

MRP 0.0500 Average market premium

Beta 0.6

CAPM 0.08

EVA Capital:

C = NWC + NPPE (assets approach) C = Debt + Equity (financing approach) (Can use EOY, BOY or average capital)

Year 2011

LT debt 11709 Est. debt on balance sheet

Equity 32800

Capital 44509

WACC = wd × AT debt cost + we × CAPM

Debt wgt. 0.26307 Debt/Capital ratio

Equity wgt. 0.73693

WACC 0.0692 Weighted average cost of debt and equity

$Capital cost = WACC × TC 3080

Equity Analysis Using Traditional and Value-Based Metrics 67

EXHIBIT 2.A2 (Continued)

D. EVA and EVA Spread

Year 2011

EVA = NOPAT – $WACC 4412 Wealth creator if positive

Return on capital (ROC) 0.1683 ROC = NOPAT/Capital

WACC 0.0692 Cost of capital

EVA spread 0.0991

E. EVA Dupont: Breakdown of ROC

ROC = NOPAT/C = NOPAT margin × Capital turnover

NOPAT 7491

Sales 36500

NOPAT margin 0.2052

Capital 44509

Capital turnover ratio 0.8201

ROC 0.1683

F. EVA Momentum (determination of good/bad company growth)

Delta EVA = EVA Spread × Delta CapX

EVA spread 0.0991

CapX growth

Year 2010 2011 2014

Year relative 0 1 4

CapX/Share 0.85 0.9 1

Shares 2310 2305 2285

Gross CapX 1963.5 2074.5 2285

Depreciation 1240 1250 1275

Net CapX 723.5 824.5 1010

Net CapX $ growth 101 186

Net CapX growth 0.1396 0.0700

(Annualized rate)

68 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 2.A2 (Continued)

EVA Momentum (in $): 10.0110 18.3865

[EVA spread × Net CapX $ growth] Good company growth if EVA momentum > 0 Growth creates shareholder value (or positive restructure)

PART II: Evaluation of Expected Risk (safety)

Beta 0.6 Measures macro risk (Beta < 1 = Good)

Price growth persistence % (Enter value)

30 Measures consistency in price growth (Scale 0 to 100; High = Good)

Earnings predict % (Enter value)

100 Measures earnings consistency (High = Good)

Capital structure % (LT debt/Capital)

26.31% Measures sebt capacity (Low = Good: scale of 0% to 100%)

Part III: Equity Fundamental Summary and Rating

Date: 10/1/2010

Company COCA-COLA

Ticker KO

Fundamentals: Risk:

(Traditional/VBM) (Macro/Company specific)

Growth rates (excluding CapX) Good Beta (macro risk) Good User assigned (good, mixed, poor)

FSR vs. CAPM Good Stock price growth Poor User assigned

EVA Good Earnings predictability Good User assigned

EVA & RI spread Good Capital structure Good User assigned

Net CapX growth Mixed Company’s financial strength

Good User assigned

Source: “Timeliness” “Safety”

Value Line 3 1

Analyst Rating: 2 2 User assigned (Scale of 1 to 5): Ratings = (5 – Number of

“good” + 1) for Number of “good” ≥ 1

Rating = 5 if number of “good” = 0

Disclaimer: JLG Research Templates are not provided to users with the intent of providing investment advice. Past performance is no guarantee of future performance. EVA® is a registered trademark of Stern Stewart & Co.

Equity Analysis Using Traditional and Value-Based Metrics 69

QUESTIONS

Use the Value Line report for IBM dated October 8, 2010, reproduced on the following page, to answer the questions regarding a traditional and value- based metrics analysis of this computers and peripherals company:

1. What are the estimated annualized growth rates in revenue, cash flow, and earnings per share for IBM over the period 2011 to 2014? Are these rates favorable or unfavorable?

2. What is the estimated ROE for IBM for 2011? Conduct a five-factor ROE Dupont analysis in answering this question. Is the estimated ROE for IBM attractive or unattractive?

3. What is the fundamental stock return for IBM for 2011? Does IBM plot above or below the Securities Market Line? Assume a risk-free rate of 5% and a market risk premium of 5% in answering this question.

4. What is estimated NOPAT, $WACC, and EVA of IBM for 2011? Based on the estimated EVA (economic value added), is IBM a potential wealth creator or wealth waster?

5. What is the prospective EVA style quadrant of IBM for 2011? Interpret the meaning of this quadrant.

6. Based on an integrated analysis of traditional and value-based metrics, do you agree with the Value Line ratings of Timeliness and Safety for IBM? Be sure to assign your own stock ratings and explain whether you think IBM is a potential buy or sell opportunity.

70 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

320

200 160 120 100 80 60

40

18 Percent shares traded

21 14 7

Target Price Range 2013 2014 2015

INT’L BUS. MACH. NYSE-IBM 134.89 11.7 12.817.0 0.76 2.0% TIMELINESS 2 Raised 7/16/10 SAFETY 1 Raised 4/15/05 TECHNICAL 3 Raised 1/1/10 BETA .85 (1.00 = Market)

2013-15 PROJECTIONS Ann’l Total

Price Gain Return High 240 (+80%) 17% Low 195 (+45%) 11% Insider Decisions

N D J F M A M J J to Buy 0 0 0 0 0 0 0 0 0 Options 6 0 0 3 0 2 4 0 1 to Sell 6 0 1 5 0 3 9 0 1 Institutional Decisions

4Q2009 1Q2010 2Q2010 to Buy 639 607 638 to Sell 762 760 728 Hld’s(000) 789371 752705 746912

High: 139.2 134.9 124.7 126.4 94.5 100.4 99.1 97.9 121.5 130.9 132.9 135.1 Low: 80.9 80.1 83.8 54.0 73.2 81.9 71.9 72.7 88.8 69.5 81.8 116.0

% TOT. RETURN 8/10 THIS VL ARITH. STOCK INDEX

1 yr. 6.3 11.1 3 yr. 11.5 -3.7 5 yr. 65.7 19.4

CAPITAL STRUCTURE as of 6/30/10

Total Debt $26650 mill. Due in 5 Yrs $16511 mill. LT Debt $21017 mill. LT Interest $1050 mill. (LT interest earned: 17.9x; total interest coverage:

)l’paCfo%05()x4.71

Leases, Uncapitalized Annual rentals $1625 mill. Pension Assets-12/09 $81.7 bill. Oblig. $95.5 bill. Pfd Stock None Common Stock 1,261,278,072 shs.

MARKET CAP $170 billion (Large Cap) CURRENT POSITION 2008 2009 6/30/10

($MILL.) Cash Assets 12907 13974 12241 Receivables 27555 26793 23492 Inventory (Avg Cst) 2701 2494 2595 Other 5841 5674 6567 Current Assets 49004 48935 44895 Accts Payable 7014 7436 7233 Debt Due 11237 4168 5633 Other 24184 24398 22127 Current Liab. 42435 36002 34993 ANNUAL RATES Past Past Est’d ’07-’09 of change (per sh) 10 Yrs. 5 Yrs. to ’13-’15 Revenues 5.0% 7.0% 6.5% ‘‘Cash Flow’’ 7.0% 12.0% 10.5% Earnings 10.0% 14.5% 13.0% Dividends 15.5% 23.5% 11.5% Book Value 4.0% - - 22.0%

lluF-laC raeYradne

QUARTERLY REVENUES ($ mill.) Mar.31 Jun.30 Sep.30 Dec.31

2007 22029 23772 24119 28866 98786 2008 24502 26820 25302 27006 103630 2009 21711 23250 23566 27231 95758 2010 22857 23724 24200 27819 98600 2011 23400 24400 25000 28700 101500

lluF-laC raeYradne

EARNINGS PER SHARE A Mar.31 Jun.30 Sep.30 Dec.31

2007 1.21 1.55 1.68 2.80 7.18 2008 1.65 1.98 2.05 3.28 8.93 2009 1.70 2.32 2.40 3.59 10.01 2010 1.97 2.61 2.75 3.92 11.25 2011 2.25 2.90 3.05 4.20 12.40

lluF-laC raeYradne

QUARTERLY DIVIDENDS PAID B■ Mar.31 Jun.30 Sep.30 Dec.31

2006 .20 .30 .30 .30 1.10 2007 .30 .40 .40 .40 1.50 2008 .40 .50 .50 .50 1.90 2009 .50 .55 .55 .55 2.15 2010 .55 .65 .65

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 27.25 32.87 37.38 40.54 44.10 48.52 50.14 49.83 47.14 52.60 58.52 57.90 60.69 71.31 3.90 5.42 5.34 5.72 6.10 7.50 7.41 7.27 6.53 7.27 8.24 8.71 9.56 11.28 1.23 2.76 2.76 3.01 3.29 3.72 4.44 4.35 3.95 4.34 5.05 5.22 6.01 7.18 .25 .25 .33 .39 .44 .47 .51 .55 .59 .63 .70 .78 1.10 1.50

1.31 2.17 2.90 3.51 3.52 3.30 3.19 3.28 2.76 2.59 2.65 2.44 2.90 3.34 9.50 10.13 10.52 10.10 10.36 11.23 11.56 13.70 13.23 16.44 18.08 21.03 18.92 20.55

2350.8 2188.9 2031.9 1936.5 1851.8 1804.2 1762.9 1723.2 1722.4 1694.5 1645.6 1574.0 1506.5 1385.2 12.8 8.3 10.7 15.1 19.0 28.9 24.8 24.7 21.4 19.6 18.0 16.1 13.9 14.8 .84 .56 .67 .87 .99 1.65 1.61 1.27 1.17 1.12 .95 .86 .75 .79

1.6% 1.1% 1.1% .9% .7% .4% .5% .5% .7% .7% .8% .9% 1.3% 1.4% 88396 85866 81186 89131 96293 91134 91424 98786 19.6% 16.4% 18.0% 16.6% 16.8% 16.0% 19.3% 20.7% 4995.0 4820.0 4379.0 4701.0 4915.0 5188.0 4983.0 5201.0 8093.0 7723.0 6868.0 7613.0 8643.0 8519.0 9416.0 10418 29.8% 29.5% 30.3% 30.0% 30.0% 30.3% 29.3% 28.1%

9.2% 9.0% 8.5% 8.5% 9.0% 9.3% 10.3% 10.5% 7474.0 7342.0 7102.0 7098.0 7172.0 10509 4569.0 8867.0 18371 15963 19986 16986 14828 15425 13780 23039 20624 23614 22782 27864 29747 33098 28506 28470 22.0% 20.5% 16.7% 17.5% 19.9% 18.3% 23.1% 21.3% 39.2% 32.7% 30.1% 27.3% 29.1% 25.7% 33.0% 36.6% 35.2% 28.6% 25.7% 23.4% 25.1% 22.0% 27.1% 29.1%

11% 13% 15% 14% 14% 15% 18% 21%

2008 2009 2010 2011 © VALUE LINE PUB., INC. 13-15 77.39 73.36 79.50 84.60 Revenues per sh 106.80 13.28 14.11 15.60 16.95 ‘‘Cash Flow’’ per sh 23.40 8.93 10.01 11.25 12.40 Earnings per sh A 18.00 1.90 2.15 2.50 2.75 Div’ds Decl’d per sh B ■ 3.60 3.11 2.64 3.00 3.50 Cap’l Spending per sh 4.75

10.06 17.43 20.55 27.10 Book Value per sh D 52.10 1339.1 1305.3 1240.0 1200.0 Common Shs Outst’g C 1100.0

12.3 10.9 Bold figures are Value Line estimates

Avg Ann’l P/E Ratio 12.0 .74 .72 Relative P/E Ratio .80

1.7% 2.0% Avg Ann’l Div’d Yield 1.7% 103630 95758 98600 101500 Revenues ($mill) 117500 20.6% 23.0% 23.0% 24.0% Operating Margin 26.5% 5450.0 4994.0 4825 4800 Depreciation ($mill) 5500 12334 13425 14525 15550 Net Profit ($mill) 20250 26.2% 26.0% 26.0% 26.0% Income Tax Rate 26.0% 11.9% 14.0% 14.7% 15.3% Net Profit Margin 17.2% 6569.0 12933 10000 10000 Working Cap’l ($mill) 15000 22689 21932 21000 20000 Long-Term Debt ($mill) 15000 13465 22755 25500 32500 Shr. Equity ($mill) 57300 35.6% 31.2% 32.5% 30.5% Return on Total Cap’l 28.5% 91.6% 59.0% 57.0% 48.0% Return on Shr. Equity 35.5% 72.4% 46.4% 44.5% 37.5% Retained to Com Eq 28.5%

21% 21% 22% 22% All Div’ds to Net Prof 20%

Company’s Financial Strength A++ Stock’s Price Stability 95 Price Growth Persistence 40 Earnings Predictability 100

(A) Based on average shares until ’97, then diluted. Excludes nonrecurring gains (losses): ’94, 2¢; ’95, (94¢); ’96, (20¢); ’99, 40¢; ’02, ($1.89); ’04, (11¢); ’05, (34¢); gain (losses)

from discontinued operations; ’03, (2¢), ’04, (1¢); ’05, (2¢); ’06, 5¢. Quarters may not sum due to change in shares. Next earnings report late Oct. (B) Dividends historically paid in early

March, June, September, and December. ■Dividend reinvestment plan available. (C) In mill., adjusted for splits. (D) Includes in- tangibles. In ’09, $22.7 bill., $17.39 a share.

BUSINESS: International Business Machines Corporation is a worldwide supplier of advanced information processing technology, communication systems, services, and program products. 2009 rev- enue breakdown: Global Technology Services, 39%; Global Busi- ness Services, 19%; Systems and Technology, 17%; Software, 22%; Global Financing, 2%; Other, 1%. Foreign business: 64% of

2009 revenues. Research, development, and engineering costs, 6.1%. ’09 depreciation rate: 12.6%. Has 399,409 employees. Of- ficers & directors control less than 1% of stock; BlackRock, 5.57%; State Street, 5.2% (3/10 proxy). Chairman, President, and CEO: Samuel J. Palmisano. Inc.: NY. Add.: New Orchard Road, Armonk, NY 10504. Tele.: 914-499-1900. Internet: www.ibm.com.

The June quarter was IBM’s 30th con- secutive period of higher year-to-year earnings. Consolidated revenue rose 2%, but would have increased 3% if not for a divestiture of a software business at the end of March. (Software revenues, up 2%, would have risen 6%.) Revenues in the U.S. grew for the first time in seven quarters, and emerging markets were strong. Margins in the business services and software operations expanded. Sys- tems & Technology (hardware) margins contracted due to an unfavorable revenue mix and new product costs. Selling ex- penses declined. Other income/expense im- proved in the absence of a $120 million charge for a joint venture taken in the comparable period of 2009. The tax rate fell slightly. Stock repurchases boosted share net, which rose 13%, despite an es- timated $0.10-$0.11 drag from currency translation and hedging activity. The company has raised its full-year 2010 earnings outlook a nickel, to at least $11.25 a share, and we look for re- sults to advance at a double-digit clip in 2011. IBM may encounter occasional chal- lenges in public sector markets stateside

and in Europe. Still, increased new out- sourcing business signings in the June quarter augur well for services revenue, and the workforce rebalancing initiative in the March quarter should support a better technology services margin over the rest of 2010. In software products, IBM expects the good June-period top-line momentum to continue. And systems revenues and profits ought to benefit from new System z servers and POWER7 entry- and high-end systems introduced in September. Finances are healthy. All but $5.5 bil- lion of IBM’s debt supports its financing business. The nonfinancing debt-to-capital ratio at mid-2010 was only 23%, and IBM had over $12 billion of cash on the balance sheet. High-quality, timely IBM shares are a solid selection for total return poten- tial to 2013-2015. The company’s goal is to earn $20 a share by 2015, aided by an- nual revenue growth of 5%, better operat- ing leverage, and stock repurchases. Even based on our somewhat less ambitious projections, the issue should prove a mod- erately rewarding long-term investment. Theresa Brophy October 8, 2010

LEGENDS 9.0 x ″Cash Flow″ p sh. . . . Relative Price Strength

2-for-1 split 5/97 2-for-1 split 5/99 Options: Yes Shaded areas indicate recessions

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71

CHAPTER 3 A Franchise Factor Approach

to Modeling P/E Orbits Stanley Kogelman, Ph.D.

President and Founder Delft Strategic Advisors, LLC

Martin L. Leibowitz, Ph.D. Managing Director

Morgan Stanley & Co.

The standard dividend discount model (DDM) is still a commonly used equity valuation model. The DDM has the advantage of simplicity, intui- tive appeal and broad generality, but these advantages often mute or disguise the extreme variations in growth expectations, return on equity and sustain- able earnings that dramatically change valuations and move markets.1

The DDM provided the starting point for the development of the fran- chise factor model (FFM) that is the subject of this chapter. This model is based on a body of work that began as a series of papers that later were consolidated into two books on franchise value.2

In contrast to the DDM, the FFM provides a window through which we can peer more deeply into how variations in equity prices of companies or markets reflects the interplay between (1) optimistic and pessimistic growth projections, (2) return expectations on existing and potential businesses, and (3) long-term stable earnings. We find that competitive market forces,

1For further discussion see Zvi Bodie, Alex Kane, and Alan Marcus, Investments (New York: McGraw-Hill/Irwin, 2010) and Myron J. Gordon, The Investment Financing and Valuation of the Corporation (Homewood, IL: Richard D. Irwin, 1962). 2Martin L. Leibowitz and Stanley Kogelman, Franchise Value and the Price/Earnings Ratio (Charlottesville, VA: The Research Foundation of Chartered Financial Analysts, 1994); and Martin L. Leibowitz, Franchise Value: A Modern Approach to Security Analysis (Hoboken, NJ: John Wiley & Sons, 2004).

72 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

like magnetic attractors, tend to drive the P/Es of even the most outstanding companies toward equilibrium levels that fall well below current P/Es.

For the FFM, as with all models, the mathematics may be correct but the underlying assumptions will drive the results. When a model yields extremely optimistic price projections, you must look beneath the sur- face and evaluate the embedded underlying assumptions. In the DDM, for example, you typically find that continuous profitable growth is taken as a given, without any deeper examination of the fundamental sources of return or of the competitive forces that will, over time, likely drive P/Es toward lower equilibrium levels. When all visible future earnings are embedded in a model estimate, you should expect the firm’s growth prospects and P/E ratio to gradually decline as prospective investments are executed and the firm’s franchise is successfully consumed.

To mitigate this decline, firm management must uncover new, previously unknown and unanticipated investment opportunities of ever-increasing size. A $1 million investment is significant for a $1 million firm but, when that firm grows to a $10 billion firm, a $1 million investment becomes rather insignificant. To maintain a high P/E, a firm must continually reinvent itself by creating new products and identifying additional markets for both new and existing products. In a global market, the truly scarce resource will be the franchise opportunities themselves, not the capital required to exploit them. A firm will always be able to access funding needed to develop demon- strably productive opportunities through public and/or private markets.

Whenever the FFM leads to intrinsic value estimates that differ signif- icantly from a security’s market price, the model assumptions should be questioned first. If underlying flaws in the assumptions are uncovered, the assumptions should be adjusted to better reflect reality. Then the FFM-based P/E should be recalculated. If under a wide range of scenarios, the model results are stable, the model may be providing an important reality check relative to current valuations. This reality check is especially important when distinguishing between hyper-franchise firms with exceptional fran- chise value and growth prospects and anti-franchise firms with very limited growth prospects and negative franchise value.

BACKGROUND

At the heart of the FFM is the separation of firm value into two distinct parts: tangible value (TV) and franchise value (FV). Each of these value components separately contributes to the P/E. TV can be reasonably esti- mated because it reflects current businesses that produce steady earnings streams. From a valuation perspective, the TV makes a more predictable

Use of Options in Portfolio Management 73

contribution to the firm’s price-to-earnings ratio (P/E) than does the FV. The P/E contribution, P/ETV, will be somewhat sensitive to inflation, to interest rates and to the equity market risk premium. Since these factors typically change more slowly than estimates of future opportunities, P/ETV is rela- tively stable.

The total P/E is the sum of P/ETV and P/EFV. FV is dramatically differ- ent than TV and much more difficult to estimate accurately. This difficulty is related to the futuristic nature of FV. FV reflects businesses that a firm is expected to create at some (possibly indeterminate) point in the future by means of new, yet to be realized, investments. As investors, market analysts and corporate executives polish their crystal balls and peer into the future, their projections of a firm’s growth opportunities will continually change along with estimates of FV.

Because of their prospective nature, FV estimates are more vulnerable to sudden changes in markets and in the global economy than TV estimates. Such changes can work in either a positive or negative direction. Long-term projections can just as easily under-estimate as overestimate future projects. As time passes and the fog of uncertainty clears, new markets may develop that earlier were inconceivable. Similarly, some perceived robust opportuni- ties later may turn out to barely exist. Other previously anticipated projects, with uncertain prospects, may have a clearly improved likelihood of success and therefore make a more positive contribution to FV—or vice versa. In summary, P/E

FV inevitably will undergo more frequent and more dramatic

changes than P/E TV

. In our FFM, future investments that provide a return in excess of the

cost of capital add to FV. Firms with global brands, unique products, and/ or substantial pricing power may even possess a hyper-franchise that, for long periods, enables them repeatedly to uncover significant new investment opportunities that provide returns that substantially exceed the cost of capi- tal. In this case, P/E

FV will make a more substantial contribution to the total

P/E than will P/E TV

. But, no franchise is unlimited and sooner or later P/E FV

will decline, leading to a corresponding decline in the total P/E.

At the other extreme, we find anti-franchise firms. Such firms may cur- rently hold earlier investments that have become losers from which they cannot easily extricate themselves. For example, an anti-franchise firm may have reached a point where it is challenged to find big, new, high-return investments. The firm’s CEO then may feel tempted to make new invest- ments (rather than return money to shareholders) even in the face of, at best, an only modest probability that those investments will provide a long-term return that exceeds the cost of capital.

In the language of the FFM, all new investments that return less than the cost of capital will make a negative contribution to FV. If the overall FV

74 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

is negative, the P/EFV will also be negative. Thus, a negative FV will drag the total P/E down to a level below P/ETV alone. In this respect, an anti-franchise firm is a value destroyer.

Some years ago, in a lunch conversation with Warren Buffett, Marty Leibowitz presented the anti-franchise concept. Buffett not only grasped the idea immediately, but provided an illustration of the concept in the form of story that Marty later used to open a keynote talk with a rather light touch:

A man came to the United States and became a successful business- man. One day, he received a letter from a long-lost cousin in the old country informing him that an equally long-lost uncle had just passed away. The letter went on to talk of the poverty back home and requested some help to give the uncle a decent burial. Our busi- nessman quickly complied and sent the requested funds along with a brief note of consolation. A few weeks later, he received a second letter explaining that the uncle didn’t have a suit to his name, and could some additional funds be sent over to cover the cost of a burial suit? Once again, a bit more warily, our businessman com- plied with this request, thinking that this should surely be the end of the saga. However, after a few weeks, a third letter came, again asking for more money to cover the expense of the suit. This time, our exasperated businessman, wondering why he should repeatedly pay for the same suit, dashed off an indignant response. Shortly thereafter, a reply came back from the cousin. It turns out that the suit they had used to bury the uncle was rented.

The moral of the story: Antifranchise firms throw good money after bad! Unfortunately, we do not have to look too hard to find examples of

anti-franchise firms. Such firms enthusiastically announce new projects with overstated forecasts and unrealizable returns. When anti-franchise firms seek earnings growth at any (capital) cost, they may be tempted to engage in imperialistic expansions that include overly optimistic acquisition pro- grams. Entrenched corporate executives may become wedded to pet projects while failing to jettison failing projects in a timely fashion.

Hyper- and antifranchise firms form the extremes between which most firms fall. A “typical” company is likely to take on a range of projects. Some projects will do very well while others, in hindsight, will turn out to be in error and yield poor results. Other projects will turn out to be value neutral, yielding returns that just equal the cost of capital. Value-neutral projects may create a positive cash flow and add to earnings, but their FV will be zero and such projects will not contribute to the firm’s P/E, regardless of how large they may be. Value-neutral projects are simply part of the stable P/ETV.

Use of Options in Portfolio Management 75

When firm value is primarily attributable to FV, as is the case for many growth firms, the more stable TV is a relatively small part of the firm’s overall valuation. In this case, the market valuation is likely to respond dramatically to changing market conditions and to any doubts about future investment opportunities. P/E volatility is further exacerbated for newer firms with a small earnings base. A small change in earnings estimates will lead to a substantial change in the ratio of price to earnings.

For more mature value firms, TV often far exceeds FV. In this case, the relative stability of TV brings with it a more stable P/E

TV and lower price

volatility.

HISTORICAL DATA OBSERVATIONS

Over the almost 25-year period from January 1, 1985, to June 30, 2010, an investment of $100 in the S&P 500 multiplied more than 11 times to $1,143, if no money was withdrawn and all dividends were reinvested. This growth represents a remarkable 10.0% annualized compound return over a period of dramatic market changes, upheavals and challenges.

The mid-1980s marked the beginning of an extraordinary bull market that accelerated through the Internet boom of the late 1990s. Prior to this time, value investing was viewed as the favored long-term strategy. But, during this period, value investing fell out of favor and growth dominated.

Between 2000 and 2002, the Internet bubble collapsed and the Septem- ber 11, 2001, attacks on the World Trade Center brought further market declines. The weak markets of the early 2000s were followed by a new bull market in which value investing moved back into favor. But, all gains were erased with the so-called Great Recession that began in 2007.

Exhibit 3.1 plots the growth paths of hypothetical $100 investments in the S&P 500 Index and in the Russell 1000 Value Index. In a more subtle way, these paths underscore the challenges inherent in market forecasting. On January 1, 1985, no market observer could possibly have foreseen the unfolding of events that would rock the market. For reference, the exhibit also includes a smooth 10% growth path with the same beginning point and approximately the same end point as the market investments. The mar- ket does not follow this path! Rather the market lunges forward, corrects, lunges forward and then corrects, over and over again.

Note the interlacing of the growth paths of broad U.S. market index and the value index. Each crossing represents a point at which the cumula- tive investment value to date produces precisely the same result. For exam- ple, during the late 1990s an initial investment in the S&P500 raced ahead of a similar investment in the Russell 1000 Value Index. But, by the end

76 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

of 2001 a crossing point occurred as a consequence of the sudden rapid fall in the broad market and the steady rise in value stocks. Starting in late 2002, value stocks grew faster than the broad market and collapsed more quickly during the Great Recession. Once again, there was a crossing of the cumulative value graphs. Relevant investment results were dependent on an investor’s ability to time the market, correctly switching between the broad market and value. But few if any investors have the forecasting skill required to consistently and accurately time markets. For truly long-term investors, the results of maintaining an investment in one index or the other were quite similar.

Rather than attempting to forecast the events that mark the beginning of major market corrections, we take a 60,000-foot view of both individual firms and broad regional markets. From this vantage point, we conceptualize market behavior as a reflection of a changing composite of views of inherent growth prospects. During periods of optimism and high expectations, it is hard to escape the feeling that companies have virtually unlimited opportuni- ties to make new, profitable investments. Companies viewed as “undervalued”

EXHIBIT 3.1 Growth of $100 Investment in S&P500 Index and Russell 1000 Value Index (including dividend reinvestment)

0

400

800

1,200

1,600

2,000

C um

ul at

iv e

V al

ue (

$)

Month End

S&P 500 Index

Russell 1000 Value Index

10% Growth

D ec

-8 4

D ec

-8 6

D ec

-8 8

D ec

-9 0

D ec

-9 2

D ec

-9 4

D ec

-9 6

D ec

-9 8

D ec

-0 0

D ec

-0 2

D ec

-0 4

D ec

-0 6

D ec

-0 8

Use of Options in Portfolio Management 77

are expected to soon realize their “true” potential. Growth companies are projected to capitalize on seemingly boundless “franchise potential.”

Growth potential is expressed in rising P/Es and a corresponding price escalation that may persist for years. Inevitably, boundless optimism is replaced by a dark pessimism and implicit revaluation of “franchise poten- tial” is sudden, dramatic and relentless. Our Franchise Factor Model (FFM) does not make market forecasts. Rather, the FFM quantifies the return and investment assumptions that are implicit in a given P/E. In so doing, the FFM provides concrete and intuitive measures that the investment analyst can test against realizable return and investment prospects.

One of the great overestimates of market growth potential occurred in Japan in the late 1980s. Exhibit 3.2 shows how an investment of $100 in the Nikkei index more than tripled in value in the five years, beginning January 1, 1985. One analyst after another “capitulated” and began to join the bull market bandwagon. Going into 1989, Japan was widely viewed as an example of a new paradigm in which traditional valuation measures did not apply. We note that much of the same reasoning later applied during the Internet boom.

EXHIBIT 3.2 Cumulative Value of an Investment of $100 in the Nikkei Index

0

50

100

150

200

250

300

350

400

C um

ul at

iv e

V al

ue (

$)

Month End

Nikkei 225 Index

D ec

-8 4

D ec

-8 6

D ec

-8 8

D ec

-9 0

D ec

-9 2

D ec

-9 4

D ec

-9 6

D ec

-9 8

D ec

-0 0

D ec

-0 2

D ec

-0 4

D ec

-0 6

D ec

-0 8

78 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

At the end of 1989, the Japanese market collapsed. In 1991, market observers began to take the view that the market could not get any worse and was about to turn. Instead, the market went nowhere. In 1998, the market began to rally along with the internet boom in the United States. But the market collapsed again in 1999. Finally, in 2003 signs seemed to appear that recovery was underway. Hopes were dashed again with the onset of the Great Recession. In mid-2010, the Nikkei 225 remained at only 24% of the peak realized more than 20 years earlier!

The Nikkei performance illustrates an inherent danger and warning sig- nals in extreme peaking behavior. In a sense, the Japanese market was, for some time, viewed as having a hyper-franchise reflecting superior manage- ment, better work ethic, and manufacturing prowess. Even if these observa- tions were to some extent correct, their macro valuation was unrealistic.

In the language of our model, over the course of time, hyper-franchise firms are likely to transition to no-growth, low-growth, or anti-franchise firms. Sometimes such firms eventually go out of business, although mar- kets do not. In fairness, we do not mean to suggest that market observers and participants literally speak of franchise value. Rather, we argue that when application of our model to the market yields an implicit FV that is inconsistent with any reasonable assumptions, there should be an explicit questioning of the sustainability of valuations.

The phenomenon just observed for markets is equally apparent for some of America’s greatest growth companies, as illustrated in the Exhibits 3.3 and 3.4. For an extended time, both of these Fortune 500 companies were viewed as holding a hyper-franchise, enabling the firm to make ever larger and more profitable investments. Firm A is a highly regarded well- diversified Fortune 50 company. Firm B is one of the great innovative mega- cap tech companies. The prices of both firms escalated for almost 15 years, with unprecedented acceleration occurring in the late 1990s. Early buyers who sold at the peak made fortunes. Long-term shareholders made modest or negative returns, depending on their entry point.

When market optimism came to an end in 2000, so did optimism regarding the FV of individual firms. The market could no longer foresee the investment opportunities required to justify sky-high valuations. During the run-up, the price of Firm A grew about 25 times. That remarkable growth pales in comparison to Firm B which grew about 120 times! As might have been expected, the correction in Firm B’s price was far greater than for Firm A’s price. But, both quickly returned to 1998 levels and then fell further.

Firm A bottomed in early 2003 when its price was only 40% of the peak. Then, prices began to escalate modestly, reflecting the view that the firm still had growth potential. Between 2003 and 2006, the firm provided a modest price return to investors. To raise the P/E the firm would have to

Use of Options in Portfolio Management 79

reveal new unanticipated growth prospects that were large in comparison to the already enormous (Fortune 50!) firm size. Absent the discovery of such new opportunities (or improvement in the probability that previously envisioned projects would succeed), the firm’s perceived FV would likely decrease and P/E declines would occur in lockstep with that decrease in FV. In the Great Recession, any such positive views of the firm collapsed and the price dropped even more sharply than during the burst of the Internet bubble. By mid-2010, the price was at 1996 levels!

From peak to trough, Firm B saw its price decline by 90%. Then, from 2002 to mid-2010, the price oscillated within a trading range and there remained no sign of a change in growth prospects. That is, FV was not about to change.

Firm size helps to some extent, but it also exacerbates the challenge an FV-driven firm faces in maintaining a high P/E (P/EFV). On the one hand, big firms may dominate markets, have access to cheaper sources of produc- tion, achieve favorable pricing and realize lower capital costs. On the other hand, the dollar size of the investments that must be made to impact the P/E is enormous. A $1 billion investment is very meaningful to a $500 million company, but a mere “drop in the bucket” for a $30 billion company.

EXHIBIT 3.3 Firm A, Diversified Fortune 50 Company

0

5

10

15

20

25

30

35

Pr ic

e G

ro w

th o

f $ 1

In ve

st m

en t (

$)

D ec

-8 4

D ec

-8 6

D ec

-8 8

D ec

-9 0

D ec

-9 2

D ec

-9 4

D ec

-9 6

D ec

-9 8

D ec

-0 0

D ec

-0 2

D ec

-0 4

D ec

-0 6

D ec

-0 8

Month End

80 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Successful companies like Firms A and B ultimately reach a point where few potential investments are large enough to significantly impact overall firm valuation. Is it possible that the same is also true for some broad markets?

The usual stable P/E assumption may not be realistic. In theory, there should be a smooth path of escalating and ultimately declining P/Es, reflecting the full cycle of future investment opportunities. In practice, P/E changes are often sudden and dramatic. In contrast to Firms A and B, the relatively unexciting midcap industrial Firm C in Exhibit 3.5 appears to be successfully navigating the FV challenge. This firm had a good but slower and less spectacular run-up from 1985 to 1998. Then there was a steep decline through 1997, with the trough being only 50% of the peak. But this drop was not as deep as it was for the other firms and we see a period of stability following the decline. In the terms of FFM, new unanticipated growth prospects began to emerge adding to FV and driving C’s value to unprecedented levels. The 2007 price run up was too fast and the gains quickly evaporated in 2008. Through 2009–2010, the price continued to rise and the patient long-term investor saw price grow 10 times, along a path that was relatively stable.

EXHIBIT 3.4 Firm B, Mega-Cap Tech Company

0

25

50

75

100

125

150

Pr ic

e G

ro w

th o

f $ 1

($ )

D ec

-8 4

D ec

-8 6

D ec

-8 8

D ec

-9 0

D ec

-9 2

D ec

-9 4

D ec

-9 6

D ec

-9 8

D ec

-0 0

D ec

-0 2

D ec

-0 4

D ec

-0 6

D ec

-0 8

Month End

Use of Options in Portfolio Management 81

EXHIBIT 3.5 Firm C, Midcap Industrial Firm

0

5

10

15

20

25

30

35

Pr ic

e G

ro w

th o

f $1

( $)

D ec

-8 4

D ec

-8 6

D ec

-8 8

D ec

-9 0

D ec

-9 2

D ec

-9 4

D ec

-9 6

D ec

-9 8

D ec

-0 0

D ec

-0 2

D ec

-0 4

D ec

-0 6

D ec

-0 8

Month End

FORMULATION OF THE BASIC MODEL

Our basic FFM expresses a firm’s theoretical value as the sum of two level payment annuities reflecting a current earnings stream (the tangible value, TV) and a flow of net profits from expected future investments (the fran- chise value, FV):

Market value = Tangible value + Franchise value

TV is the economic book value associated with annual earnings derived from current businesses without the addition of new capital. In the FFM, we obtain a valuable simplification by viewing this earnings stream as a perpetual annuity, with annual payments E. This model annuity is presumed to have the same present value as the actual projected earnings stream. Any pattern of projected earnings can be replicated, in present value terms, by an appropriately chosen perpetual earnings stream.

82 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

In actuality, analysts use either trailing or forward-looking earnings pro- jections. Realized earnings exhibit considerable year-to-year variability and optimistic earnings projections are often “front-loaded” with rapid growth in the early years and more stable and possibly declining earnings in later years. The opposite path is also possible: slow earnings growth projected in the early years and more rapid growth later.

If k is the risk-adjusted discount rate (usually taken as equivalent to the cost of equity capital), then3

TV E k

=

The contribution of TV to the P/E ratio is obtained by dividing the above formula by E:

P E/ TV k = 1

From the above formula, we see that P/E TV

depends only on the equity capitalization rate k. Since k depends on inflation, real rates and the equity risk premium, so does P/E

TV . These variables change over time, but they

do so rather slowly. Consequently, we conclude that the P/E TV

is relatively stable.

In order to simplify the discussion in this chapter, we do not address the impact of inflation on both current and future earnings. It should be noted that a firm that can, even partially, “pass-through” inflation into earnings will be intrinsically more valuable and command a higher P/E than a firm that lacks the pricing power to pass-through inflation. More detailed dis- cussion of the impact of inflation flow through on both TV and FV can be found in our earlier works.

The remaining source of value stems from future prospects to invest capital and obtain a premium return. Evaluations of such prospects require peering into a proverbial crystal ball in order to see the future. As such, these evaluations are subject to continual revision and have higher volatility.

There seems to be an almost congenital human need to view all growth as smooth and consistent, but any forced smoothing of growth prospects is likely to lead to a number of fundamental evaluation errors. In fact, invest- ments in new businesses can only be established as opportunities arise in some irregular pattern over time. At the outset, each new business will

3Modigliani and Miller showed that the theoretical total cost of capital is independent of both dividend policy and of the balance between debt and equity financing. See Franco Modigliani and Merton H. Miller, Dividend Policy, Growth, and the Valuation of Shares,” Journal of Business 31, no. 4 (October 1958): 411–443.

Use of Options in Portfolio Management 83

require years of investment inflows, followed by subsequent years of (hope- fully) positive returns. These returns will themselves vary from year to year. In the standard DDM, a fixed growth rate is chosen, and the size and tim- ing of future projects are implicitly set by the level of earnings available for reinvestment.

In the FFM, we allow for a varying pattern of investments and returns. To do so, we model a project’s investment and net return pattern as equiva- lent (in present value, PV) to a level annuity returning an appropriately chosen fixed rate R per dollar invested, year after year in perpetuity. The net new contribution to the firm’s value is based on a fixed “franchise spread” (R – k) over the cost of capital earned on dollars invested. In the standard DDM, the return on new investments, R, is implicitly assumed to be the same as the return on the current book of business r. This rather restrictive return equality is not required implicitly or explicitly in the FFM.

Since investment dollars are contributed at various points in the future, we normalize each of those investment dollars by measuring them in terms of today’s dollars (the PV). We then compute the sum of all PVs of investment dollars. This sum is the single dollar amount that, if invested today, would act as a surrogate for all future investments. The concept of the PV equiva- lence of the totality of future growth prospects has the virtue of consider- able generality. No longer are we restricted to smooth compounded growth at some fixed rate. Virtually any future pattern of future opportunities— no matter how erratic—can be modeled through PV equivalence.

The PV of all growth opportunities will generally sum to a massive dollar value. To make this term intuitive and estimable, we represent it as a multiple, G, of current book value, B. That is,

PV of investable opportunities = G × B

or,

G B

= PV of investment opportunities

The totality of projected investments provides a perpetual stream of “net” profits with annual payments from the net spread earned by these investments:

Annual net payments Franchise spread PV of= × iinvestible opportunities = − ⋅ ×( ) ( )R k G B

FV is the present value of this perpetuity, which is calculated by dividing the above expression by k:

84 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

FV R k G B

k = − ⋅ ×( ) ( )

The contribution of FV to the P/E ratio is obtained by dividing the above formula by E, which can be represented as the product of the book value B and the current return on equity r:

E r B

R k rk

GFV

= ×

= − ⋅P E/

We call the first factor on the right side of the above equation, the fran- chise factor (FF),

FF R k

rk = −

The above formulation allows for any pattern of new investments and returns over time including returns on new investments, R, that may be vastly different from the current return on equity, r. By focusing on the net PV of new investments, we avoid having to consider whether the financing is internal or external. While the classic DDM requires self-financing via earnings retention, there is no such limitation in the FFM.

The FFM formulation enables us to see through potentially unrealiz- able growth assumptions. In essence, the formulas above provide a “sanity check” against future expectations that are, in fact, unreasonable and virtu- ally impossible to justify. The following examples illustrate how this works.

Imagine a growth firm that is presumed capable of providing a perpetual annual return on equity of 15%. The firm has a unique franchise that gives it substantial pricing power. By exercising this franchise, the firm is pro- jected to be able to make new investments that will provide an even more attractive 18% perpetual annual return. This is surely would be considered a terrific firm if the cost of capital was only 9%! Under these assumptions,

k = 9% r = 15% R = 18%

and

P/ETV = 11.1 FF = 6.7 P/E = 11.1 + 6.7G

Use of Options in Portfolio Management 85

We leave G unspecified because it is the most difficult number to esti- mate but G will be the key to analyzing the P/E that the market currently assigns to this firm. For example, suppose the market multiple is 25×. In order to justify that P/E, G would have to be about 2.1.

The G factor is a bit mysterious, but worth exploring. G is the PV of all future invested dollars, expressed as a percentage of the firm’s current economic book value. If we are thinking of a $100 million Firm V, then a G of 2.1 means that the PV of all future investments would be about $210 million. If this firm possesses new technology that the market is likely to embrace, $210 million of additional high return investments might be a modest, achievable requirement. Taken to the extreme, such a firm might have far greater future possibilities if, as expected, the new the new technol- ogy is widely embraced. In that case, the P/E might be far greater than 25×.

Now suppose Firm W is already a $10 billion dollar firm. Propor- tionately, Firm W must do exactly the same as Firm V to justify the same P/E. Firm W’s challenge is really formidable—the required PV of all future investments is $21 billion!

The $21 billion figure is even more imposing when we realize that it represents the present value dollars of investments that earn and maintain, in perpetuity, a 9% average excess spread over the cost of capital. For exam- ple, if the firm made $3.2 billion in new investments every year for the next 10 years, the PV would be $21 billion but the total dollars invested would be $32 billion. Even for extraordinary firms with market sector dominance, finding such investments is not easy.

By using the FFM in this way, investors and analysts are positioned to ask the right questions. Does Firm W have the ability to find and execute $21 billion (in PV) of new investments that, on average, will provide an 18% return on equity in perpetuity? Does Firm V have that ability? The market, by assigning a P/E of 25× is saying the answer to both questions is a resounding “yes.”

This active questioning can be taken several steps further. What are the implications if the actual R is a little lower or higher than expected? How do the results change if the estimates of r are overly optimistic? What will happen if changing inflation expectations or changing equity risk premiums lead to changes in k?

P/E MYOPIA: THE FALLACY OF A STABLE P/E

To this point, we have utilized projections of future investments and returns to calculate the theoretical prospective P/E ratio at a single point in time. We

86 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

now take a multiyear look at the time evolution of the relationship between realized earnings growth and realized P/E.

When estimating future earnings growth, historical earnings growth is the commonly used baseline around which an analyst will make some (typi- cally modest) adjustments. Price appreciation is often assumed to follow the projected earnings growth with P/E remaining stable. In this way, investors tacitly elevate earnings growth to the central determinant of investment value.

Theoretically, stable P/Es are unlikely to be achieved, even under equi- librium conditions in which market returns and a company’s long-term prospects remain stable. Rather there is a natural time-path of P/E evolu- tion. This observation stands in stark contrast to the valuation methodol- ogy typically used to estimate the long-term potential of investment bank- ing deals involving mergers, acquisitions and buyouts. In such valuations, growing earnings are projected along with a horizon P/E that is close to the current value. The combination of these growth and stability assumptions is likely to lead to excessively optimistic estimates of the IRR (internal rate of return) potential of such deals.

Given current P/E values, we ask how the P/E theoretically changes over subsequent years under varying earnings growth assumptions. By analogy to fixed income terminology, we label the equilibrium-implied future P/E, the P/E forward. We call the trace over time the P/E orbit. This seemingly straightforward approach leads to a number of striking implications. For example, it shows that high growth stocks can induce a P/E myopia, leading otherwise thoughtful analysts to an overestimation of holding-period returns.

In order to fruitfully discuss P/E orbits, we need to review a few basic relationships. The first of these relationships is the basic single-period return produced by an equity investment. The holding-period return is the sum of just two quantities, the dividend yield (DY), and price return (% price change):

Holding period return = Dividend yield + Price return

The dividend yield is usually fairly stable, so this component of return will provide a reliable, steady addition to return. Price return is more vari- able and is therefore the critical ingredient in return volatility. The price return can be shown mathematically to be the sum of the growth in earn- ings, g

E , and growth in P/E, g

P/E , over the holding period:

Price return = g E + g

P/E

Armed with these basic formulas, we can compare the P/E orbit of a high growth stock with the P/E orbit of a low growth stock. We will use a

Use of Options in Portfolio Management 87

numerical example, starting with k = 9% as the market discount rate for all stocks discussed in this chapter. In reality, of course, the discount rate varies from company to company, with changing market conditions, and should probably even be used to differentiate the risk prospects of the TV from the FV. If our hypothetical stock is fairly priced, it will provide a 9% holding period return. This equilibrium return assumption tells us a great deal about what theoretically should be happening to the P/E.

The discount rate k will actually change over time along with changes in interest rates and equity risk premiums. However, for simplicity and clarity we discount all earnings at a fixed k = 9%.

P/E Orbits for High-Growth Stocks

Suppose the stock of the high-growth Firm D trades at a P/E multiple of 25×. The expected earnings growth is 12.4% (the rationale for choosing this particular growth rate will become evident later) and the dividend yield is 1.6%.

Since the holding period return is the sum of the dividend yield and the price return, a 9% return and a 1.6% dividend yield implies that the price return must be 7.4% (9% – 1.6%). Repeating the formula above:

Price return = + = + = −

g g

g

g

E P E

P E

P E

/

/

/

. % . %

%

7 4 12 4

5

This result suggests that, over a one-year holding period, the P/E is implicitly expected to fall –5% from the current 25× to a forward P/E of 23.8×.

At first, this result is surprising. Why should the P/E register such a sharp decline over the course of a single year, especially after a 12.4% growth in earnings? The result is a direct consequence of our assumption that the initial P/E of 25× represents fair equilibrium pricing. The fair pric- ing assumption implies that, given the long-term prospects for the company, an appropriately specified valuation model would validate the P/E of 25× if the earnings discount rate was 9%. In this example, the first year of earnings growth was specified at 12.4%.

The P/E decline is also implicitly related to the assumption that, at the outset, the firm has a fixed FV that is consumed/utilized over time. High earnings growth in the early years can then be viewed as leading to rapid realization of the firm’s potential.

We note that earnings growth rates can fluctuate widely from year- to-year and long-term growth forecasts are shrouded in more uncertainty

88 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

short-term forecasts. In actuality, many future sequences of subsequent annual earnings growth rates can lead to the precisely the same initial fair value P/E of 25×.

Regardless of the future earnings growth path, an equilibrium 9% return assumption and 12.4% first year growth necessitates an expected 5% P/E decline and a new year-end fair value of 23.8×.

As long as Firm D’s earnings growth rate remains at 12.4% and the market discount rate stays at 9%, the P/E should continue to decline by 5%. Thus, in the second year the P/E should decline from 23.8× to 22.6×. Continuing at this rate for 10 years brings the P/E down to 15×, as depicted in the curve that emanates from a P/E of 25× in Exhibit 3.6.

As an example, imagine a pharmaceutical company currently enjoying a healthy 12.4% earnings growth from sales of a proprietary drug. If the drug goes generic and the company’s research pipeline is unpromising, the eroding franchise (i.e., the consumption of FV) will be reflected in a corre- sponding decline in P/E.

A few words of caution are needed so that Figure 3.6 is not misinter- preted. First, the descending P/E orbit does not imply a decline in the equity price. The 12.4% earnings growth brings investment gains that more than offset losses due to the P/E induced 5% price decline. The corresponding stock price trajectory will be one of 7.4% positive growth. When we add a 1.6% dividend to 7.4% price growth we achieve a 9% return, just as we

EXHIBIT 3.6 P/E Orbits with Constant Earnings Growth

0

5

10

15

20

25

30

P/ E

R at

io

Years

5.0% Earnings Growth

7.4% Earnings Growth

12.4% Earnings Growth

0 2 4 6 8 10 12 14 16 18 20

Use of Options in Portfolio Management 89

would expect with a 9% discount rate. Exhibit 3.7 illustrates how dividends, earnings growth and P/E decay combine to provide a 9% annual return.

The basic assumption is that the initial P/E of 25× represents fair-value discounting of the company’s future earnings growth. But, the high 12.4% level of earnings growth cannot continue indefinitely. With a 9% discount rate, perpetual earnings growth at 12.4% would require an infinite starting P/E and necessarily violates the assumption that 25× represents fair pricing. The 12.4% curve in Exhibit 3.6 should be viewed as portraying the P/E descent for just so long as earnings growth remains at 12.4%.

The depicted P/E orbit does not depend on the choice of 25× as the starting P/E. As long as k = 9% and g = 12.4%, the projected P/E “should” decline by 5% each and every year. Under these return and growth and assumptions, the same 5% year over year decline will apply for all initial P/E values!

There may be a myriad of reasons why a specific investor may hold to the belief that the P/E will not experience any such decline—improvement in the stock’s prospects, the market’s better appreciation of the stock’s promise, the salutary effect of realized earnings growth (even if it only confirms the previ- ously expected high 12.4% level), general market improvements, changes in required discount rates, and so on. All of these events constitute a depar- ture, however, from the equilibrium conditions as they have been defined. Hence, excluding the P/E movements induced by such nonequilibrium

EXHIBIT 3.7 Growth of $100 Investment (1.6% dividend, 12.4% earnings growth, −5%. P/E decline

Time Dividend Payment

Price Gain from Earnings

Growth

Price Loss from P/E

Decay

Total Value Including Dividend

Reinvestment Percent Return

0 100.0

1 1.6 12.4 −5.0 109.0 9%

2 1.7 13.5 −5.5 118.8 9%

3 1.9 14.7 −5.9 129.5 9%

4 2.1 16.1 −6.5 141.2 9%

5 2.3 17.5 −7.1 153.9 9%

6 2.5 19.1 −7.7 167.7 9%

7 2.7 20.8 −8.4 182.8 9%

8 2.9 22.7 −9.1 199.3 9%

9 3.2 24.7 −10.0 217.2 9%

10 3.5 26.9 −10.9 236.7 9%

90 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

factors that result in unanticipated additions to FV, the stock’s P/E should decline by 5%.

P/E Orbits for Low-Growth Stocks

For low-growth stocks, the same formulation as above also leads to con- tinuous P/E change, but the change results in an ascending P/E orbit, as displayed in the 5% growth curve in Exhibit 3.6. If the starting P/E is 11.8× and the same 1.6% dividend yield and 9% market discount rate as in the previous example apply, the P/E will grow to 15× over 10 years.

Moving toward a higher P/E in the face of lower earnings growth seems contrary to basic intuition but it does make sense when we think in terms of FV consumption. High-growth firms rapidly consume their FV while low-growth firms consume FV slowly. In the equilibrium framework, the consensus investor expects a 9% total return. With a 1.6% dividend yield and expected 5% earnings growth, the only way we can reach that return is through expected P/E growth of 2.4%! Any P/E growth below this “required level” will be disappointing, and any greater increase will be a source of excess return.

The P/E orbit for g = 5% appears to rise without limit. Of course, this cannot be, either in practice or in any reasonable theory. Thus, the 5% P/E orbit must be viewed as the path for the early years for a company. In those years, new investments proceed slowly and FV is “under-consumed” but anticipated opportunities remain. At some later point in time, the firm is expected to invest more aggressively to take full advantage of its opportu- nities, thereby consuming FV and generating accelerated earnings growth.

An example of a low-growth company with a high and growing P/E might be a pharmaceutical company that has low current earnings but enjoys a pipeline of potentially blockbuster drug prototypes. The new drugs constitute a sizable franchise that will grow in value as their approval and launch times draw closer. At first, growth may accelerate, but eventually P/E will stabilize and then possibly decline.

The Stable P/E

The previous examples suggest that, under equilibrium assumptions the P/E will naturally change from year to year. There is one special case in which there is no change in P/E: when the earnings growth rate plus the dividend yield equals the 9% discount rate. In our example, that would be a 7.4% growth rate. We call this growth rate the “stabilizing” growth rate, g

S . With

g S = 7.4%, the P/E will remain unchanged, providing an orbit that consists

Use of Options in Portfolio Management 91

of a single horizontal line. This is illustrated by the middle line in Exhibit 3.6 where the P/E starts at 15× and remains at this level.

For growth rates that exceed gS, the P/E orbit is descending. For growth rates below gS the orbit is ascending. Neither continual ascent nor continual descent makes sense over the long term. Continual ascent would imply the P/E approaching infinity; continual descent would imply the P/E approach- ing zero. To achieve “sensible” orbits, the growth rate must undergo at least one future shift that is sufficient to change the orbit’s basic direction. The simplest such orbital shift is a transition to a stabilizing growth rate that produces a horizontal orbit from the transition point forward. Such an orbit represents a going-forward version of the classic two-phase growth model.

TWO-PHASE P/E ORBITS

The examples of constant growth rates in Exhibit 3.6 illustrate the natural path of P/Es when the market provides the equilibrium 9% return and earn- ings growth and dividend yield are constant. To achieve “sensible” orbits, growth rates must undergo at least one future shift that changes the orbit’s basic direction. The simplest such shift in growth rates is a transition to a stabilizing rate that produces a horizontal orbit from the transition point forward. Such an orbit represents a going-forward version of the classic two-phase DDM, in which one growth rate holds prior to a defined horizon and then a second growth rate prevails in perpetuity.4

In the most common situation, the first phase has a higher growth rate than the final phase. In such cases, the starting fair-value P/E is always higher than the final P/E. The P/E descends along its orbit until the horizon point, where it should match the stable P/E of the final phase.

As an illustration, we revisit the earlier example (Exhibit 3.6) of a firm with a dividend yield of 1.6%, initial P/E of 25× and 12.4% earnings growth, leading to a P/E decline to 15× after 10 years. Instead of maintaining a single growth rate, we now assume that earnings growth slows in year 10 and the company enters a final phase of perpetual 7.4% growth. The upper curve in Exhibit 3.8 illustrates this P/E orbit, including the stabilizing growth rate that leaves the P/E unchanged at 15× for the remainder of time. The two growth rates in this example totally determine that 25× is a fair value for the starting P/E and that 15× is the fair value for the terminal P/E.

This example clarifies why the P/E descent, which at first seems counter- intuitive, makes sense in the context of fair valuation. The high growth rate in the first phase leads to the high starting P/E of 25×. From this height, FV

4Aswath Damodaran, Damodaran on Valuation (New York: John Wiley & Sons, 1994).

92 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

is consumed quickly and the P/E must move downward to its final-phase P/E of 15× where FV is lower but sustainable.

Similarly, in the relatively unusual case in which a stock has a lower growth rate in its first phase, the fair value for the starting P/E would be expected to be lower, reflecting slower FV consumption, and then rise until it ultimately reaches its final-phase level. This is illustrated in the lowest, dotted curve in Exhibit 3.8 where after 10 years, the growth rate accelerates from 5% to the 7.4% stabilizing rate.

For each starting P/E, there is one specific growth rate that will move the P/E from its initial level to a final P/E of 15× after 10 years. For example, a starting P/E of 20× would require a 10.2% initial growth rate to bring the P/E down to 15×, as illustrated in the middle curve of Exhibit 3.8.

Tracing out these P/E orbits brings to the surface several of the prob- lems inherent in standard valuation models. In many short- and interme- diate-term models, earnings are assumed to grow at a specified rate until some given horizon date—anywhere from 1 year to 10 years hence. Then, the attained earnings level on the horizon date forms the basis for estimating terminal price. Unfortunately, an all-too-common tendency is to determine this terminal price by simply applying the current P/E to the horizon earn- ings level. In other words, the P/E is simply assumed to remain stable. But, as the preceding examples show, this myopic assumption of P/E stability is

EXHIBIT 3.8 10-Year Two-Phase Growth with Various Starting P/Es and Required Initial Growth Rates

0

5

10

15

20

25

30

20151050

P/ E

R at

io

Years

5.0% Growth

7.4% Growth

12.4% Growth

10.2% Growth

Use of Options in Portfolio Management 93

highly questionable—especially when a high rate of earnings growth pre- vails in the early years. To the extent that high growth rates and the divi- dend yield exceed the expected return, the baseline equilibrium estimate of forward P/Es should follow the orbital descent to lower values.

We now turn to our basic FFM to gain some further insights into the orbits we have just uncovered.

The Franchise Factor Model and P/E Orbits

The single- and multiphase P/E orbits in Exhibits 3.6 and 3.8 are related to how the balance between TV and FV evolves over time. FV always incor- porates a consolidated market view of the totality of a firm’s potential in- vestments. Whenever some of that investment potential is realized through the execution of an anticipated investment, FV shrinks and TV grows. For example, FV depletion occurs when a pharmaceutical company brings an anticipated new drug to market or a when a restaurant chain opens a new restaurant. As such new products or businesses become valuable compo- nents of the firm’s ongoing businesses, their related earnings streams become part of the TV. Thus, FV depletion equals TV expansion. But this equality does not hold for P/E

TV and P/E

FV .

Since TV = E/k, TV grows at exactly the same rate as E, provided all other parameters remain unchanged.

g TV

= g E

Earnings growth may come from a variety of sources, many of which are unrelated to franchise consumption. For example, prospective investments with return, R, equal to the market rate, k, do not provide a net positive return to investors and make no contribution to FV, but they do add to TV. Since TV = E/k grows with earnings, any investment with a positive return will add to TV as soon the investment begins to generate earnings. However, there is no addition to P/E

TV since the ratio TV/E = 1/k remains unchanged.

Earlier in this chapter, we exhibited the following price return relationship:

Price return = +g gE P E/ (3.1)

The second component of price return, g P/E

, mathematically can be shown to be

g w g g

w FV

TV FV

P E FV E/ ( )= −

= +

(3.2)

94 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

For growth firms, FV dominates TV and the price impact of any deple- tion in FV will be amplified in three ways. First, an FV decline means gFV is negative. Second, a drawdown in FV means new investments have been made and add to earnings. Thus, gE will increase, and the corresponding term in equation (3.2) will become more negative. Since both terms within the parentheses in equation (3.2) become more negative, the rate of decrease in gP/E increases.

Finally, the dominance of FV (over TV) for growth firms implies that the weight, w, will be relatively large. The combination of all three factors leads to substantial theoretical P/E declines for growth firms, especially dur- ing periods of high earnings growth, as illustrated in Exhibit 3.6.

Unless growth comes from previously unexpected sources, the 5% growth curve in Exhibit 3.6 illustrates a special situation in which firms with high FV actually can experience positive P/E growth. When FV is uti- lized at a slow pace, earnings grow slowly and FV can grow with time. This potential FV growth is related to the present value calculations embedded in FV. FV includes the present value of future investments as well as the present value of the returns they provide. In calculating FV, we discount future flows to the present. If the first investment does not occur for several years, then after the first year we will be discounting that flow as well as other future flows for one period less. As a result, it will appear as if FV has grown at the market rate. Ultimately, however, as the FV is “consumed” growth will accelerate and the P/E will level off and eventually begin to decline.

In contrast to growth firms, for value firms where TV dominates FV, w will be relatively small and the P/E impact of FV decay will be rather muted.

FV Growth, FV Decay and FV Bubbles

Equation (3.2) implicitly shows that, under our equilibrium assumptions, the P/E will be stable (i.e., g

P/E = 0) if FV growth, g

FV , equals earnings growth,

g E . This basic relationship underscores the challenge and tyranny of success.

Whenever a CEO succeeds in meeting investor expectations by appropri- ately and effectively bringing anticipated premium investments to fruition, he is utilizing a portion of the firm’s franchise value. As FV declines, so will its contribution to the firm’s P/E. That is, FV and P/E decay are natural con- sequences of the effective utilization of a firm’s franchise.

We view FV as consumed whenever anticipated capital investments are made in new businesses. If the P/E is to be maintained, the consumed FV must be replenished. “Replenishment” is challenging because it means adding more FV than was just consumed. This high replenishment follows because the G factor in FV is measured relative to economic book value.

Use of Options in Portfolio Management 95

Business growth increases book value, so replenishment will be measured relative to a larger base.

In essence, each time a new business is added, the CEO must develop and convey a surprising new vision of business opportunities that are larger than the ones just built out. If this vision is not a surprise, the opportunities already would have been incorporated in previous business visions and in the existing FV.

To some extent, the market does reward high-octane CEOs with implicit votes of confidence in their ability to identify new opportunities. This confi- dence may even be expressed through a lowering of the discount rate as the perceived risk declines. But the challenge remains because each success will inevitably be met with ever greater expectations!

CEOs of hyper-franchise firms may for some time be able to uncover new opportunities at an increasing rate. In a global market place, the reach and brand of big firms may offer distinct advantages and facilitate the open- ing of unexpected new markets. Over time, the CEO may see possibilities that earlier were inconceivable. For example, the firm’s market dominance may turn out to be an even greater advantage than anticipated, resulting in more pricing power and a higher franchise spread. When new, previously unimagined possibilities are announced, there is likely to be P/E growth or even a significant “jump” whenever a positive surprise is incorporated in the market’s estimate of FV.

But the tyranny of size looms large. As a successful business transform a small firm into a big firm, only mega-investments can move the P/E dial. To some extent, a firm’s size, expertise, and market dominance may be a major advantage that does, for a time, enable the firm’s leadership to find precisely such investments. However, despite such advantages, big invest- ments become harder and harder to find and to execute—even for the most talented executive.

The natural path of P/E decline may accelerate if a firm mistakenly engages in anti-franchise growth. For example, the FV might initially incor- porate the expectation that large cash holdings would soon be used for investments or acquisitions yielding a positive franchise spread. If instead, it turns out that cash holdings turn out to become long-term investments with a bond-like return, then they will be P/E-depleting. From a shareholder per- spective, it would be better to distribute cash through increased dividends or share repurchases. Shareholders then would have the opportunity to achieve the equity market rate (not the bond rate) through other investments.

A second example of anti-franchise growth stems from mega-mergers based on perceived but yet-to-be-attempted synergies. Unrealizable syner- gies may result in a negative franchise spread, thereby causing FV decay. Worse still, a change in market perceptions of a firm’s franchise can lead

96 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

to a sudden dramatic FV decay (and P/E collapse). Therefore, the pricing of mergers is critical. As the price increases, the probability of achieving a positive franchise spread declines.

Because FV estimation is an art rather than a science, FV estimates can easily reflect exaggerated euphoria or dismay as market conditions and per- ceptions wax and wane. When firms appear to be able to regularly rediscover and reinvent themselves, the opportunities seem boundless and momentum- driven FV estimates may be revised upward over and over again. In some cases, such optimism may be justified for years or even decades, as illus- trated in Exhibit 3.3 and 3.4, possibly creating FV bubbles.

With the passage of time, in one way or another, a given level of uncer- tainty may slowly be transformed into greater certainty. Some former opti- mistic estimates may be realized, but others may turn out to have been wildly excessive. If doubts and negative sentiment grow, the FV bubble may burst via a precipitous drop in FV and P/E. Following such a decline, a company will be challenged to reinvent itself and show that it has a renewed franchise that will lead to an increasing estimate of FV. Some firms can do this; some cannot. As a result, many outstanding firms will see their P/Es gradually decline as they convert from growth to value firms.

FRANCHISE VALUATION UNDER Q-TYPE COMPETITION

In the two-phase growth model, we assumed that the firm with 12.4% growth (see Exhibit 3.8), transitioned after 10 years to a more stable 7.4% growth rate. This model is generally intended to reflect an initial span of growth and prosperity followed by a second-phase regression to a competi- tive equilibrium. This terminal stage can be construed as the period when sales growth stabilizes but the company’s earnings continue to change as the pricing margin moves toward some competitive equilibrium. This margin- equilibrating process can usefully be described in terms of the ratio of asset replacement costs to the company’s economic book value, B, and is related to Tobin’s q.5

The valuation impact of this terminal-phase effect will depend totally on the nature of the company’s business and its long-term competitive posture. Some companies will be positioned to gain from post-growth margin expan- sion. For some businesses, growth itself builds a relatively unassailable effi- ciency of scale with distinct organizational, distributional, and technological advantages. Patent protection and/or extraordinary brand acceptance may 5James Tobin, “A General Equilibrium Approach To Monetary Theory,” Journal of Money, Credit, and Banking 1, no. 1 (1969): 15–29.

Use of Options in Portfolio Management 97

assure franchise-level margins for years to come. Leading-edge products may themselves act as germinators for subsequent generations of even more advanced products. For such fortunate companies, potential competitor’s cost of building a new enterprise and comparable revenue stream might far exceed the existing firm’s economic book value. In this case, the ratio, Q, of the competitive capital costs to B might be far greater than one. Investors in such companies may look forward to a future period of sustained high sales with margins that are maintained or even enhanced. At this point, the com- pany begins to enjoy a “franchise ride” and the patient investor will finally be rewarded with the significant cash returns that formed the foundation for the value ascribed to the company at the outset.

For less fortunate growth companies, barriers to entry will indeed become porous over time. In this case, new technologies and efficiencies may offer competitors a Q value that is much less than one. In this case, the existing firm’s high franchise margins will be vulnerable to erosion as the firm attempts to compete with lower prices. Earlier extraordinary earn- ings will be subject to the gravitational pull of commoditization and the P/E reduction will result from this “franchise slide.”

Inevitably, large, technologically proficient, well-capitalized competi- tors lurk in the shadows of even the greatest franchise, even if the competi- tive Q is greater than one. Theoretically, such competitors will be eager to replicate a company’s products and services provided their return offers a modest spread over their cost of capital. That is, the new business will be attractive if the competitor’s cost of capital is Q times the original firm’s cost of capital (that is, Qk) and the corresponding return on equity is greater than Qk. This Q-type competition implies that the original firm’s premium pricing could be so adversely impacted that its initially high ROE would be eroded down towards the competitor’s Qk. This situation raises questions about many two-phase growth models that assume the terminal earnings level can be sustained in perpetuity, even when high initial growth would elevate the ROEs to the point of attracting sufficient Q-type competition to lower all pricing margins.6

FRANCHISE LABOR

Many businesses are becoming ever more dependent on one key factor of production—the super-skilled or “franchise” employee. Exceptional man- agers have always been recognized as central to a company’s success, but the new franchise cadre may reach far beyond the traditional managerial levels.

6For further discussion see Leibowitz, Franchise Value: A Modern Approach to Security Analysis.

98 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Its ranks are certainly broader than the usual suspects—the sports star, the dynamic lawyer, the corporate deal maker, the software guru, the (currently) renowned media hero, and so on. The role of key individuals has been great- ly enhanced by the growth of large enterprises—often highly knowledge based—that service global markets through extensive use of modern distri- bution and communication channels. In this environment, an incremental level of skill can be efficiently levered so as to have a major economic impact on a company’s profitability.

We view franchise labor as comprising all employees who can effec- tively make an exceptional claim regarding their impact on the profitability of the business activities in which they are involved.7 In any company, the franchise employee is always a scarce resource. The challenge is to accu- rately assess true current and future franchise labor. When a firm is doing well, franchise labor may be overestimated because of the firm’s difficulty in discerning precisely which employees really are the key drivers of earnings. There is a certain temptation to assign franchise value to an overly large cohort of employees involved in an area that is generating an exceptional stream of profits. In such high profit areas, managers are reluctant to chance losing seemingly key employees and have to seek replacements. There is a natural tendency to doubt that any such replacements would actually turn out to be immediate and complete substitutes for lost on-board employees with their “right-on-point” experience.

The subject of franchise labor and identification of the truly “super- skilled” is further complicated by the fact that the composition of this criti- cal group of employees is not stable. Rather, the critical group fluctuates along with changes in markets and changes in the firm’s opportunities. It is also likely that management and employees have disparate views regarding who is super-skilled.

Of the employees who perceive themselves as “super-skilled” there are four possibilities:

■ These employees really are super-skilled and: ■ The firm recognizes them as exceptional, critical to the firm’s fran-

chise, and reasonable in making a claim on excess earnings. ■ The firm does not perceive them as exceptional.

■ These employees are mistaken in their belief and: ■ The firm knows they are not super-skilled. ■ The firm does not realize that, while these employees may be doing an

excellent job, they are not critical to the firm’s franchise.

7Gary S. Becker, Human Capital (Chicago: University of Chicago Press, 1993).

Use of Options in Portfolio Management 99

The ambiguity of franchise labor often leads to a certain moral hazard for management. Managers may find themselves being judged by their effec- tiveness in retaining the visible players on a winning team, which exacer- bates the tendency to provide greater largesse, as a kind of retention “glue,” to the presumptively super-skilled.

The accurate evaluation of franchise labor can have a material effect on company valuation in a number of ways. While public discussion has centered on ways in which stock options can distort the standard account- ing statement of current earnings, relatively little attention has been given to the more subtle effects of franchise labor on future profits from brand new initiatives. These future franchise effects can be surprisingly large, depend- ing on whether the claim is applied to the current book of earnings or to the incremental future earnings associated with new investment.

It can be shown that when an incremental claim of 10% is applied to current earnings (reflected in the TV portion of the firm’s value), the valuation will be reduced by a percentage that depends critically on the stock’s P/E.8 This case is illustrated by the declining curve in Exhibit 3.9. At the base P/E of 11.1×, there is no FV and the impact of the claim applies directly to the TV, reducing the firm’s value by 10%. At higher P/E multiples, the P/E impact is lower because the TV (on which the claim has

8Leibowitz, Franchise Value: A Modern Approach to Security Analysis.

EXHIBIT 3.9 Effects of 10% Franchise Labor Claims

0

2

4

6

8

10

12

14

16

18

20

V al

ue R

ed uc

ti on

( %

)

P/E Ratio

Current earnings only

Future gross earnings only

Current earnings + Future gross earnings

0 5 10 15 20 25 30 35 40

100 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

been applied) forms a decreasing portion of the firm’s value. For example, at a P/E of 25×, the value reduction is 4.4%. Note that in Exhibit 3.9, we make the same assumptions as we did earlier in this chapter: k = 9%, R = 18%. For each curve, the incremental franchise labor claim is 10%. That is, either current earnings, future net earnings or future gross earnings are reduced by 10%.

When a franchise labor situation exists, the likelihood is strong that the earnings from future growth will be subject to labor claims that can severely depress valuations. In this case, franchise employees act as if they were a kind of “super shareholder,” extracting payments from gross rev- enues without consideration of appropriate returns to capital providers. The rising curve in Exhibit 3.9 shows the explosive effect of what might be called a “gross claim” of 10% on future profitability. This FV claim is modest for low P/Es where future investments contribute relatively little to overall firm value. As the P/E and FV become larger, however, the valu- ation impact of such claims rises rapidly. At a P/E of 25×, the gross claim grows to 11.1% of firm value. The combination of gross claims on future earnings and franchise claims on current earnings will erode firm value by 15.6%.

This leverage effect of FV claims is derived from the assumption that the 10% claim is applied to visible gross profit, ahead of any repayment to shareholders who supplied the fresh capital for the new initiatives. The key factor here is that the current shareholders begin to reap the rewards of any new initiative only after the suppliers of the new capital have been paid their due.

If the market rate for equity is 9%, suppliers of such equity capital will expect the newly issued stock to be priced so that it can provide a 9% annual return over time. Thus, in assessing the payoff from a new proj- ect with an 18% return on equity (ROE), the first 9% should be viewed as going to the new investors who supplied the needed capital, with the other 9% going to the earlier shareholders who, theoretically, owned the original “opportunity” for the high return investment. If a 10% franchise labor claim is now applied to the gross 18% ROE, then the available return declines to 16.2%. Consequently, the return reserved for current sharehold- ers shrinks from 9% to 7.2%.

With so much at stake, the organization would be well advised to expend extraordinary effort to:

■ Identify the true key employees and their respective contributions. ■ Reward the real rainmakers in a way that is fair and aligns their inter-

ests with those of shareholders in terms of risk as well as reward.

Use of Options in Portfolio Management 101

■ Properly assess the “net” payoff from new initiatives in a way that takes account of the legitimate claims of the employees needed to realize the company’s promise.

■ Assure that the management planning process, return estimates and investor’s valuations incorporate consideration of such prospective franchise labor claims.

■ Recognize that future gross franchise claims will have a much greater impact on valuation than claims based on current earnings.

KEY POINTS

■ A “fundamental no-growth firm” with no prospects for productive investments will have the same intrinsic “tangible value” (TV) today, whether it pays out all its earnings or reinvests part or all of them at the market rate. The no-growth firm’s “base” P/E will be the reciprocal of the market capitalization rate, k, for equities. A “growth firm” with significant “franchise value” (FV) must make future investments that provide a positive “franchise spread” (a return that exceeds the market- based cost of financing). For reasonable franchise spreads, high levels of future franchise investments (measured in today’s dollars) are required to significantly raise the FV. Typically, the required magnitude of the future investments may be as much as two or more times the firm’s cur- rent book value.

■ The “natural orbit” of the P/E ratio is a decaying one. As anticipated investments are made and new businesses develop and grow, the firm’s franchise value is “consumed” and converted into TV. Absent surprise opportunities, the balance between TV and FV shifts toward TV and the P/E inevitably declines. It is as if there is a natural gravitational pull toward the base P/E ratio.

■ Hyper-franchise firms may experience bouts of “supercharged” growth from capitalizing on outsized returns on equity, especially in their early years. This growth is theoretically limited in scope and duration even though there are many examples where supercharged growth persists for 5, 10, or more years.

■ The shorter-term, hyper-growth phase of exceptional franchise oppor- tunities should be distinguished from longer-lasting, more stable, “mature” franchise opportunities. Such mature opportunities are likely to achieve a modest incremental return over the cost of capital that can be sustained for long periods of time.

■ Ultimately, a firm’s growth will stabilize to the growth rate of the mar- ket as a whole. Once the firm’s franchise is consumed with new invest-

102 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

ment returns just meeting the cost of capital, the firm will have migrated into an almost pure TV firm with P/E close to the base value of 1/k.

■ The P/E impact of potential new investments depends on their size rela- tive to the current firm. To maintain a high P/E, a firm must continue to uncover new and previously unforeseen investment opportunities of ever-greater magnitude. This tyranny of size reflects a kind of CEO par- adox. A CEO who successfully fulfills a firm’s initial promise will suffer a declining P/E as the firm’s franchise is consumed.

■ To maintain the firm’s P/E, the CEO must continually uncover entirely new visions for the firm. For every anticipated investment that the CEO undertakes, that same CEO must identify future opportunities of ever greater magnitude. To the market, this newly revealed investment potential must be a complete surprise!

■ Q-type competition can drive down profits because large, technologi- cally proficient competitors lurk in the shadows of even the greatest franchise.

■ Organizations should make every effort to accurately identify true key employees and to appropriately and effectively reward the real rain- makers.

QUESTIONS

1. Firm D and Firm E have the same performance characteristics. They both have a P/E of 20× and they also have the same cost of capital, return on equity, etc. The only difference is that Firm E’s economic book value is $25 billion and Firm D’s economic book value is $25 million. Explain why, in the language of the FFM, Firm E’s P/E is more likely to decline than Firm D’s.

2. Firm F is an excellent firm with superior management and a long history of steady earnings. After a long period of expansion, the Firm F has run out of opportunities to expand by building out new businesses. Toward what values are its TV, FV, and P/E likely to converge?

3. Why is it hard for CEOs of large successful companies to maintain the firm’s P/E?

4. What is a reasonable level for the long-term P/E of a market under the following assumptions: economic book value = $500 billion, roe = 15%, cap rate = 9%, return on new investments = 18%, total invest- ment in new businesses = $20 billion per year for the next 10 years? How does the projected P/E change if the cap rate is 8% or 10%? How does the projected P/E change if total investment is (a) $20 billion per

Use of Options in Portfolio Management 103

year for 20 years? (b) $300 billion per year for 20 years? (c) $400 bil- lion per year for 20 years?

5. Explain the long term decline in value of an investment in Firm A or Firm B in terms of the FFM.

105

CHAPTER 4 Relative Valuation Methods

for Equity Analysis Glen A. Larsen Jr., Ph.D., CFA

Professor of Finance Indiana University, Kelley School of Business–Indianapolis

Frank J. Fabozzi, Ph.D., CFA, CPA Professor of Finance

EDHEC Business School

Chris Gowlland, CFA Senior Quantitative Analyst

Delaware Investments*

Much research in corporate finance and similar academic disciplines is tilted toward the use of discounted cash flow (DCF) methods. How- ever, many analysts also make use of relative valuation methods, which compare several firms by using multiples or ratios. Multiples that are com- monly used for such purposes include price–earnings, price–book, and price–free cash flow.

Relative valuation methods implicitly assume that firms that are “simi- lar” are likely to be receive “similar” valuations from investors. Therefore, on average, we would expect that firms that are generally comparable are likely to trade at similar multiples, in terms of price-to-earnings, price-to- book, or various other metrics. If this assumption is approximately cor- rect, then relative valuation methods can be used to identify firms that look “cheap” or “expensive” relative to their peers. When a particular firm’s mul- tiples are extremely different from the rest of the universe, this may indicate

*The material discussed here does not necessarily represent the opinions, methods or views of Delaware Investments.

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a potential investment opportunity—though further analysis will likely be required to determine whether there are reasons why such a firm is valued differently from other companies which otherwise appear comparable.

The basis of relative valuation methods is to use one or several ratios to determine whether a firm looks “cheap” or “expensive” by comparison with other firms that are generally similar. Relative valuation methods do not attempt to explain why a particular firm is trading at a particular price; instead, they seek to measure how the market is currently valuing a set of comparable companies, with the underlying assumption that the average multiple for a group of companies is probably a reasonable approximation to overall market sentiment toward that particular industry. In other words, relative valuation work assumes that on average, the share prices of compa- nies in a particular universe are likely to trade at similar multiples relative to their own financial or operating performance. Baker and Ruback provide a more formal presentation of these concepts.1 However, it is important to realize that at any particular time, some firms are likely to be trading at higher or lower multiples than would be justified under “fair value.”

Making effective use of relative valuation methods does require careful selection of “similar” companies. Sometimes this is relatively simple, for instance when an analyst is dealing with industries where there are a large number of roughly homogeneous firms providing goods or services that are generally similar. However, sometimes there can be considerable difficulties in identifying “similar” companies, particularly if the firms under consider- ation are unusually idiosyncratic in terms of their product mix, geographical focus, or market position. In this chapter, we provide some tentative guid- ance about how to build a universe of comparable companies. However, ultimately this part of the process will depend on the skill and knowledge of the individual analyst; two different experts may pick different sets of “similar” firms, and thus generate different values from their relative valu- ation analysis.

BASIC PRINCIPLES OF RELATIVE VALUATION

Analysis based on relative valuation requires the analyst to choose a suit- able universe of companies that are more or less comparable with each other. There is no standardized approach concerning how to choose such a universe of similar firms, and the process relies to some extent on an ana- lyst’s personal judgment concerning the particular industry and geography

1Malcolm Baker and Richard Ruback, Estimating Industry Multiples (Cambridge MA: Harvard Business School, 1999).

Relative Valuation Methods for Equity Analysis 107

involved. However, it is possible to lay out some general principles that combine practitioners’ insights with the results of academic inquiry.

Sources of Data Relative valuation approaches can only be employed if there is sufficient information, produced on an approximately consistent footing, about the various companies that are the subjects of analysis. In most countries, com- panies that are publicly listed on stock exchanges are required by law and regulation to report their historical results publicly in a timely manner, or risk being delisted from the exchange. (There may be occasional exceptions to this general pattern, particularly for entities that are majority owned or controlled by their home country government. But such anomalies are not frequently observed except during crisis periods.) Consequently, it is almost always possible to obtain information about listed companies’ historical re- sults. However, multiples based solely on historical data may not provide a complete picture, as most analysts would probably agree that forward- looking estimates are likely to provide more useful insights into the market’s opinion of a particular company.2

Investment banks, rating agencies, and other firms can provide esti- mates of a firm’s future earnings, revenues, and other metrics, typically over the next two or three years. Various data providers, such as Bloomberg or Thomson Reuters, collect such information and use it as the basis for “con- sensus” estimates, which can be viewed as representing the market’s general opinion of a company’s future prospects. It is also possible to use a firm’s own in-house estimates for the companies under coverage, as these may incorporate insights that are not yet reflected in current pricing. However, for precisely this reason, in-house estimates should be used as a supplement rather than as a replacement for consensus figures.

It is conventional to consider more than one year of data, as there may be disparities in how the market is valuing results in the immediate future and in the slightly longer term. However, it is often difficult or impossible to obtain consensus estimates more than two or three years into the future. Consequently, relative valuation approaches generally focus on relatively short periods into the future, rather than seeking to gauge how the mar- ket is valuing expected performance five or ten years hence. In this respect, relative valuation gives less attention to the distant future than is the case for DCF analysis. However, because expectations about firm value in the distant future are also presumably reflected in current multiples, the results

2See James J. Valentine, Best Practices for Equity Research Analysts (New York: McGraw-Hill, 2011), p. 271.

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of analysis based on relative valuation analysis are arguably still compatible with those from DCF-based approaches.

Number of Comparable Firms In general, an analyst would like to use data from other firms that are as similar as possible to each other. However, if the criteria for “similarity” are specified too stringently, then there may be too few firms included in the universe. And if the sample is too small, then the idiosyncrasies of individual firms may exert an excessive influence on the average multiple, even if the analyst focuses on the median rather than the mean when calculating the “average” multiple.

Generally speaking, we believe that it is desirable to have at least five or six comparable companies, in order to begin drawing conclusions about rel- ative valuation for a particular industry. Conversely, there may be few ben- efits from considering more than twelve companies, particularly if the larger universe contains firms that resemble less closely the particular company that is the focus of the analyst’s attention.3 For most practical purposes, a group of between six and 12 comparable firms should be sufficiently large to produce usable results.

Basis for Selecting Comparable Firms

In an ideal situation, a universe of comparable companies would be similar in terms of level of risk. In order to create such a universe, it is common to rely on criteria such as size, industry focus, and geography. This tends to be easier when considering firms that are small or mid-sized—say, with market caps between $100 million and $10 billion (based on 2010 U.S. dollars). Firms that are below this size limit, in other words microcap stocks, may be more difficult to use for relative valuation purposes. Even if these firms are public, they may receive less coverage from research analysts, who typically are more interested in companies that are large, liquid, and already owned by institutional investors.4

3By contrast, in an example of how to assess a small wine producer, the proposed universe of comparables consisted of 15 “beverage firms,” including both small and large caps, and covering specialists in beer, wine, and soft drink production. Arguably, some of these are unlikely to be very similar to the proposed target of analysis. (Aswath Damodaran, Chapter 7 in Damodaran on Valuation: Security Analysis for Investment and Corporate Finance, 2nd edition, New York: John Wiley & Sons, 2006.) 4Ravi Bhushan, “Firm Characteristics and Analyst Following,” Journal of Accounting and Economics 11, nos. 2–3 (1989): 255–274.

Relative Valuation Methods for Equity Analysis 109

Conversely, it can also be difficult to perform relative value analysis on companies with relatively high market capitalization. Many large firms are dominant players in their particular market niches, in which case they may be more likely to trade at a premium reflecting their higher degree of mar- ket power. Alternatively, large firms may be effectively a conglomerate of numerous smaller entities, each engaged in a specific activity, and there may be no other large or small firm that produces an approximately equivalent blend of goods and/or services.

When attempting to assess the relative value of firms that are large and/ or complex, it can often be useful to assess “relative value” using two sepa- rate approaches. The first approach is to consider the firm as a complete entity, and trying to find other firms that are at least somewhat comparable in terms of size and complexity, even if their business mix is not precisely identical. In such cases, it can often be useful to consider similar firms that may be located in other countries, even though their different geographical positioning may affect their level of risk and thus the multiples at which they trade. The second approach, as already mentioned, is to use a sum-of-the- parts valuation method.

Geography and Clientele

Differences related to geographic location can affect the extent to which companies can be viewed as broadly similar. For instance, in the U.S. public utilities are predominantly regulated at the state level, and the public utility commissions in one state may operate quite differently from their counter- parts elsewhere. Consequently, a public utility operating in one state may not be directly comparable with a public utility located in another state. In recent decades, there has been a wave of acquisition activity in the U.S. utility industry, so that there are now some utilities that have operations in multiple states. In such instances, the valuation placed on a utility will pre- sumably incorporate investors’ perceptions of the regulatory environment affecting each of its state-level operations. For relative value purposes, a group of multistate public utilities may not be very similar to a public utility that is operating in only one state.

Regional differences in regulatory regimes may only affect a subset of companies. However, firms in the same industry may well have quite differ- ent client bases and geographic exposures. For instance, one retailer may aim to sell a wide range of goods to a mass-market client base at the regional or national level, while another retailer might instead focus on selling a lim- ited number of luxury products to the most affluent members of the global population. These two firms are likely to have substantially different prod- uct quality, cost bases, profit margins, and sensitivity to macroeconomic

110 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

conditions. In particular, retailers of luxury goods to a global client base may have developed brands that transcend national borders, and a high proportion of their current and future revenues and profits may come from outside their home country. Under such conditions, it is possible that a suit- able universe of comparable companies might include at least a few foreign firms, particularly if they have similarly broad geographic reach.

In past decades, analysts focusing on U.S. firms would probably have only rarely used foreign firms in their analysis of “comparable companies.” However, as both U.S. and foreign firms have become increasingly global- ized, and as accounting standards around the world have gradually started to become more similar, we believe that for some types of relative value analysis, there may be benefits to including firms that are generally compa- rable in terms of size and product mix, even if their legal headquarters are not located in the United States.5

Many companies have “depositary receipts” in other markets, such as ADRs. Consensus estimates may be available for a firm’s local results and/ or its depositary receipts. The estimates for the depositary receipts may be affected by actual or expected movements between the currencies of the two countries, which may bias the analysis. We therefore recommend that when calculating figures for companies that are listed in different countries, all multiples should be consistently calculated in terms of local currency throughout, in order to ensure that anticipated or historical currency fluc- tuations will not affect the results.

Sector and Industry Characteristics

Some academic research has examined different ways of selecting a universe of comparable firms. Bhojraj, Lee, and Oler compared the effect of using four different industry classification methods, and concluded that at least for a universe of U.S. securities, the Global Industry Classification Standard (jointly developed and maintained by Standard & Poor’s and Morgan Stan- ley Capital International) appeared to do the best job of identifying firms with similar valuation multiples and stock price movements.6 Chan, Lakon- ishok, and Swaminathan compared the effect of using industry classifica- tion schemes with statistically-based clustering approaches, and found that examining stocks in terms of industry membership seemed to give better

5For more insight into these issues, see Chapter 18 in Tom Copeland, Tim Koller, and Jack Murrin, Valuation: Measuring and Managing the Value of Companies, 3rd edition (New York: John Wiley & Sons, 2000). 6Sanjeev Bhojraj, Charles M.C. Lee, and Derek K. Oler, “What’s My Line? A Com- parison of Industry Classification Schemes for Capital Market Research,” Journal of Accounting Research 41, no. 5 (2003): 745–774.

Relative Valuation Methods for Equity Analysis 111

explanatory power than working in terms of either sectors or sub-indus- tries.7 To our knowledge, there have not been any parallel investigations into the effectiveness of different industry classification schemes for cross- national analysis. The results of Phylaktis and Xia suggest that the impor- tance of sector-level effects has been increasing in recent years, while the influence of country-level effects has waned slightly.8

Technology and Intra-Industry Diversity

As discussed above, some academic research has suggested that firms from similar industries tend to trade at similar multiples, and to experience simi- lar stock price movements. Industry membership therefore would seem to be a useful starting point for analysis. Thus, for instance, trucking companies and railroad companies both provide transportation services, but railroads will generally trade at different multiples from trucking companies because their cost structure and balance sheets tend to be quite different.

In some cases, there can be substantial variation even within a par- ticular sub-industry. For instance, “publishing” covers a wide variety of different business models, including daily newspapers, weekly magazines, publishers of textbooks and professional journals, printers of fiction and nonfiction books, and suppliers of financial data. Each of these individual industries is likely to have different sources of revenue, different technologi- cal requirements, different cost structures, and different rates of expected growth. Admittedly, the larger publishing houses may have operations span- ning several different fields, but the relative contributions of each division to the firm’s overall revenues and profits may differ substantially. In such instances, relative value analysis may result in a wide range of valuation multiples, possibly with several different clusters reflecting each firm’s com- petitive position. We consider such difficulties in the next section.

There are also some industries in which technological differences are the principal basis on which relative values are assigned. For instance, small companies in the field of biotechnology may have only a handful of prod- ucts, each of which could potentially be a great success or a dismal failure. Some companies of this type may be still at the prerevenue stage when they go public, so that their valuation is entirely based on the market’s expec- tations about the ultimate value of technology that has not yet generated

7Louis K. C. Chan, Josef Lakonishok, and Bhaskaran Swaminathan, “Industry Clas- sifications and Return Comovement,” Financial Analysts Journal 63, no. 6 (2007): 56–70. 8Kate Phylaktis and Lichuan Xia, “The Changing Roles of Industry and Country Effects in the Global Equity Markets,” European Journal of Finance 12, no. 8 (2006): 627–648.

112 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

actual sales. In such instances, relative value analysis might require par- ticularly careful selection of companies that are truly comparable in terms of the market’s perception of their stage of development and the likelihood that their key products will ultimately be successful. Arguably, relative value analysis in such cases may not generate particularly useful results because the spread of potential outcomes is so broad.

Bimodal and Multimodal Patterns

Sometimes the outcome of a relative value analysis will show that the valu- ation multiples are not evenly spread between low and high, but instead are bimodal or multimodal—in other words, if there seem to be two or more clusters of results. We show an example of this in our hypothetical example below, which suggests that in a universe of seven firms, two are expected to achieve a return on equity (ROE) of 11% to 12% in FY0 and FY1, whereas the other companies are generally projected to deliver ROE of 8% to 9%. Such differences may appear relatively minor, but if the market really does expect these outcomes, then the two companies with higher profitability may legitimately be expected to trade at a premium to their peers.

When a relative valuation table appears to have bimodal or multimodal characteristics, an analyst will generally be well advised to investigate further. In any given sector or industry, there may well be some firms that are truly capable of producing higher returns than their peers, perhaps as a result of better management, a stronger market position, or a more supportive regula- tory environment. Relative valuation methods can identify potential outliers of this type, but cannot test whether the estimates themselves are reasonable.

One potentially useful approach is to extend the analysis further back into the past, using historical prices for valuation purposes, and if possible also using as-was projections for the relevant period. Such projections are now widely available from various different data vendors, including Bloom- berg, FactSet, and Thomson Reuters. Consider the companies that are cur- rently trading at a premium or a discount to their peers—did they also trade at a discount to their peers in the past? A logical extension of relative value analysis based on a single period is to gauge whether a particular firm per- sistently tends to trade at a lower or higher multiple than its peers, and then assess whether its current multiple is above or below what would be expected on the basis of prior periods. Damodaran notes that relative valu- ations frequently have low persistence over time: for industries in which this is the case, then relative valuation methods may indeed provide useful investment signals.9

9Damodaran, Damodaran on Valuation: Security Analysis for Investment and Cor- porate Finance, p. 244.

Relative Valuation Methods for Equity Analysis 113

Choice of Valuation Multiples

Many relative valuation methods compare a company’s share price with some measure of its performance, such as earnings per share (EPS) or free cash flow per share. Other relative valuation methods compare a company’s share price with some measure of its size, such as book value per share. Block has reported that the majority of practitioners consider that when analyzing securities, measures of earnings and cash flow are somewhat more important than measures of book value or dividends.10 However, many practitioners will make use of various metrics in their work, in the expectation that the dif- ferent multiples will provide varying perspectives. Liu, Nissim, and Thomas compared the efficacy of six different metrics for relative valuations of U.S. firms on a universe-wide basis.11 They subsequently extended the analysis to seven different metrics applied to 10 different countries and multiple in- dustries.12 Hooke presents an example using eight different metrics applied to the single industry of temporary staffing companies.13 In a hypothetical example below, we use three different metrics for relative valuation analysis, and we believe that most practitioners would consider that between three and six different metrics is probably justifiable. It is certainly possible to have a much larger number of metrics,14 but the results may be harder to interpret.

A ratio such as price–earnings can be calculated in terms of share price or EPS, or alternatively can be interpreted as market cap or net income. For most purposes, these two ratios will be the same. However, share issuance or buyback activity may impair the comparability of figures expressed in terms of EPS. If there is any possibility of ambiguity, then we would gener- ally recommend using market cap or net income.

For instance, a company may currently have 100 million shares out- standing, a current share price of $40, and expected earnings of $2 in FY0 and $3 in FY1. If the P/E ratio is calculated in terms of price or EPS, then the FY0 ratio is 20 and the FY1 ratio is 13.3. However, analysts may be expecting that the company will buy back and cancel 20% of its shares dur- ing FY1. If so, then the projected net income in FY1 would presumably be

10Stanley B. Block, “A Study of Financial Analysts: Practice and Theory,” Financial Analysts Journal 55, no. 4 (1999): 86–95. 11Jing Liu, Doron Nissim, and Jacob Thomas, “Equity Valuation Using Multiples,” Journal of Accounting Research 40, no. 1 (2002): 135–172. 12Jing Liu, Doron Nissim, and Jacob Thomas, “Is Cash Flow King in Valuations?” Financial Analysts Journal 63, no. 2 (2007): 56–68. 13See Chapter 15 in Jeffrey Hooke, Security Analysis on Wall Street: A Comprehensive Guide to Today’s Valuation Methods, 2nd edition (Hoboken, NJ: John Wiley & Sons, 2010). 14Damodaran, Damodaran on Valuation: Security Analysis for Investment and Cor- porate Finance, p. 650.

114 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

$240 million rather than $300 million. If the P/E ratio is calculated using market cap and net income, then the FY1 ratio would be 16.7 rather than 13.3. This hypothetical example indicates the importance of ensuring that the denominator is being calculated on a basis that reflects the historical or projected situation for the relevant period. (An investor might consider that if a firm’s management is indeed strongly committed to buying back its own shares, then this might indicate that the firm’s management views the shares as being undervalued. However, such considerations would presumably be included as a qualitative overlay to the relative valuation analysis.)

Choice of Numerator: Market Cap vs. Firm Value

In some instances, the choice of numerator may have a significant impact on the multiple. For instance, many analysts will use price–sales ratios for valuation purposes. However, a firm’s revenues are generated from the total of its capital base, comprising both equity and debt.

Consider two companies, A and B, which both have a current market cap of $300 million, and projected annual revenues of $600 million in FY0, so that they both have a current price/sales ratio of 2. But suppose that Company A has no outstanding borrowings, whereas Company B has net debt of $300 million. One could argue that Company B is actually rather less attractive than Company A, as apparently it requires twice as much capital to generate the same volume of sales. In effect, analyzing the com- pany in terms of “firm value/sales” rather than price/sales would reveal that Company B is making less efficient use of its capital than Company A.

There is no single definition of “firm value” that is generally accepted by all practitioners. In an ideal world, one would want to have the market value of the firm’s equity capital and of the firm’s debt capital. However, because corporate bonds and bank loans typically are not traded in liquid markets, there may not be any reliable indicator of the market value of debt capital. Consequently, it is conventional to use market capitalization to estimate how investors are valuing the firm’s equity capital, but then to use figures from the firm’s most recent balance sheet together with the notes to the financial statements as a proxy for net debt. The broadest definition of which we are aware is the following:

Net debt = Total short-term debt + Total long-term debt + Minority interest + Unfunded pension liabilities – Cash and equivalents

In practice, for most firms, the biggest components of net debt are likely to be total short-term debt, total long-term debt, and cash and equivalents.

Relative Valuation Methods for Equity Analysis 115

In most cases, using an alternative definition of firm value will often have only a small impact on the calculated multiple.

Conceptually, it is possible to divide the income statement between the line items that are generated on the basis of total capital, and those that per- tain solely to equity capital. For most firms, the separator between these two categories is net interest expense or net interest income. Analyzing relative valuation for banks and insurance companies can be somewhat more com- plex, as discussed in Copeland, Koller, and Murrin.15 Generally speaking, it is usually desirable that the numerator and denominator of a valuation metric should be consistent with each other.16

Industry-Specific Multiples

Analysts covering some industries may make use of information that is spe- cific to that industry, such as paid miles flown for airlines, same-store sales for retailers, or revenue per available room for hotel chains. Such data can provide insights into how the market is valuing individual firms’ historical or expected operating performance. However, we consider that they should be viewed as a supplement to other multiples, rather than as a replacement for them, because it can be difficult to reconcile a company’s operating per- formance with its financial results, and also because there may be little or no intuition about what would be a “reasonable” estimate for long-run valuation levels.17 Natural resource producers tend to be valued in terms of both their operating efficiency and the resources that they control, so it may be useful to include some measure of their reserves in the analysis.18 Many practitioners make use of efficiency metrics when using relative valuation approaches to assess some types of banks and other lending institutions.19

HYPOTHETICAL EXAMPLE

Suppose that an analyst is seeking to gauge whether Company A is attrac- tive or unattractive, on the basis of relative valuation methods. Suppose that the analyst has determined that there are six other listed companies in

15See Chapters 21 and 22 in Copeland, Koller, and Murrin, Valuation: Measuring and Managing the Value of Companies. 16Damodaran, Damodaran on Valuation: Security Analysis for Investment and Cor- porate Finance, pp. 239–240. 17Ibid., pp. 237–238. 18See Chapter 21 in Hooke, Security Analysis on Wall Street: A Comprehensive Guide to Today’s Valuation Methods. 19See Chapter 22 in Hooke, Security Analysis on Wall Street: A Comprehensive Guide to Today’s Valuation Methods.

116 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 4.1 Hypothetical Relative Valuation Results

Share Price

Market Cap P/E P/FCF P/B

Company ($) ($m) FY0 FY1 FY0 FY1 FY0 FY1

A 20.00 400 12.0 10.0 8.5 7.0 1.30 1.20

B 16.00 550 11.5 11.5 5.0 6.0 1.00 0.95

C 40.00 500 13.0 12.0 8.0 7.5 1.50 1.40

D 15.00 450 12.5 12.0 8.0 7.0 1.10 1.05

E 13.00 350 14.5 13.0 9.0 8.0 1.25 1.15

F 30.00 350 12.5 12.5 7.0 4.5 1.15 1.15

G 15.00 300 15.0 14.0 7.0 6.0 1.20 1.15

Median 400 12.75 12.25 7.50 6.50 1.18 1.15

Standard Deviation 98.3 1.33 0.89 1.37 1.26 0.17 0.15

A versus median 0% –6% –18% 13% 8% 11% 4%

Notes: P/E refers to price–earnings before extraordinary items; P/B refers to price–book value; P/FCF refers to price–free cash flow (defined as earnings before extraordinary items plus noncash items taken from the cash flow statement); FY0 refers to the current fiscal year; FY1 refers to the next fiscal year; figures for FY0 and FY1 could have been derived from consensus sell-side estimates or other sources.

the same industry that are approximately the same size and comparable in terms of product mix, client base, and geographical focus.20 Based on this information, the analyst can calculate some potentially useful multiples for all seven companies. A hypothetical table of such results is shown in Exhibit 4.1. (For the purposes of this simple hypothetical example, we are assuming that all the firms have the same fiscal year. We consider calendarization later in this chapter.)

In this hypothetical scenario, Company A is being compared to compa- nies B through G, and, therefore, Company A should be excluded from the calculation of median and standard deviation, to avoid double-counting. The median is used because it tends to be less influenced by outliers than the statistical mean, so it is likely to be a better estimate for the central tendency. (Similarly, the standard deviation can be strongly influenced by outliers, and it would be possible to use “median absolute deviation” as a more robust 20For further examples using real firms and actual figures, see Chapters 7 and 8 in Damodaran, Damodaran on Valuation: Security Analysis for Investment and Cor- porate Finance, and Chapter 15 in Hooke, Security Analysis on Wall Street: A Com- prehensive Guide to Today’s Valuation Methods.

Relative Valuation Methods for Equity Analysis 117

way of gauging the spread around the central tendency. Such approaches may be particularly appropriate when the data contains one or a hand- ful of extreme outliers for certain metrics, which might be associated with company-specific idiosyncrasies.) Exhibit 4.1 has been arranged in terms of market cap, from largest to smallest, which can sometimes reveal patterns associated with larger or smaller firms, though there don’t appear to be any particularly obvious trends in this particular set of hypothetical numbers.

Exhibit 4.1 suggests that the chosen universe of comparable companies may be reasonably similar to Company A in several important respects. In terms of size, Companies B, C, and D are slightly larger, while Companies E, F, and G are slightly smaller, but the median market cap across the six firms is the same as Company A’s current valuation. In terms of P/E ratios, Company A looks slightly cheap in terms of FY0 earnings and somewhat cheaper in terms of FY1 earnings. In terms of P/FCF ratios, Company A looks somewhat expensive in terms of FY0 free cash flow, but only slightly expensive in terms of FY1 free cash flow. And finally, in terms of P/B ratios, Company A looks somewhat expensive in terms of FY0 book value, but roughly in line with its peers in terms of FY1 book value.

Analysis of the Hypothetical Example

So what are the implications of these results? Firstly, Company A looks rela- tively cheap compared to its peer group in terms of P/E ratios, particularly in terms of its FY1 multiples. Secondly, Company A looks rather expensive compared to its peer group in terms of P/FCF and P/B ratios, particularly in terms of FY0 figures. If an analyst were focusing solely on P/E, then Com- pany A would look cheap compared with the peer group, and this might suggest that Company A could be an attractive investment opportunity.

However, the analyst might be concerned that Company A looks com- paratively cheap in terms of P/E, but somewhat expensive in terms of price– book value. One way to investigate this apparent anomaly is to focus on ROE, which is defined as earnings–book value. Using the data in Exhibit 4.1, it is possible to calculate the ROE for Company A and for the other six companies, by dividing the P/B ratio by the P/E ratio—because this effectively cancels out the “price” components, and thus will generate an estimated value for EPS divided by book value per share, which is one way to calculate ROE.

The results suggest that Company A is expected to deliver an ROE of 10.8% in FY0 and 12% in FY1, whereas the median ROE of the other six firms is 8.7% in FY0 and 8.8% in FY1. Most of the comparable companies are expected to achieve ROE of between 8% and 9% in both FY0 and FY1, though apparently Company C is expected to achieve ROE of 11.5% in FY0 and 11.7% in FY1. (A similar analysis can be conducted using “free

118 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

cash flow to equity,” which involves dividing the P/B ratio by the P/FCF ratio. This indicates that Company A is slightly below the median of Com- panies B through G in FY0, but in line with its six peers during FY1.)

These results suggest that Company A is expected to deliver an ROE that is substantially higher than most of its peers. Suppose that an analyst is skeptical that Company A really can deliver such a strong performance, and instead hypothesizes that Company A’s ROE during FY0 and FY1 may only be in line with the median ROE for the peer group in each year. Based on the figures in Exhibit 4.1, Company A’s book value in FY0 is expected to be $15.38, and the company is projected to deliver $1.67 of earnings. Now suppose that Company A’s book value remains the same, but that its ROE during FY0 is only 8.7%, which is equal to the median for its peers. Then the implied earnings during FY0 would only be $1.35, and the “true” P/E for Company A in FY0 would be 14.9, well above the peer median of 12.75.

The analysis can be extended a little further, from FY0 to FY1. The figures in Exhibit 4.1 suggest that Company A’s book value in FY1 will be $16.67, and that the company will generate $2.00 of earnings during FY1. But if Company A only produced $1.35 of earnings during FY0, rather than the table’s expectation of $1.67, then the projected FY1 book value may be too high. A quick way to estimate Company A’s book value in FY1 is to use a “clean surplus” analysis, using the following equation:

Book FY1 = Book FY0 + Net income FY1 – Dividends FY1

Based on the figures in Exhibit 4.1, Company A is expected to have earnings of $1.67 during FY0, and $2.00 during FY1. The implied book value per share is $15.38 in FY0, and $16.67 during FY1. According to the clean surplus formula, Company A is expected to pay a dividend of $0.38 per share in FY1.

Assuming that the true earnings in FY0 are indeed $1.35 rather than $1.67, and that the dividend payable in FY1 is still $0.38, then the expected book value for Company A in FY1 would be $16.35 rather than $16.67. Taking this figure and applying the median FY1 peer ROE, the expected FY1 earnings for Company A would be $1.42 rather than $2.00, and conse- quently the “true” P/E for FY1 would be 13.9 instead of the figure of 10.0 shown in Exhibit 4.1. At those levels, the stock would presumably no longer appear cheap by comparison with its peer group. Indeed, Company A’s FY1 P/E multiple would be roughly in line with Company G, which has the high- est FY1 P/E multiple among the comparable companies.

This quick analysis therefore suggests that the analyst may want to focus on why Company A is expected to deliver FY0 and FY1 ROE, which is at or close to the top of its peer group. As noted previously, Company A

Relative Valuation Methods for Equity Analysis 119

and Company C are apparently expected to have ROE, which is substan- tially stronger than the other comparable companies. Is there something special about Companies A and C that would justify such an expectation? Conversely, is it possible that the estimates for Companies A and C are reasonable, but that the projected ROE for the other companies is too pessi- mistic? If the latter scenario is valid, then it’s possible that the P/E ratios for some of the other companies in the comparable universe are too high, and thus that those firms could be attractively valued at current levels.

Other Potential Issues

Multiples Involving Low or Negative Numbers

It is conventional to calculate valuation multiples with the market valuation as the numerator, and the firms’ financial or operating data as the denomi- nator. If the denominator is close to zero, or negative, then the valuation multiple may be very large or negative. The simplest example of such prob- lems might involve a company’s earnings. Consider a company with a share price of $10 and projected earnings of $0.10 for next year. Such a company is effectively trading at a P/E of 100. If consensus estimates turn more bear- ish, and the company’s earnings next year are expected to be minus $0.05, the company will now be trading at a P/E of –200.

It is also possible for a firm to have negative shareholders’ equity, which would indicate that the total value of its liabilities exceeds the value of its assets. According to a normal understanding of accounting data, this would indicate that the company is insolvent. However, some companies have been able to continue operating under such circumstances, and even to retain a stock exchange listing. Firms with negative shareholders’ equity will also have a negative price–book multiple. (In principle, a firm can even report negative net revenues during a particular period, though this would require some rather unusual circumstances. One would normally expect few firms to report negative revenues for more than a single quarter.)

As noted previously, averages and standard deviations tend to be rather sensitive to outliers, which is one reason to favor using the median and the median absolute deviation instead. But during economic recessions at the national or global level, many companies may have low or negative earnings. Similarly, firms in cyclical industries will often go through periods when sales or profits are unusually low, by comparison with their average levels through a complete business cycle. Under such circumstances, an ana- lyst may prefer not to focus on conventional metrics such as price–earnings, but instead to use line items from higher up the income statement that will typically be less likely to generate negative numbers.

120 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Calendarization

Some of the firms involved in the relative valuation analysis may have fiscal years that end on different months. Most analyst estimates are based on a firm’s own reporting cycle. It is usually desirable to ensure that all valuation multiples are being calculated on a consistent basis, so that calendar-based effects are not driving the analysis.

One way to ensure that all valuation multiples are directly comparable is to calendarize the figures. Consider a situation where at the start of Janu- ary, an analyst is creating a valuation analysis for one firm whose fiscal year ends in June, while the other firms in the universe have fiscal years that end in December. Calendarizing the results for the June-end firm will require taking half of the projected number for FY0, and adding half of the projected number for FY1. (If quarter-by-quarter estimates are available, then more precise adjustments can be implemented by combining 3QFY0, 4QFY0, 1QFY1, and 2QFY1.)

Calendarization is conceptually simple, but may require some care in implementation during the course of a year. One would expect that after a company has reported results for a full fiscal year, the year defined as “FY0” would immediately shift forward 12 months. However, analysts and data aggregators may not change the definitions of “FY0” and “FY1” for a few days or weeks. In case of doubt, it may be worth looking at individual esti- mates in order to double-check that the correct set of numbers is being used.

Sum-of-the-Parts Analysis

When attempting to use relative valuation methods on firms with multiple lines of business, the analyst may not be able to identify any company that is directly similar on all dimensions. In such instances, relative valuation methods can be extended to encompass “sum-of-the-parts” analysis, which considers each part of a business separately, and attempts to value them individually by reference to companies that are mainly or solely in one par- ticular line of business.21

Relative valuation analysis based on sum-of-the-parts approaches will involve the same challenges as were described above—identifying a suitable universe of companies that are engaged in each particular industry, collect- ing and collating the necessary data, and then using the results to gauge what might be a “fair value” for each of the individual lines of business. But in addition to these considerations, there is an additional difficulty that is specific to sum-of-the-parts analysis. This problem is whether to apply a “conglomerate discount,” and if so how much. 21See Chapter 18 in Hooke, Security Analysis on Wall Street: A Comprehensive Guide to Today’s Valuation Methods.

Relative Valuation Methods for Equity Analysis 121

Much financial theory assumes that all else equal, investors are likely to prefer to invest in companies that are engaged in a single line of business, rather than to invest in conglomerates that have operations across multiple industries. Investing in a conglomerate effectively means being exposed to all of that conglomerate’s operations, and the overall mix of industry expo- sures might not mimic the portfolio that the investor would have chosen if it were possible instead to put money into individual companies.

A possible counterargument might be that a conglomerate with strong and decisive central control may achieve synergies with regard to revenues, costs or taxation would not be available to individual free-standing firms dealing at arms’ length with each other. A skeptical investor might wonder, on the other hand, about whether the potential positive impact of such syner- gies may be partly or wholly undermined by the negative impacts of central- ized decision making, transfer pricing, and regulatory or reputational risk.

For these reasons, an analyst might consider that it is reasonable to apply a discount to the overall value that emerges from the “sum of the parts.” Some practitioners favor a discount of somewhere between 5% and 15%, for the reasons given earlier. Academic research on spinoffs has sug- gested that the combined value of the surviving entity and the spun-off firm tends to rise by an average of around 6%, though with a wide range of variation.22 (Some analysts have suggested that in some particular contexts, for instance in markets where competent managers are very scarce, then investors should be willing to pay a premium for being able to invest in a conglomerate that is fortunate enough to have such executives. However, this appears not to be a mainstream view.)

Relative Valuation vs. DCF: A Comparison

Relative valuation methods can generally be implemented fairly fast, and the underlying information necessary to calculate can also be updated quickly. Even with the various complexities discussed above, an experienced analyst can usually create a relative valuation table within an hour or two. And the calculated valuation multiples can adjust as market conditions and relative prices change. In both respects, relative valuation methods have an advan- tage over DCF models, which may require hours or days of work to build or update, and that require the analyst to provide multiple judgment-based inputs about unknowable future events. Moreover, as noted by Baker and Ruback, if a DCF model is extended to encompass multiple possible scenar- ios, it may end up generating a range of “fair value” prices that is too wide

22See Timothy R. Burch and Vikram Nanda, “Divisional Diversity and the Conglomerate Discount: Evidence from Spinoffs,” Journal of Financial Economics, 70, no. 1 (2003): 69–98.

122 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

to provide much insight into whether the potential investment is attractive at its current valuation.23

Relative valuation methods focus on how much a company is worth to a minority shareholder, in other words an investor who will have limited or zero ability to influence the company’s management or its strategy. Such an approach is suitable for investors who intend to purchase only a small percentage of the company’s shares, and to hold those shares until the valu- ation multiple moves from being “cheap” to being “in line” or “expensive” compared with the peer group. As noted above, relative valuation methods make no attempt to determine what is the “correct” price for a company’s shares, but instead focuses on trying to determine whether a company looks attractive or unattractive by comparison with other firms that appear to be approximately similar in terms of size, geography, industry, and other parameters.

DCF methods attempt to determine how much a company is worth in terms of “fair value” over a long time horizon. DCF methods can readily incorporate a range of assumptions about decisions in the near future or the distant future, and therefore can provide a range of different scenarios. For this reason, most academics and practitioners consider that DCF methods are likely to produce greater insight than relative valuation methods into the various forces that may affect the fair value for a business. More specifi- cally, DCF methods can be more applicable to situations where an investor will seek to influence a company’s future direction—perhaps as an activist investor pushing management in new directions, or possibly as a bidder for a controlling stake in the firm. In such situations, relative valuation analysis is unlikely to provide much insight because the investor will actually be seeking to affect the company’s valuation multiples directly, by affecting the value of the denominator.

Nevertheless, even where an analyst favors the use of DCF approaches, we consider that relative valuation methods can still be valuable as a “san- ity check” on the output from a DCF-based valuation. An analyst can take the expected valuation from the DCF model, and compare it with the pro- jected values for net income, shareholders’ equity, operating cash flow, and similar metrics. These ratios drawn from the DCF modeling process can then be compared with the multiples for a universe of similar firms. If the multiples that are generated by the analyst’s DCF model are approximately comparable with the multiples that can be derived for similar companies already being publicly traded, then the analyst may conclude that the DCF model’s assumptions appear to be reasonable. However, if the multiples from the analyst’s model appear to diverge considerably from the available information concerning valuation multiples for apparently similar firms, 23Baker and Ruback, Estimating Industry Multiples.

Relative Valuation Methods for Equity Analysis 123

then it may be a good idea to reexamine the model, rechecking whether the underlying assumptions are truly justifiable.

Relative valuation methods can also be useful in another way when con- structing DCF models. Most DCF models include a “terminal value” that represents the expected future value of the business, discounted back to the present, from all periods subsequent to the ones for which the analyst has developed explicit estimates. One way to calculate this terminal value is in terms of a perpetual growth rate, but the choice of a particular growth rate can be difficult to justify on the basis of the firm’s current characteristics. An alternative approach is to take current valuation multiples for similar firms, and use those values as multiples for terminal value.24

KEY POINTS

■ Relative valuation methods tend to receive less attention from academ- ics than DCF approaches, but such methods are widely used by prac- titioners. If relative valuation approaches suggest that a company is cheap on some metrics but expensive on others, this may indicate that the market views that company as being an outlier for some reason, and an analyst will probably want to investigate further.

■ Choosing an appropriate group of comparable companies is perhaps the most challenging aspect of relative valuation analysis. Where possi- ble, an analyst should seek to identify 6 to 12 companies that are similar in terms of risk characteristics, perhaps with attention to criteria such as size, geography, and industry. If this is not possible, then an analyst should feel free to relax one or more of these parameters in order to obtain a usable universe.

■ Determining an appropriate set of valuation multiples is also important. Calculating a single set of multiples is likely to provide fewer insights than using several different metrics that span multiple time periods. It is conventional to use consensus estimates of future financial and operat- ing performance, as these presumably represent the market’s collective opinion of each firm’s prospects.

■ Most relative valuation analysis is performed using standard multiples such as price–earnings or firm value–sales. Under some conditions, using industry-specific multiples can be valuable, though there may be fewer consensus estimates for such data, and there may also be less intuition about what is the “fair” price for such ratios.

24See Damodaran, Damodaran on Valuation: Security Analysis for Investment and Corporate Finance, pp. 143–144.

124 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

■ Relative valuation methods are particularly useful for investors who aim to take minority stakes in individual companies when they are “cheap” relative to their peers, and then sell those stakes when the companies become “expensive.” Such methods are likely to be less directly useful for investors who will seek to influence a company’s management, or who aim to take a controlling stake in a company. For such investors, DCF methods are likely to be more applicable.

QUESTIONS

1. Applying relative valuation approaches is typically more challenging for very small or very large companies. Why?

2. Historical results for the financial and operating performance of listed companies are readily available. Getting reasonable numbers for fore- cast performance is typically more difficult, and sometimes impossible. Why not rely solely on historical numbers?

3. Consensus forecasts do not incorporate the unique insights into each company that are available from our in-house expert. Why not use our own internal estimates, rather than consensus numbers?

4. Many analysts favor the use of industry-specific multiples for relative valuation purposes. What are some notable examples, and what advan- tages or disadvantages might be associated with using such metrics?

5. Relative valuation approaches can be used for sum-of-the-parts analy- sis, but many practitioners will apply a “conglomerate discount” to the results of such analysis. Why do they do so, and what is the normal range applied?

125

CHAPTER 5 Valuation over the Cycle and the

Distribution of Returns* Anders Ersbak Bang Nielsen, Ph.D.

Portfolio Strategist Goldman Sachs International

Peter C. Oppenheimer Chief Global Equity Strategist Goldman Sachs International

There is substantial empirical evidence that valuation is a good predictor of returns over the long run.1 Put simply, as intuition would suggest, buy- ing an equity market when the valuation multiples are low, and the dividend yield and required equity risk premium are high, typically generates much better future returns than if buying an equity market when the opposite holds. However, while valuation today provides a great deal of information about future expected returns, it tells us nothing about how these returns should be distributed over time. Are they evenly distributed over several years, or are the returns bunched into short periods of time? What, if any- thing, determines the way that these returns are generated?

Historical observation suggests that the answer to this questions can be found in the relationship between valuation, earnings, and the economic cycle. For example, during periods when investors are expecting the onset of recession and falling profits, returns to shareholders deteriorate as a result both of declining expectations about the near term prospects for profits as 1See the discussion in John Y. Campbell, “Estimating the Equity Premium,” NBER Working Paper 13423 (2007), and the references therein for the arguments on both sides of this debate.

*We would like to thank Hanyi Lim and Matthieu Walterspiler for research assistance for the analysis used in this chapter.

126 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

well as a result of lower valuations attached to future expected cash flows. The opposite tends to occur at the peak of the cycle when investors are more confident. By contrast, at the trough of the equity market cycle, typi- cally during recessions when profits remain depressed, the initial recovery is virtually always driven by rising valuations as investors anticipate future profit recovery. The observation that valuations and returns shift over the economic cycle suggests that any practical analysis of valuation should also take into account these important relationships.

In this chapter, we first show that the price–earnings (P/E) multiple exhibits both cyclical and lower frequency fluctuations. We then look at the theoretical drivers of the P/E multiple, how a typical equity market cycle evolves in terms of earnings growth, valuation and returns, and how this evolution is related to the economic cycle. In addition to looking at aggre- gated data through history, we also look at the performance of different asset classes and investment styles over the equity market cycle. Finally, we suggest how to adjust valuation analysis to take into account the cyclical fluctuations in valuation that we have documented.

THE LINK BETWEEN EARNINGS AND RETURNS

The P/E multiple that investors put on current earnings when valuing them, as well as other commonly used valuation metrics, shift significantly over time. Exhibit 5.1 shows the U.S. trailing P/E multiple since 1871. As can be seen, there is both a cyclical component to the changes in the multiple as well as movements at lower frequencies. The P/E multiple stayed below long term averages for most of the 1970s and above for a big part of the 1990s.

There are many potential reasons for these movements in the P/E ratio. One way to think about these drivers is to use a simple dividend discount model (DDM) with constant growth rates to measure the fair value of the market. In such a model, we have that

P PO E G

R ERP

PO E

R ERP

t

f t

i f

= × × + + +

= ×

+ −=

∞

∑ 0 1

11

1

( )

( ) GG (5.1)

where P is the theoretical market price, E0 is the level of earnings over the last year, E1 is the level of earnings over the next year, PO is the payout ra- tio, Rf is the nominal risk-free interest rate, ERP is the equity risk premium, and G is the nominal growth rate.

Dividing through by E gives

P E

PO R ERP Gf

= + −

Use of Options in Portfolio Management 127

EXHIBIT 5.1 The P/E Multiple has both Cyclical and Lower Frequency Movements

0

5

10

15

20

25

30

35

40

45

50

1871 1881 1891 1901 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001 2011

S&P 500

Trailing P/E Average P/E

Note: P/E was above 50 between Dec 2008–Sept 2009, peaking at 123.7 in May 2009 due to cyclically low earnings.

Source: Robert Shillers long run data series on the U.S. stock market.

Therefore, changes in the P/E multiple over time could arise from changes in payout ratios, interest rates, the equity risk premium and expec- tations of long-run growth. Changes in the equity risk premium and long- run growth assumptions are particularly hard to account for as they are not directly observable.

The cyclical fluctuations in the P/E multiple shown in Exhibit 5.1 means that there is not a direct translation from earnings growth into returns over shorter horizons, even though the mean reversion of the P/E multiple over longer horizons implies that earnings growth is the principal driver of equity market performance in the long run. In reality, earnings growth is only paid for to a very limited extent when it occurs.

To better understand the relationship between earnings and returns, we take a descriptive approach. We show that the equity market moves in cycles. Each of the five cycles from one peak of the market to the next since 1973 can be divided into four distinct phases, each with its own economic context and drivers of stock market returns.

The four phases are illustrated in Exhibit 5.2. We identify the phases of each cycle by determining the extent to which equity price performance is driven by actual profit growth and by “expectations” about future growth, measured as changes in the 12 month trailing P/E multiple. We look at broad market indexes for the United States, continental Europe, and the United Kingdom. The four phases we define are:

128 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

1. The Despair phase is defined as the period where the market moves from its peak to its trough. This correction is mainly driven by P/E mul- tiple contraction as the market anticipates and reacts to a deteriorat- ing macroeconomic environment and its implications in terms of lower future earnings.

2. The Hope phase is typically a short period (on average nine months in the United States), where the market rebounds from its trough through multiple expansion. This occurs in anticipation of a forthcoming trough in the economic cycle as well as future profit growth and is leading to a local peak in the trailing P/E multiple. We define the end of the Hope phase as this local peak of the trailing P/E multiple. It occurs when earn- ings are typically depressed or falling and often begins in the late stages of a recession.

3. The “Growth phase” is a typically longer period (on average 34 months), where earnings growth drives returns. We define the end of this period to be when multiple expansion again starts to provide a larger proportion of the returns than earnings growth.

EXHIBIT 5.2 Diagram of the Phases

4. Optimism P/E multiple grows faster than earnings -Expectation extrapolated -Second best return, 24.9% -Poor earnings growth, –1.9%

1. Despair Market moves from peak to trough -Expectations are disappointed -Worst return, –32.9% -Poor earnings growth, –0.2%

3. Growth Earnings grow faster than the P/E multiple -Reality catches up to expectations -Second lowest return, –1.2% -Strong earnings growth, 12.6%

Cycle of the Equity Market for the United States (all growth rates are annualized averages)

Volatility increases

Volatility decreases

2. Hope P/E multiple expands -Expectation of a better future -Highest return, 50.9% -Poor earnings growth, –6.0%

Use of Options in Portfolio Management 129

4. The Optimism phase is the final part of the cycle, where returns driven by P/E multiple expansion outpace earnings growth, thereby setting the stage for the next market correction.

This pattern shows up in every single cycle in the United States, United Kingdom, and continental Europe since the early 1970s. As an example of how the phases in the market can be identified Exhibit 5.3 shows the performance of the U.S. market from its peak in March 2000 to its peak in October 2007.

The returns line shows the real price performance indexed to 100 at the peak of the market when the new cycle begins. The Despair phase starts at the peak and ends when the returns line troughs in October 2002. The end of the Hope phase is identified by the PE line, which measures the 12 month trailing PE, again indexed to 100 at the peak of the market. The PE rises during the Hope phase, and the end of the Hope phase is defined as the local peak in this line.

The Hope phase is followed by the Growth phase. The end of this phase is defined as the peak in the Earnings/(P/E) line. This is the ratio of the Earn- ings and the P/E line multiplied by 100. While this line is less intuitive at first glance, it is interesting because the change in the line over a period of time measures the contribution to returns from earnings growth compared to the contribution to returns from P/E expansion. If earnings contribute more to the return over this period of time than multiple expansion the line goes up.

EXHIBIT 5.3 Derivation of the Phases in the 2000–2007 Cycle in the United States

0

50

100

150

200

250

300

350

40

60

80

100

120

140

160

180

200

220

240

Mar-00 Mar-01 Mar-02 Mar-03 Mar-04 Mar-05 Mar-06 Mar-07

U.S. Recessions Returns Earnings PE Earnings/ PE (RHS)

Cumulative Change <-------------Despair----------> <-----------------Growth---------------><Hope> <Optimism>

Data sources: Compustat and Haver Analytics.

130 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Otherwise it goes down. We define the start of the Optimism phase as the point, where a larger part of the return starts to be due to multiple expan- sion rather than earnings growth and therefore as the point where the Earn- ings/(P/E) line peaks. Here we ignore the short “blip” up in the Earnings/PE line in March 2007, as it is above the levels reached in July 2006 for just five days, and there is a clear fall in the line both before and after those five days.

Nielsen and Oppenheimer2 shows similar diagrams for all the cycles in the United States, continental Europe, and the United Kingdom. Here we just show the average return for each phase in the cycle for these three mar- kets in Exhibit 5.4. Appendix A shows the dates and returns for each phase in the three markets used to calculate the averages.

The framework demonstrates that the relationship between earnings growth and price performance changes systematically over the cycle. While earnings growth is what fuels equity market performance over the very long run (because the P/E multiple tends to mean revert), most of the earnings growth is not paid for when it occurs but rather when it is correctly antici- pated by investors in the Hope phase, and when investors get overly opti- mistic about the potential for future growth during the Optimism phase.

As can be seen from the exhibits, the situation is particularly extreme in the United States, where the quarterly reporting frequency of earnings makes it possible to make a more accurate separation of which part of

2Anders E. B. Nielsen and Peter Oppenheimer, “The Equity Cycle Part 1: Identifying the Phases,” Goldman Sachs European Portfolio Strategy, 2009.

EXHIBIT 5.4 Average Earnings Growth, P/E Expansion, and Return by Phase United States

–40

–20

0

20

40

60

80 Real earnings growth (%) Average P/E multiple expansion (%) Real price returns (%)

16 months 9 months 34 months 24 months

Despair Hope Growth Optimism

–0.2%

24.9%

–1.9%

–12.0%–32.9%

–1.2%

26.6

–6.0%

12.6%

–32.1%

58.6% 50.9%

Use of Options in Portfolio Management 131

the return is due to earnings growth and which part is due to P/E multiple expansion. Here, on average over the last five cycles, all the earnings growth has occurred during the growth phase, yet, the real price returns in that phase have been slightly negative.

EXHIBIT 5.4 (Continued) Europe (excluding United Kingdom)

–30

–20

–10

0

10

20

30

40

50

60 Real earnings growth (%) Average P/E multiple expansion (%) Real price returns (%)

26 months

Despair Hope Growth Optimism

–24.9%

–7.3%

51.2%

0.7%

10.9%

22.5% 27.1 %

24.2%

–19%

50.2%

–9.5%

2.3%

14 months33 months10 months

United Kingdom

–40

–30

–20

–10

0

10

20

30

40

50

60 Real earnings growth (%) Average P/E multiple expansion (%) Real price returns (%)

21 months

Despair Hope Growth Optimism

–7.5% –2.1%

45.3%

3.0%

19.8%

28.0 % 25.3%

–29.3%

34.3%

–14.0%

2.2%

–30.8%

17 months27 months17 months

Data sources: Compustat, Worldscope, Datastream, and Haver Analytics.

132 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 5.5 The Market Rise from Through to Peak (The proportion of total across the three phases that falls in each phase)

Phase Hope Growth Optimism

United States

Average length (in months) 9.3 34.1 24.1 Real earnings growth (%) –5.3 109.7 –4.3 P/E expansion (%) 35.6 –5.7 70.1

Real price return (%) 32.3 –1.3 69.0

Europe (excluding United Kingdom)

Average length (in months) 9.9 32.5 14.3 Real earnings growth (%) 0.2 98.8 1.0 P/E expansion (%) 69.9 –11.8 41.9

Real price return (%) 42.2 28.4 29.4

United Kingdom

Average length (in months) 17.1 27.5 16.7 Real earnings growth (%) –6.5 104.0 2.5 P/E expansion (%) 81.6 –5.1 23.5

Real price return (%) 58.8 3.3 37.9

Data sources: Compustat, Worldscope, Datastream, and Haver Analytics.

It is not surprising that the market rises in expectation of future earn- ings growth and that a part of the earnings growth in the Growth phase is therefore paid for during the Hope phase. But the degree to which price returns and earnings growth is separated is surprising. Almost the entire earnings growth for each region occurs during the growth phase, yet only –1%, 28%, and 3% of the index real price return from the trough to the peak of the market accumulates during that phase for the United States, Europe, and the United Kingdom respectively (Exhibit 5.5).

In terms of returns, the highest annualized returns occur during the Hope phase, followed by the Optimism phase, the Growth phase, and finally the Despair phase. This has been true in every cycle in the United States and holds in all regions on average.

THE PHASES CAN BE INTERPRETED IN RELATIONSHIP TO THE ECONOMY

The pattern in the way the equity market values earnings over the cycle documented in the previous section is far from arbitrary. The Nielsen and

Use of Options in Portfolio Management 133

Oppenheimer study mentioned earlier, shows that the phases in the equity market are linked to the underlying macroeconomy. This allows for a clear- er interpretation of the phases and can help to identify when the market is moving from one phase to the next. This section covers these results.

We first look at investors real forward looking return requirements on investment. In the valuation model in equation (5.1), this would be the nom- inal risk free rate plus the equity risk premium minus expected inflation. This variable is interesting as it measures the real hurdle rate for investment in the stock market.

As mentioned above this is not directly observable, but we measure this Real Required Return (RRR) as the 10-year nominal government bond yield, plus a measure of the Equity Risk Premium that we will discuss further below, minus five-year average historical inflation as a measure of inflation expectations. This measure of the RRR generally increases in the Despair phase, decreases in the Hope and Optimism phases and is somewhat mixed in the Growth phase. Exhibit 5.6 shows the change in the RRR from the beginning to the end of each phase for each of the regions we consider.

EXHIBIT 5.6 Change in the RRR in Each Phase United States

Cycles Despair Hope Growth Optimism

Nov. 1980–Aug. 1987 NA –1.7 1.5 –2.8 Aug. 1987–Jun. 1990 1.6 –0.5 0.3 –0.9 Jun. 1990–Mar. 2000 0.8 –1.3 –0.3 –1.9

Mar. 2000–Oct. 2007 2.1 –0.5 0.2 –0.3

Average 1.5 –1.0 0.4 –1.4

Europe (excluding United Kingdom)

Cycles Despair Hope Growth Optimism

Oct. 1987–Jul. 1990 NA NA NA 0.1 Jul. 1990–Mar. 2000 2.5 –2.8 –1.2 –0.9

Mar. 2000–Jul. 2007 3.7 –0.9 –0.7 –0.3

Average 3.1 –1.9 –1.0 –0.3

United Kingdom

Cycles Despair Hope Growth Optimism

Jun. 1990–Mar. 2000 1.3 –2.0 0.5 –2.2

Mar. 2000–Oct. 2007 3.6 –0.6 –0.8 –0.2

Average 2.5 –1.3 –0.2 –1.2

134 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

We interpret the movements in investors’ forward-looking return requirements across the phases as follows:

■ During the Despair phase, investors get increasingly concerned about future prospects, and therefore require an increasingly high future expected return for holding equities. This reaction happens against a backdrop of an increase in volatility, an increase in the output gap and in four out of five cycles the start of a recession during this phase in the United States. This leads to lower P/E multiples and a falling market.

■ In the Hope phase, an end to the crisis starts to be visible and this vis- ibility caps the potential downside risk. Investors respond to the lower tail risk by accepting lower future expected returns. This drives up multiples and the market. While volatility is still high, it tends to fall towards the end of the Hope phase. In this phase investors essentially prepay for the expected recovery in earnings during the Growth phase.

■ In the beginning of the Growth phase, investors have been through a period with high volatility. This is likely to make investors perceive equities as more risky and therefore less attractive. Investors have also already been paid for expected future earnings growth during the Hope phase, but the growth has yet to materialize. The output gap typically peaks some time during the Hope phase, but remains very high at the beginning of the Growth phase. The onset of the Growth phase is therefore a reasonable point in time for investors to question long-run growth expectations.

These initial negatives tend to make investors less willing to pay for the earnings growth they see in the early stages of the Growth phase. This gives lower rates of return, which reinforces the negative picture of equities and makes investors less willing to pay for the improvements in fundamentals that they see on an ongoing basis. The result is that value in terms of expected future returns are rebuilt during the Growth phase in several cases, as earnings growth outpaces returns, and volatil- ity declines.

Another likely driver of the higher real return requirements in the equity market that are seen in many cases in this phase is the increase in the real yield which is seen in bond markets.

■ Eventually, in the Optimism phase, the built-up value becomes large enough to attract investors and to reverse the dynamic of poor returns keeping away investors despite strengthening fundamentals. In the Optimism phase, returns outpace earnings and expected future returns consequently decline. Towards the end of the phase volatility picks up as the sustainability of the high returns are being tested by the market.

Use of Options in Portfolio Management 135

Next, we look at the broader macroeconomic backdrop. While there are few conclusions that hold up in every single cycle in every single region, the broad patterns which hold most of the time identified in the Nielsen and Oppenheimer study are:

■ In the Despair phase, the economic environment deteriorates and the fall in the stock market is an early indicator of this: The output gap first rises but then begins to fall, as the economy weakens. Unemployment rises as well as initial claims. The Institute for Supply Management man- ufacturing survey (ISM) and the Markit Economics Purchasing Manag- ers Survey (PMI) indexes of manufacturing activity are falling. There are no robust patterns in the real bond yield. The RRR rises as investors demand higher compensation for future risk as described above.

■ In the Hope phase, economic indicators tend to reach their worst levels and the stock market rebounds in expectation of future improvements: The output gap continues to fall and normally troughs very close to the end of the Hope phase. Both unemployment and initial claims tend to peak in the Hope phase, but initial claims peak first. The ISM troughs. Volatility declines from the peak it reached at the initiation of the Hope phase. The real bond yield falls. The RRR falls as investors start to pay for expected future earnings growth.

■ In the Growth phase, the economy recovers but stock market perfor- mance is weaker: The output gap rises, often sharply as realized eco- nomic growth outpaces the long-run potential. The majority of the decline in the unemployment rate occurs in this phase and initial claims decline. The ISM normally peaks in this phase. Volatility continues its decline in the first part of the phase but starts to pick up again at the later stages of the phase. The real bond yield rises. The RRR often rises in the early parts of the phase but the results over the entire phase are mixed.

■ In the Optimism phase, the limits of the economy are tested and stock market performance is strong until the limit is found with the initiation of the next Despair phase: The behavior of the output gap is mixed. Unemployment continues to decline and initial claims level out. The ISM moderates from its peak in the Growth phase. Equity volatility continues the increase that began in the Growth phase. The real bond yield has a relatively flat profile and the RRR declines as stock market returns outpace earnings growth.

As an example of these developments the two charts in Exhibit 5.7 show the development of a number of macroeconomic indicators in the last cycle in the United States, which lasted from March 2000 to October

136 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

2007. Nielsen and Oppenheimer show similar charts for all the cycles in the United States, Continental Europe and the United Kingdom since 1973 to support the conclusions above.

In line with the general patterns described above, equity volatility increased during the Despair phase, peaked around the end of that phase and then gradually declined until some time towards the end of the Growth

EXHIBIT 5.7 Macroeconomic Backdrop for the 2000–2007 Cycle in the United States

0

10

20

30

40

50

60

70

–4

–3

–2

–1

0

1

2

3

4

5

6

Mar-00 Mar-01 Mar-02 Mar-03 Mar-04 Mar-05 Mar-06 Mar-07

Output gap Real interest rate Volatility (RHS) ISM (RHS)

%

250

300

350

400

450

500

3

3.5

4

4.5

5

5.5

6

6.5

7

Mar-00 Dec-00 Sep-01 Jun-02 Mar-03 Dec-03 Sep-04 Jun-05 Mar-06 Dec-06 Sep-07

Unemployment RRR Initial claims (RHS)

%

Data source: Haver Analytics.

Use of Options in Portfolio Management 137

phase at which point it started to pick up again. The output gap declined during the Despair phase, troughed close to the end of the Hope phase, improved dramatically during the Growth phase and remained flat from there. The ISM is less in line with the typical pattern, as it rises towards the end of the Despair phase. It does, however, have a local trough towards the end of the Hope phase, and its cycle peak in the Growth phase. The real bond yield falls a bit during the Hope phase and rises during the Growth phase after which it flattens out. Unemployment rose during the Despair and Hope phases, peaked at the end of the Hope phase, fell strongly dur- ing the Growth phase and was stable in the Optimism phase. Initial claims peaked before unemployment as is typically the case, but did so earlier than normal in the middle of the Despair phase. There was a second local peak in the Hope phase however, more in line with the typical experience. Finally the RRR was in line with the historical pattern.

ASSET CLASS PERFORMANCE VARIES ACROSS THE PHASES

The performance of other asset classes and investment styles also vary sys- tematically with the phases. Exhibit 5.8 shows annualized real total return for U.S. equities, bonds, and the S&P GS Commodity Index for each of the phases in all of the five cycles. The general conclusions are:

■ In the Despair phase a risk averse investor should own bonds, while a less risk averse investor should consider commodities. In this phase, bonds have always outperformed equities and commodities have out- performed equities in four out of five cases. The relative performance of bonds and commodities is more mixed, with commodities outperform- ing in three out of five cases. On a median basis, commodities have strongly outperformed bonds, but bonds are less risky with the worst annualized return being –3.7% as opposed to –20.2% for commodi- ties. It is not surprising that equities are the poorest performer, since the Despair phase is marked by the move from the peak to the trough of the equity market, but the analysis shows how large the potential is for outperformance by diversifying into other asset classes at this point in the cycle.

■ In the Hope phase, equities offer by far the best returns. In this phase there is a clear ranking of the asset classes. In all five cycles, equities outperform bonds and in four out of the five cycles, bonds in turn out- perform commodities.

■ In the Growth phase, commodities lead. Commodities outperformed both bonds and equities in four out of five cycles. On average commodities

138 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

outperformed bonds and equities by roughly 10% per annum whereas on a median basis the outperformance was around 3.5% per annum. Both equities and bonds perform poorly in this phase, with the relative ranking being somewhat unstable.

EXHIBIT 5.8 Asset Class Returns by Phase U.S. Equities

Despair Hope Growth Optimism

Jan. 1973–Nov. 1980 –34.8 65.2 –2.9 59.9

Nov. 1980–Aug. 1987 –18.6 83.7 –13.2 30.3

Aug. 1987–Jun. 1990 –77.7 93.4 –0.2 21.4

Jun. 1990–Mar. 2000 –48.7 32.2 9.1 27.6

Mar. 2000–Oct. 2007 –24.2 47.7 6.3 20.9

Average –40.8 64.5 –0.2 32.0

Median –34.8 65.2 –0.2 27.6

U.S. 10-year Treasuries

Despair Hope Growth Optimism

Jan. 1973–Nov. 1980 –3.7 0.2 –3.1 2.4

Nov. 1980–Aug. 1987 3.2 19.4 –0.3 10.4

Aug. 1987–Jun. 1990 1.6 13.1 0.2 5.9

Jun. 1990–Mar. 2000 –2.0 9.3 3.7 4.1

Mar. 2000–Oct. 2007 6.7 4.7 –0.3 3.9

Average 1.2 9.3 0.0 5.4

Median 1.6 9.3 –0.3 4.1

Commodities

Despair Hope Growth Optimism

Jan. 1973–Nov. 1980 –54.2 –27.7 1.5 41.0

Nov. 1980–Aug. 1987 –20.2 5.9 1.0 6.6

Aug. 1987–Jun. 1990 10.7 –1.5 25.8 17.5

Jun. 1990–Mar. 2000 221.1 –18.3 3.4 –1.9

Mar. 2000–Oct. 2007 2.6 18.2 17.8 –8.3

Average 53.7 –4.7 9.9 11.0

Median 10.7 –1.5 3.4 6.6

Data sources: Worldscope, Haver Analytics, and Datastream.

Use of Options in Portfolio Management 139

The general conclusions for asset classes together with the general con- clusions for style performance from another study by Nielsen and Oppen- heimer3 are summarized in Exhibit 5.9. The conclusions are general in the sense that most patterns are not true in every single cycle in all markets but rather hold in most of the cases.

Typically cyclical stocks underperform defensive stocks in the Despair phase and outperform in the Hope phase. This speaks to the beta-driven environment of those two phases. Later in the cycle this is less important and results are more mixed on this dimension. Small caps outperform large caps in the Hope phase, whereas large caps historically have outperformed towards the end of the cycle in the Optimism phase. As noted in academic literature value stocks tend to outperform growth stocks.4 This is particu- larly pronounced in the Growth phase, where it is true in every cycle and every market that were considered in the analysis. In line with the idea that investors in the Optimism phase extrapolate growth trends beyond what is sustainable, this is the only phase where growth stocks normally outperform.

INCORPORATING CYCLICALITY INTO VALUATIONS

The previous sections have described how valuations vary with the cycle and how those variations are tied to the macroeconomy. These variations imply that investors are not rewarded for most of the earnings growth when it occurs, but rather before it occurs during the Hope phase, and when in- vestors get overly optimistic about the future during the Optimism phase.

This section describes how to adjust valuation analysis to take this cyclicality into account in a quantified way. In our view, the long run growth assumptions for company profits and payout ratios should remain relatively stable over time as long as there are no big structural shifts in the growth rate of the underlying economy. This has been a reasonable assumption for both the United States and Europe over the last few decades, and we think it still remains so. If long run growth assumptions are relatively stable, interest rates and the equity risk premium become key drivers of fluctuations in the P/E multiple over time as shown in equation (5.1).

Interest rates are observable but the ERP is not. The fact that the ERP cannot be directly observed is an even bigger challenge for valuation when

3Anders E. B. Nielsen and Peter Oppenheimer, “The Equity Cycle Part 2: Investing in the Phases,” Goldman Sachs European Portfolio Strategy (2009). 4See, for example, Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance 47, no. 2 (1992): 427–465; and Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics 33, no. 1 (1993): 3–56.

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Use of Options in Portfolio Management 141

you accept that it is likely to change over time. Our recommended solution to this problem is to estimate the ERP by fixing the long run growth assump- tion and turning the Dividend Discount model on its head to calculate what risk premium is required at any given point in time, in order for the theoreti- cal value from that model to equal the observed market price.

Taking this approach and using a slightly more advanced dividend dis- count model than the one in equation (5.1), Daly, Nielsen, and Oppen- heimer5 estimate the time series path of the ERP shown in Exhibit 5.10 as the Market implied ERP. The exhibit shows that the market implied ERP is mean reverting and clearly fluctuates with the economic cycle. It rises around the U.S. economic recessions and then declines during prolonged economic expansions.

This dependency is formalised in Exhibit 5.11, which shows R-squareds from univariate regressions of the market implied ERP on a number of macroeconomic variables. The U.S. output gap alone (as measured using the congressional budget offices measure of potential output) explains 74% of the variation over time of the market implied ERP.

The tight link between macroeconomic variables and the market implied ERP, can be used to estimate where the ERP “should” be at a given point in time given the macroeconomic environment. This normative measure of the ERP is the macro-benchmarked ERP in Exhibit 5.10. It is the fitted value from a regression of the market implied ERP on the one quarter ahead out- put gap in the United States, the two-quarter ahead output gap in Europe (since the European economy is often lagging the United States a bit, yet the

5Kevin Daly, Anders E. B. Nielsen and Peter Oppenheimer, “Finding Fair Value in Global Equities: Part II—Forecasting Returns,” Journal of Portfolio Management 36, no. 3 (2010): 56–77.

EXHIBIT 5.10 U.S. Market Implied and Macro-Benchmarked ERP

–1 0 1 2 3 4 5 6 7 8

Jun-81

United States

Market implied ERP Macro-benchmarked ERP

Jun-08Jun-05Jun-02Jun-99Jun-96Jun-93Jun-90Jun-87Jun-84

Pe rc

en t

142 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

equity markets tend to trade together) and a four-quarter lag of the market implied ERP.

With the two measures of the ERP from Exhibit 5.10, it is possible to adjust valuation for the cycle. If the goal is to value a company relative to the market, it makes sense to use the market implied ERP and adjust it for the beta of the company when valuing the company. If, on the other hand, the goal is to value the company on an absolute basis, it makes more sense to use the macro-benchmarked ERP adjusted for beta, as that gives a mea- sure of the appropriate compensation for risk, based upon the state of the economy rather than current market prices. Finally, if the goal is to get a long run equilibrium measure of value, one should use the long run average market implied equity risk premium of approximately 3% together with an equilibrium interest rate on government bonds.

APPENDIX: DATES AND RETURNS OF THE PHASES

Returns, P/E expansion, and earnings growth rates are measured as annual- ized geometrical averages in all regions.

EXHIBIT 5.11 R2 from Univariate Regressions of the Market Implied ERP on Macro Variables

Sign R-Squared

Output gap – 74%

Unemployment + 58

Five-year core inflation + 30

Ten-year bond + 13

World GDP growth – 9

Government debt/GDP – 8

U.S. GDP growth – 5

Two-year bond + 5

Balance of payment + 1

ERP 1 quarter ago + 84

ERP 2 quarters ago + 64

ERP 3 quarters ago + 47

ERP 4 quarters ago + 34

Use of Options in Portfolio Management 143

United States

Phase Despair Hope Growth Optimism

1973–1980 Start date 11-Jan-73 03-Oct-74 15-Jul-75 27-Mar-80 End date 03-Oct-74 15-Jul-75 27-Mar-80 20-Nov-80 Length (in months) 20.7 9.4 56.4 7.8 Real earnings growth (%) 11.9 –19.5 7.1 –12.1 P/E expansion (%) –43.4 99.2 –13.3 78.6 Real price return (%) –36.6 60.3 –7.1 56.9

1980–1987 Start date 20-Nov-80 12-Aug-82 22-Jun-83 24-Jul-84 End date 12-Aug-82 22-Jun-83 24-Jul-84 25-Aug-87 Length (in months) 20.7 10.3 13.1 37.1 Real earnings growth (%) –9.3 –3.9 18.9 –6.6 P/E expansion (%) –15.7 83.9 –30.1 34.4 Real price return (%) –23.5 76.6 –16.9 25.5

1987–1990 Start date 25-Aug-87 04-Dec-87 17-Mar-88 03-Jan-89 End date 04-Dec-87 17-Mar-88 03-Jan-89 04-Jun-90 Length (in months) 3.3 3.4 9.6 17.0 Real earnings growth (%) 27.7 23.4 29.0 –10.8 P/E expansion (%) –82.9 52.8 –24.6 31.3 Real price return (%) –78.1 88.5 –2.7 17.1

1990–2000 Start date 04-Jun-90 11-Oct-90 15-Jan-92 24-Jul-96 End date 11-Oct-90 15-Jan-92 24-Jul-96 23-Mar-00 Length (in months) 4.2 15.2 54.3 44.0 Real earnings growth (%) 5.1 –14.2 13.4 7.5 P/E expansion (%) –51.5 47.7 –6.5 16.0 Real price return (%) –49.1 26.8 6.0 24.7

2000–2007 Start date 23-Mar-00 09-Oct-02 17-Jun-03 17-Jul-06 End date 09-Oct-02 17-Jun-03 17-Jul-06 09-Oct-07 Length (in months) 30.6 8.3 37.0 14.8 Real earnings growth (%) –4.8 15.2 14.1 0.1 P/E expansion (%) –21.4 26.0 –8.5 18.6 Real price return (%) –25.2 45.1 4.4 18.7

Data sources: Compustat and Haver Analytics.

144 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Europe (excluding United Kingdom)

Phase Despair Hope Growth Optimism

1973–1978 Start date 22-Mar-73 07-Oct-74 15-Apr-75 15-Jul-77 End date 07-Oct-74 15-Apr-75 15-Jul-77 20-Oct-78 Length (in months) 18.5 6.2 27.0 15.2 Real earnings growth (%) 12.3 2.4 19.3 –7.0 P/E expansion (%) –45.2 85.9 –11.5 18.4 Real price return (%) –38.5 90.4 5.6 10.1

1978–1987 Start date 20-Oct-78 17-Aug-82 01-Feb-84 01-Apr-85 End date 17-Aug-82 01-Feb-84 01-Apr-85 05-Oct-87 Length (in months) 45.9 17.5 14.0 30.1 Real earnings growth (%) –10.0 –0.4 32.6 3.6 P/E expansion (%) –3.0 36.6 –21.7 19.0 Real price return (%) –12.7 36.1 3.7 23.3

1987–1990 Start date 05-Oct-87 10-Nov-87 18-Mar-88 07-Nov-89 End date 10-Nov-87 18-Mar-88 07-Nov-89 18-Jul-90 Length (in months) 1.2 4.2 19.7 8.3 Real earnings growth (%) 2.9 –3.2 15.6 –12.0 P/E expansion (%) –98.6 59.5 –0.6 36.7 Real price return (%) –98.5 54.4 14.9 20.3

1990–2000 Start date 18-Jul-90 05-Oct-92 31-Jan-94 18-Oct-99 End date 05-Oct-92 31-Jan-94 18-Oct-99 06-Mar-00 Length (in months) 26.6 15.9 68.6 4.6 Real earnings growth (%) –11.5 –9.9 21.4 40.2 P/E expansion (%) –6.8 56.1 –7.3 74.8 Real price return (%) –17.6 40.7 12.4 145.1

2000–2007 Start date 06-Mar-00 12-Mar-03 03-Sep-03 13-Jun-06 End date 12-Mar-03 03-Sep-03 13-Jun-06 16-Jul-07 Length (in months) 36.2 5.8 33.3 13.1 Real earnings growth (%) –10.2 42.3 27.5 9.4 P/E expansion (%) –18.9 36.8 –11.5 21.0 Real price return (%) –27.1 94.8 12.8 32.4

Data sources: Worldscope, Datastream, and Haver Analytics.

Use of Options in Portfolio Management 145

United Kingdom

Phase Despair Hope Growth Optimism

1973–1979 Start date 10-Jan-73 12-Dec-74 30-Jan-76 09-Mar-78 End date 12-Dec-74 30-Jan-76 09-Mar-78 04-May-79 Length (in months) 23.0 13.6 25.3 13.8 Real earnings growth (%) 30.2 –41.6 11.4 –7.8 P/E expansion (%) –63.5 247.2 –16.2 36.1 Real price return (%) –52.5 102.6 –6.6 25.4

1979–1987 Start date 04-May-79 28-Sep-81 24-Jun-83 24-Sep-85 End date 28-Sep-81 24-Jun-83 24-Sep-85 16-Jul-87 Length (in months) 28.9 20.8 27.1 21.7 Real earnings growth (%) –4.9 0.5 20.3 6.5 P/E expansion (%) –9.1 27.1 –9.4 31.3 Real price return (%) –13.5 27.8 9.0 39.9

1987–1989 Start date 16-Jul-87 09-Nov-87 24-Jun-88 14-Dec-88 End date 09-Nov-87 24-Jun-88 14-Dec-88 05-Sep-89 Length (in months) 3.8 7.5 5.7 8.7 Real earnings growth (%) 1.0 3.9 35.1 –0.6 P/E expansion (%) –76.3 19.8 –37.3 45.9 Real price return (%) –76.1 24.5 –15.3 45.0

1989–1999 Start date 05-Sep-89 28-Sep-90 02-Feb-94 17-Dec-96 End date 28-Sep-90 02-Feb-94 17-Dec-96 30-Dec-99 Length (in months) 12.8 40.2 34.5 36.4 Real earnings growth (%) –6.7 –1.4 13.6 3.5 P/E expansion (%) –18.5 17.3 –11.1 13.3 Real price return (%) –23.9 15.7 1.0 17.3

1999–2007 Start date 30-Dec-99 12-Mar-03 18-Jun-03 14-Mar-07 End date 12-Mar-03 18-Jun-03 14-Mar-07 15-Jun-07 Length (in months) 38.4 3.2 44.9 3.1 Real earnings growth (%) –14.6 27.5 27.6 13.2 P/E expansion (%) –7.6 98.0 –14.2 31.7 Real price return (%) –21.1 152.5 9.5 49.2

Data sources: Worldscope, Datastream, and Haver Analytics.

146 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

KEY POINTS

■ Valuation multiples exhibit both cyclical and lower frequency fluctua- tions.

■ Some of the key drivers of the P/E multiple are interest rates, the equity risk premium, the payout ratio, and long term earnings growth.

■ The equity markets in the United States, continental Europe, and the United Kingdom have historically moved in cycles, each consisting of four phases.

■ On the path from the through to the peak of the market nearly all earnings growth occurs in the Growth phase on average, whereas only –1%, 28%, and 3% of the price return for the United States, continen- tal Europe, and the United Kingdom respectively occurs in this phase.

■ Between 32% and 59% of the return from through to peak occurs dur- ing the Hope phase despite its short duration and, typically declining earnings.

■ There is variation in the performance of asset classes and investment styles across these phases.

■ The market implied equity risk premium varies over time in a way that is tightly related to the output gaps of the economy at home and abroad.

■ We recommend that valuation analysis should adjust for the state of the economic cycle.

QUESTIONS

1. Identify four key drivers of the P/E multiple.

2. What has historically been the key driver of equity prices in the very long run?

3. a. What are the ranking of the phases in terms of average real price returns?

b. Which phase offers the highest average real earnings growth?

4. Which of the economic variables considered in the chapter explains most of the variation in the market implied equity risk premium?

5. What is the rational for adjusting valuation for the economic cycle?

147

CHAPTER 6 An Architecture for

Equity Portfolio Management Bruce I. Jacobs, Ph.D.

Principal Jacobs Levy Equity Management

Kenneth N. Levy, CFA Principal

Jacobs Levy Equity Management

Anyone who has ever built a house knows how important it is to start out with a sound architectural design. A sound design can help ensure that the end product will meet all the homeowner’s expectations—material, aesthetic, and financial. A bad architectural design, or no design, offers no such assurance and is likely to lead to poor decision making, unintended results, and cost overruns.

It is equally important in building an equity portfolio to start out with some framework that relates the raw materials—stocks—and the basic construction techniques—investment approaches—to the end product. An architecture of equity management that outlines the basic relationships between the raw investment material, investment approaches, potential rewards, and possible risks can provide a blueprint for investment decision making.

We provide such a blueprint in this chapter. A quick tour of this blue- print reveals the following building blocks—an all-encompassing core com- prising the whole investable universe (whether international or domestic) and its constituent style subsets of large-cap growth, large-cap value, and small-cap stocks. Investment approaches can also be roughly categorized into the following groups—passive, engineered (quantitative) active, or

148 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

traditional active, with risk generally increasing as one moves from passive to traditional. These basic approaches may be extended by various means, including dynamic trading across market subsets or combining long posi- tions with some degree of short selling. Understanding the market’s building blocks and the advantages and disadvantages of each investment approach can improve overall investment results.

ARCHITECTURAL BUILDING BLOCKS

Exhibit 6.1 provides a simple but fairly comprehensive view of the equity market.1 The heart of the structure, the core, represents the overall market. Theoretically, this would include all equity issues for the United States and other markets. In line with the practice of most equity managers, a broad- based equity index such as the S&P 500, or (even broader) the Russell 3000 or Wilshire 5000, may proxy for the aggregate U.S. market.

EXHIBIT 6.1 Equity Market Architectural Building Blocks

CORE

STYLE ROTATION

VA LU

E G

R O

W TH

SMALL CAP

1See Bruce I. Jacobs and Kenneth N. Levy, “How to Build a Better Equity Portfolio,” Pension Management (June 1996): 36–39.

An Architecture for Equity Portfolio Management 149

For both equity managers and their clients, the overall market repre- sents a natural and intuitive starting place. It is the ultimate selection pool for all equity strategies. Furthermore, the long-term returns offered by the U.S. equity market have historically outperformed alternative asset classes in the majority of multiyear periods. The aim of most institutional investors (even those that do not hold core investments per se) is to capture, or outdo, this equity return premium.

The core equity market can be broken down into subsets that comprise stocks with similar price behaviors—large-cap growth, large-cap value, and small-cap stocks. In Exhibit 6.1, the wedges circling the core represent these style subsets. The aggregate of the stocks forming the subsets equals the overall core market.

One advantage of viewing the market as a collection of subsets is the ability it confers upon the investor to mix and match. Instead of holding a core portfolio, for example, the investor can hold market subsets in market- like weights and receive returns and incur risks commensurate with those of the core. Alternatively, the investor can depart from core weights to pursue returns in excess of the core market return (at the expense, of course, of incremental risk). Investors who believe that small-cap stocks offer a higher return than the average market return, for example, can overweight that subset and underweight large-cap value and growth stocks.

Over time, different style subsets can offer differing relative payoffs as economic conditions change. As Exhibit 6.2 shows, small-cap stocks out- performed large-cap stocks by 60 percentage points or more in the rolling three-year periods ending in mid-1983 and by 45 to 55 percentage points in late 1993 and early 2006. But small-cap stocks underperformed by 20 to 40 percentage points in the rolling three-year periods between early 1986 and December 1991 and by as much as 80 percentage points in the first half of 1999. Exhibit 6.3 shows that large-cap growth stocks outperformed large-cap value stocks by over 90 percentage points in the rolling three-year period ending in March 2000 but underperformed by as much as 50 per- centage points in mid-2003.

Just as some investors attempt to time the market by buying into and selling out of equities in line with their expectations of overall market trends, investors can attempt to exploit the dynamism of style subsets by rotating their investments across different styles over time, in pursuit of profit oppor- tunities offered by one or another subset as market and economic conditions change.2 The curved lines connecting the style wedges in Exhibit 6.1 repre- sent this dynamic nature of the market.

2See Bruce I. Jacobs and Kenneth N. Levy, “High-Definition Style Rotation,” Journal of Investing 5, no. 3 (1996): 14–23.

150 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 6.2 Small-Cap Stocks Outperform Large-Cap in Some Periods and Underperform in Others

80%

60%

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0%

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Russell 2000 – Russell 1000

EXHIBIT 6.3 Large-Cap Growth Stocks Outperform Large-Cap Value in Some Periods and Underperform in Others

100%

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An Architecture for Equity Portfolio Management 151

EXHIBIT 6.4 Equity Investment Approaches

Risk

Traditional

Engineered

Passive

The equity core and its constituent style subsets constitute the basic building blocks—the equity selection universes—from which investors can construct their portfolios. Another important choice facing the investor, however, is the investment approach or approaches to apply to the selection universe. Exhibit 6.4 categorizes possible approaches into three groups— traditional, passive, and engineered. Each of these approaches can be char- acterized by an underlying investment philosophy and, very generally, by a level of risk relative to the underlying selection universe.

TRADITIONAL ACTIVE MANAGEMENT

Traditional investment managers focus on stock picking. In short, they hunt for individual securities that will perform well over the investment horizon. The search includes in-depth examinations of companies’ financial state- ments and investigations of company managements, product lines, facilities, and the like. Based on the findings of these inquiries, traditional managers determine whether a particular firm is a good buy or a better sell.

The search area for traditional investing may be wide—the equivalent of the equity core—and may include market timing that exploits the dyna- mism of the overall market. Because in-depth analyses of large numbers of securities are just not practical for any one manager, however, traditional managers tend to focus on subsets of the equity market. Some may hunt for above-average earnings growth (growth stocks), while others look to buy

152 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

future earnings streams cheaply (value stocks); still others beat the grasses off the trodden paths, in search of overlooked growth and/or value stocks (small-cap stocks). Traditional managers have thus fallen into the pursuit of growth, value, or small-cap styles.

Traditional managers often screen an initial universe of stocks based on some financial criteria, thereby selecting a relatively small list of stocks to be followed closely. Focusing on such a narrow list reduces the complexity of the analytical problem to human (that is, traditional) dimensions. Unfor- tunately, it may also introduce significant barriers to superior performance.

Exhibit 6.5 plots the combinations of breadth and depth of insights necessary to achieve a given investment return-risk level. Here, the breadth of insights may be understood as the number of independent insights—that is, the number of investment ideas or the number of stocks. The depth, or goodness, of insights is measured as the information coefficient—the correlation between the return forecasts made for stocks and their actual returns. Note that the goodness of the insights needed to produce the given return-risk ratio starts to increase dramatically as the number of insights falls below 100; the slope gets particularly steep as breadth falls below 50.

EXHIBIT 6.5 Combination of Breadth (Number) of Insights and Depth, or “Goodness,” of Insights Needed to Produce a Given Investment Return-Risk Ratioa

0.30

0.25

0.20

0.15

0.10

0.05

0.00

D ep

th (

IC )

0 50 100 150 200 250 300 350 400 450 500 Breadth (BR)

aThe plot is based on the relationship IR IC BR= , where IC is the information coefficient (the correlation between predicted and actual returns), BR is the number of independent insights, and IR is the ratio of annualized excess return to annualized residual risk (in this case, set equal to 1). Source: Richard C. Grinold, “The Fundamental Law of Active Management,” Jour- nal of Portfolio Management 15, no. 3 (1989): 30–37.

An Architecture for Equity Portfolio Management 153

Market timing strategies are particularly lacking in breadth, as an insight into the market’s direction provides only one investment decision. Quarterly timing would produce four “bets” a year—a level of diversification few investors would find acceptable. Furthermore, unless timing is done on a daily basis or the timer is prodigiously skilled, it would take a lifetime to determine whether the results of timing reflect genuine skill or mere chance.

Traditional investing in effect relies on the ability of in-depth research to supply information coefficients that are high enough to overcome the lack of breadth imposed by the approach’s fairly severe limitations on the number of securities that can be followed. As Exhibit 6.5 shows, however, the level of information coefficients required at such constricted breadth levels consti- tutes a considerable hurdle to superior performance. The insights from tradi- tional management must be very, very good to overcome the commensurate lack of breadth.

Furthermore, lack of breadth may also have detrimental effects on the depth of traditional insights. While reducing the range of inquiry makes trac- table the problem of stock selection via the labor-intensive methods of tradi- tional active management, it is also bound to result in potentially relevant (and profitable) information being left out. Surely, for example, the behavior of the growth stocks not followed by traditional growth managers—even the behavior of value stocks outside the growth subset—may contain information relevant to the pricing of those stocks that do constitute the reduced traditional universe.

Another inherent weakness of traditional investment approaches is their heavy reliance on subjective human judgments. An ever-growing body of research suggests that stock prices, as well as being moved by fundamen- tal information, are influenced by the psychology of investors. In particular, investors often appear to be under the influence of cognitive biases that cause them to err systematically in making investment decisions.3

Arrow, for example, finds that investors tend to overemphasize new information if it appears to be representative of a possible future event; thus, if investors perceive a firm’s management to be good, and the firm has recently enjoyed high earnings, they will tend to place more reliance on the higher than the lower earnings estimates provided by analysts.4 Shiller finds that investors are as susceptible as any other consumers to fads and fashions, bidding up prices of hot stocks and ignoring out-of-favor issues.5 We describe below four common cognitive errors to which investors may fall prey.

3See Daniel Kahneman, and Amos Tversky, “Prospect Theory: An Analysis of Deci- sions Under Risk,” Econometrica 47, no. 2 (1979): 263–292. 4See Kenneth J. Arrow, “Risk Perception in Psychology and Economics,” Economic Inquiry 20, no. 1 (1982): 1–8. 5See Robert J. Shiller, “Stock Prices and Social Dynamics,” Brookings Papers on Economic Activity 2 (1984): 457–510.

154 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Cognitive Errors

Loss Aversion: The “Better Not Take the Chance/What the Heck” Paradox

Investors exhibit risk-averse behavior with respect to potential gains: faced with a choice between (1) a sure gain of $3,000 and (2) an 80% chance of gaining $4,000 or a 20% chance of gaining nothing, most people choose the sure thing, even though the $3,000 is less than the expected value of the gamble, which is $3,200 (80% of $4,000). But investors are generally risk seeking when it comes to avoiding certain loss: faced with a choice between (1) a sure loss of $3,000 and (2) an 80% chance of losing $4,000 or a 20% chance of losing nothing, most people will opt to take a chance. It’s only human nature that the pain of loss exceeds the glee of gain, but putting hu- man nature in charge of investment decision making may lead to suboptimal results. Shirking risk leads to forgone gains. Pursuing risk in avoidance of loss may have even direr consequences (digging a deeper hole).

Endowment Effect: The “Pride in Ownership” Syndrome

The price people are willing to pay to acquire an object or service is often less than the price they would be willing to sell the identical object or service for if they owned it. Say you bought a stock last year and it’s quadrupled in price. If you won’t buy more because “it’s too expensive now,” you should sell it. If you won’t sell it because you were so brilliant when you bought it, you’re sacrificing returns for pride in ownership.

The Gambler’s Fallacy: “Hot Streaks, Empty Wallets”

Is it more likely that six tosses of a coin will come up HTTHTH or HHHTTT? Most people think the former sequence is more typical than the latter, but in truth both are equally likely products of randomness. In either case, the probability of the next flip of the coin turning up heads, or tails, is 50%. Market prices, too, will display patterns. It’s easy to interpret such patterns as persistent trends and tempting to trade on them. But if the latest hot streak is merely a mirage thrown up by random price movements, it will prove an unreliable guide to future performance.

Confirmation Bias: “Don’t Confuse Me with the Facts”

People search for and place more reliance upon evidence that confirms their preconceived notions, ignoring or devaluing evidence that refutes them. Four cards lie on a table, showing A, B, 2, and 3. What is the fewest number

An Architecture for Equity Portfolio Management 155

of cards you can turn over to confirm or refute that every card with a vowel on one side has an even number on the other side? Most people choose A, then 2. An odd number or a letter on the reverse of A would refute the conjecture. The 2, however, can merely confirm, not refute; the presence of a vowel on the reverse would confirm, but anything else would simply be immaterial. The correct choice is to turn A, 3, and B. A vowel on the reverse of 3 can refute, as can a vowel on the reverse of B. Investment approaches that do not have a method of systematically searching through all available evidence without prejudice, in order to find the exceptions that disprove their rules, may leave portfolios open to blindsiding and torpedo effects.

Investors who are susceptible to these biases will tend to take too little (or too much) risk, to hold on to an investment for too long, to see long- term trends where none exist, and to place too much reliance on informa- tion that confirms existing beliefs. As a result, the performances of their portfolios are likely to suffer.

The reliance of traditional investment management on the judgments of individual human minds makes for idiosyncrasies of habit that work to the detriment of investment discipline, and this is true at the level of the investment firm as well as the individual at the firm. It may be difficult to coordinate the individual mind-sets of all analysts, economists, investment officers, technicians, and traders, and this coordination is even harder to achieve when subjective standards for security analysis differ from individ- ual to individual.

Constructing Portfolios

The qualitative nature of the outcome of the traditional security evaluation process, together with the absence of a unifying framework, can give rise to problems when individual insights into securities’ performances are com- bined to construct a portfolio. However, on target an analyst’s buy or sell recommendations may be, they are difficult to translate into guidelines for portfolio construction. Portfolio optimization procedures require quantita- tive estimates of relevant parameters, not mere recommendations to buy, hold, or sell.

The traditional manager’s focus on stock picking and the resulting ad hoc nature of portfolio construction can lead to portfolios that are poorly defined in regard to their underlying selection universes. While any particu- lar manager’s portfolio return may be measured against the return on an index representative of an underlying equity core or style subset, that index does not serve as a benchmark in the sense of providing a guideline for port- folio risk. Traditional portfolios’ risk-return profiles may thus vary greatly relative to those of the underlying selection universe.

156 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

As a result, traditional portfolios are not necessarily congruent with the equity market’s basic building blocks. A traditional value manager, for example, may be averse to holding certain sectors, such as utilities. Not only will the portfolio’s returns suffer when utilities perform well, but the portfo- lio will suffer from a lack of integrity, of wholeness. Such a portfolio will not be representative of the whole value subset. Nor could it be combined with growth and small-cap portfolios to create a corelike holding.

Because the relationship between the overall equity market and tra- ditional managers’ style portfolios may be ambiguous, value and growth, small-cap and large-cap may not be mutually exclusive. Value portfolios may hold some growth stocks, or growth portfolios some value stocks. There is no assurance that a combination of style portfolios can offer a market-like or above-market return at market-like risk levels.

Because of their heavy reliance on human mind power and subjective judgment, traditional approaches to investment management tend to suffer from a lack of breadth, a lack of discipline, and a resulting lack of portfolio integrity. Traditional management, while it may serve as well as any other approach for picking individual stocks, suffers from severe limitations when it comes to constructing portfolios of stocks. Perhaps it is for this reason that traditionally managed portfolios have often failed to live up to expectations.

PASSIVE MANAGEMENT

The generally poor performance of traditional investment management ap- proaches helped to motivate the development, in the late 1960s and the 1970s, of new theories of stock price behavior. The efficient market hy- pothesis and random walk theory, the products of much research, offered a reason for the meager returns reaped by traditional investment managers: Stock prices effectively reflect all information in an efficient manner, ren- dering stock price movements random and unpredictable. Efficiency and randomness provided the motivation for passive investment management; advances in computing power provided the means.

Passive management aims to construct portfolios that will match the risk- return profiles of underlying market benchmarks. The benchmark may be core equity (as proxied by the S&P 500 or other broad index) or a style subset (as proxied by a large-cap growth, large-cap value, or small-cap index). Given the quantitative tools at its disposal, passive management can fine-tune the stock selection and portfolio construction problems in order to deliver portfolios that mimic very closely both the returns and risks of their chosen benchmarks.

Passive portfolios, unlike traditional portfolios, are disciplined. Any tendencies for passive managers to succumb to cognitive biases will be held

An Architecture for Equity Portfolio Management 157

in check by the exigencies of their stated goals—tracking the performances of their underlying benchmarks. Their success in this endeavor also means that the resulting portfolios will have integrity. A passive value portfolio will behave like its underlying selection universe, and a combination of passive style portfolios in market-like weights can be expected to offer a return close to the market’s return at a risk level close to the market’s. As the trading required to keep portfolios in line with underlying indexes is less than that required to beat the indexes, transaction costs for passive management are lower than those incurred by active investment approaches. As much of the stock selection and portfolio construction problem can be relegated to fast- acting computers, the management fees for passive management are also modest. For the same reason, the number of securities that can be covered by any given passive manager is virtually unlimited; all the stocks in the selection universe can be considered for portfolio inclusion.

Unlike traditional management, then, passive management offers great breadth. Breadth in this case doesn’t count for much, however, because pas- sive management is essentially insightless. Built on the premise that markets are efficient, hence market prices are random and unpredictable, passive management does not attempt to pursue or offer any return over the return on the relevant benchmark. Rather, its appeal lies in its ability to deliver the asset class return or to deliver the return of a style subset of the asset class. In practice, of course, trading costs and management fees, however modest, subtract from this performance.

An investor in pursuit of above-market returns may nevertheless be able to exploit passive management approaches via style subset selection and style rotation. That is, an investor who believes value stocks will outperform the overall market can choose to overweight a passive value portfolio in expectation of earning above-market (but not above-benchmark) returns. An investor with foresight into style performance can choose to rotate investments across different passive style portfolios as underlying economic and market conditions change.

ENGINEERED MANAGEMENT

Engineered management, based on quantitative techniques and methods, recognizes that markets are reasonably efficient in digesting information and that stock price movements in response to unanticipated news are large- ly random. It also recognizes, however, that significant, measurable pricing inefficiencies do exist, and it seeks to deliver incremental returns by mod- eling and exploiting these inefficiencies. In this endeavor, it applies to the same company fundamental and economic data used by traditional active

158 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

management many of the tools that fostered the development of passive management, including modern computing power, finance theory, and sta- tistical techniques, instruments that can extend the reaches (and discipline the vagaries) of the human mind.

Engineered approaches use quantitative methods to select stocks and construct portfolios that will have risk-return profiles similar to those of underlying equity benchmarks but offer incremental returns relative to those benchmarks, at appropriate incremental risk levels. The quantitative methods used may range from fairly straightforward to immensely intricate. In selecting stocks, for example, an engineered approach may use something as simple as a dividend discount model, or it may employ complex multi- variate models that aim to capture the complexities of the equity market.

The engineered selection process can deal with and benefit from as wide a selection universe as passive management. It can thus approach the invest- ment problem with an unbiased philosophy, unhampered, as is traditional management, by the need to reduce the equity universe to a tractable sub- set. At the same time, depending on the level of sophistication of the tools it chooses to use, engineered management can benefit from great depth of analysis, a depth similar to that of traditional approaches. Multivariate modeling, for example, can take into account the intricacies of stock price behavior, including variations in price responses across stocks of different industries, economic sectors, and styles.

Because engineered management affords both breadth and depth, the manager can choose a focal point from which to frame the equity mar- ket, without loss of important framing information. Analysis of a particular style subset, for example, can take advantage of information gleaned from the whole universe of securities, not just stocks of that particular style (or a subset of that style, as in traditional management). The increased breadth of inquiry should lead to improvements in portfolio performance compared with traditional style portfolios.

Engineering Portfolios

Engineered management utilizes all the information found relevant from an objective examination of the broad equity universe to arrive at numerical estimates for the expected returns and anticipated risks of the stocks in that universe. Unlike the subjective outcomes of traditional management, such numerical estimates are eminently suitable for portfolio construction via optimization techniques.6

6See Bruce I. Jacobs and Kenneth N. Levy, “Engineering Portfolios: A Unified Ap- proach,” Journal of Investing 4, no. 4 (1995): 8–14.

An Architecture for Equity Portfolio Management 159

The goal of optimization is to maximize portfolio return while tying portfolio risk to that of the underlying benchmark. The portfolio’s system- atic risk should match the risk of the benchmark. The portfolio’s residual risk should be no more than is justified by the expected incremental return. Risk control can be further refined by tailoring the optimization model so that it is consistent with the variables in the return estimation process.

The quantitative nature of the stock selection and portfolio construc- tion processes imposes discipline on engineered portfolios. With individual stocks defined by expected performance parameters, and portfolios opti- mized along those parameters to provide desired patterns of expected risk and return, engineered portfolios can be defined in terms of preset perfor- mance goals. Engineered managers have little leeway to stray from these performance mandates, hence are less likely than traditional managers to fall under the sway of cognitive errors. In fact, engineered strategies may be designed to exploit such biases as investor overreaction (leading to price reversals) or investor herding (leading to price trends).

The discipline of engineered management also helps to ensure portfolio integrity. The style subset portfolios of a given firm, for example, should be non-overlapping, and the style subset benchmarks should in the aggre- gate be inclusive of all stocks in the investor’s universe. Value portfolios should contain no growth stocks, nor growth portfolios any value stocks. The underlying benchmarks for value and growth portfolios, or large and small-cap portfolios, should aggregate to the equity core.

Engineering should reduce, relative to traditional management, portfolio return deviations from the underlying core or subset benchmark, while increas- ing expected returns relative to those available from passive approaches. While judicious stock selection can provide excess portfolio return over a passive benchmark, optimized portfolio construction offers control of portfolio risk.

Exhibit 6.6 compares the relative merits of traditional, passive, and engineered approaches to portfolio management. Traditional management offers depth, but strikes out with lack of breadth, susceptibility to cognitive errors, and lack of portfolio integrity. Passive management offers breadth,

EXHIBIT 6.6 Comparison of Equity Investment Approaches

  Traditional Passive Engineered

Depth of analysis Yes No Simple: no Complex: yes

Breadth of analysis No Yes Yes

Free of cognitive error No Yes Yes

Portfolio integrity No Yes Yes

160 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

freedom from cognitive error, and portfolio integrity, but no depth whatso- ever. Only engineered management has the ability to construct portfolios that benefit from both breadth and depth of analysis, are free of cognitive errors, and have structural integrity.

Meeting Client Needs

A broad-based, engineered approach offers investment managers the means to tailor portfolios for a wide variety of client needs. Consider, for example, a client that has no opinion about style subset performance, but believes that the equity market will continue to offer its average historical premium over alternative cash and bond investments. This client may choose to hold the market in the form of an engineered core portfolio that can deliver the all-important equity market premium (at the market’s risk level), plus the po- tential for some incremental return consistent with the residual risk incurred.

Alternatively, the client with a strong belief that value stocks will out- perform can choose from among several engineered solutions. An engi- neered portfolio can be designed to deliver a value benchmark–like return at a comparable risk level or to offer, at the cost of incremental risk, a return increment above the value benchmark. Traditional value portfolios cannot be designed to offer the same level of assurance of meeting these goals.

With engineered portfolios, the client also has the ability to fine-tune bets. For example, the client can weight a portfolio toward value stocks while retaining exposure to the overall market by placing some portion of the portfolio in core equity and the remainder in a value portfolio, or by placing some percentage in a growth portfolio and a larger percentage in a value portfolio. Exposures to the market and to its various subsets can be engineered. Again, traditional management can offer no assurance that a combination of style portfolios will offer the desired risk-return profile.

EXPANDING OPPORTUNITIES

The advantages of an engineered approach are perhaps best exploited by strategies that are not constrained to deliver a benchmark-like performance. An engineered style rotation strategy, for example, seeks to deliver returns in excess of the market’s return by forecasting style subset performance. Shift- ing investment weights aggressively among various style subsets as market and economic conditions evolve, style rotation takes advantage of the his- torical tendency of any given style to outperform the overall market in some periods and to underperform it in others. Such a strategy uses the entire selec- tion universe and offers potentially high returns at commensurate risk levels.

An Architecture for Equity Portfolio Management 161

Allowing short sales as an adjunct to an engineered strategy, whether that strategy utilizes core equity, a style subset, or style rotation, can fur- ther enhance return opportunities. While traditional management focuses on stock picking, the selection of “winning” securities, the breadth of engi- neered management allows for the consideration of “losers” as well as “winners.” With an engineered portfolio that allows shorting of losers, the manager can pursue potential mispricings without constraint, going long underpriced stocks and selling short overpriced stocks.

In markets in which short selling is not widespread, there are reasons to believe that shorting stocks can offer more opportunity than buying stocks. This is because restrictions on short selling do not permit investor pessimism to be as fully represented in prices as investor optimism. In such a market, the potential candidates for short sale may be less efficiently priced, hence offer greater return potential, than the potential candidates for purchase.7

Even if all stocks are equally efficiently priced, however, shorting can enhance performance by eliminating constraints on the implementation of investment insights. Consider, for example, that a security with a median market capitalization has a weighting of approximately 0.01% of the mar- ket’s capitalization. A manager who cannot short can underweight such a security by, at most, 0.01% relative to the market; this is achieved by not holding the security at all. Those who do not consider this unduly restrictive should consider that placing a like constraint on the maximum portfolio overweight would be equivalent to saying the manager could hold, at most, a 0.02% position in the stock, no matter how appetizing its expected return. Shorting allows the manager free rein in translating the insights gained from the stock selection process into portfolio performance.

Long-Short Portfolios

If security returns are symmetrically distributed about the underlying mar- ket return, there will be fully as many unattractive securities for short sale as there are attractive securities for purchase. Using optimization techniques, the manager can construct a portfolio that balances equal dollar amounts and equal systematic risks long and short. Such a long-short balance neutral- izes the risk (and return) of the underlying market. The portfolio’s return, which can be measured as the spread between the long and short returns, is solely reflective of the manager’s skill at stock selection.8

7See Bruce I. Jacobs and Kenneth N. Levy, “20 Myths about Long-Short,” Financial Analysts Journal 52, no. 5 (1996): 81–85. 8See Bruce I. Jacobs and Kenneth N. Levy, “The Long and Short on Long-Short,” Journal of Investing 6, no. 1 (1997): 73–86.

162 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Not only does such a market-neutral long-short portfolio neutralize underlying market risk, it offers improved control of residual risk relative even to an engineered long-only portfolio. For example, the long-only port- folio can control risk relative to the underlying benchmark only by con- verging toward the weightings of the benchmark’s stocks; these weights constrain portfolio composition. Balancing securities’ sensitivities long and short, however, eliminates risk relative to the underlying benchmark; bench- mark weights are thus not constraining. Furthermore, the market-neutral long-short portfolio can use offsetting long and short positions to fine-tune the portfolio’s residual risk.

In addition to enhanced return and improved risk control, an engi- neered long-short approach also offers clients added flexibility in asset allo- cation. A market-neutral long-short portfolio, for example, offers a return from security selection on top of a cash return (the interest received on the proceeds from the short sales). However, the long-short manager can also offer, or the client initiate, a market-neutral long-short portfolio com- bined with instruments (such as stock index futures) that provide exposure to the equity market as a whole. The resulting “equitized” portfolio will offer the market-neutral long-short portfolio’s security selection return and the equity market return. Choice of other available overlays can provide the return from security selection in combination with exposure to other asset classes, including foreign equity and bonds. The transportability of the long-short portfolio’s return offers clients the ability to take advantage of a manager’s security selection skills while determining independently the plan’s asset allocation mix.9

Enhanced active equity strategies such as 120-20 and 130-30 portfolios can provide investors with an even wider choice of risk-return trade-offs than long-only, market-neutral long-short, or equitized long-short portfo- lios can provide.10 Enhanced active equity portfolios have short positions equal to some percentage of capital (generally 20% or 30%, but possibly 100% or more) and an equal amount of leveraged long positions. The 9See Bruce I. Jacobs and Kenneth N. Levy, “Alpha Transport with Derivatives,” Journal of Portfolio Management 25, no. 5 (1999): 55–60. 10See Bruce I. Jacobs and Kenneth N. Levy, “Enhanced Active Equity Strategies: Relaxing the Long-Only Constraint in the Pursuit of Active Return,” Journal of Portfolio Management 32, no. 3 (2006): 45–55; Bruce I. Jacobs and Kenneth N. Levy, “20 Myths About Enhanced Active 120-20 Strategies,” Financial Analysts Journal 63, no. 4 (2007): 19–26; and Bruce I. Jacobs, Kenneth N. Levy, and David Starer, “On the Optimality of Long-Short Strategies,” Financial Analysts Journal 54, no. 3 (1998): 40–51. For a comparison of enhanced active strategies with equitized long-short strategies, see Bruce I. Jacobs and Kenneth N. Levy, “Enhanced Active Equity Portfolios Are Trim Equitized Long-Short Portfolios,” Journal of Portfolio Management 33, no. 4 (2007): 19–25.

An Architecture for Equity Portfolio Management 163

enhanced active portfolio retains full sensitivity to underlying market move- ments, participating fully in the equity market return. If the securities held long outperform the underlying benchmark and the securities sold short underperform the benchmark, the enhanced active portfolio will achieve a return higher than the return on the underlying benchmark (at a higher risk level). It can also be expected to outperform a long-only portfolio based on comparable insights, because relaxation of the short-selling constraint allows the enhanced active portfolio to achieve security underweights that a long-only portfolio cannot attain, while the ability to invest the proceeds from short sales in additional long positions allows the portfolio to achieve security overweights that an unleveraged long-only portfolio cannot attain.

THE RISK-RETURN CONTINUUM

The various approaches to investment management, as well as the selection universes that are the targets of such approaches, can be characterized gen- erally by distinct risk-return profiles. For example, in Exhibit 6.1, risk levels tend to increase as one moves from the core outward toward the dynamic view of the market; expected returns should also increase. Similarly, in Ex- hibit 6.4, risk can be perceived as increasing as one moves from passive in- vestment management out toward traditional active management; expected returns should also increase.

Where should the investor be along this continuum? The answer depends in part on the investor’s aversion to risk. The more risk-averse the investor, the closer to core/passive the portfolio should be, and the lower its risk and expected return. Investors who are totally averse to incurring residual risk (that is, departing from benchmark holdings and weights) should stick with passive approaches. They will thus be assured of receiving an equity market return at a market risk level. They will never beat the market.

Less risk-averse investors can make more use of style subsets (static or dynamic) and active (engineered or traditional) approaches. With the use of such subsets and such approaches, however, portfolio weights will shift away from overall equity market weights. The difference provides the opportunity for excess return, but it also creates residual risk. In this regard, engineered portfolios, which control risk relative to underlying benchmarks, have definite advantages over traditional portfolios.

The optimal level of residual risk for an investor will depend not only on the investor’s level of aversion to residual risk, but also on the manager’s skill. Skill can be measured as the manager’s information ratio, or IR, the ratio of annualized excess return to annualized residual risk. For example,

164 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

a manager that beats the benchmark by 2% per year, with 4% residual risk, has an IR of 2%/4%, or 0.5.

Grinold formulates the argument as follows:

ω λ * = IR

2

where ω* equals the optimal level of portfolio residual risk given the manag- er’s information ratio and the investor’s level of risk aversion, λ.11 Increases in the manager’s IR will increase the investor’s optimal level of residual risk and increases in the investor’s risk-aversion level will reduce it.

Exhibit 6.7 illustrates some of the trade-offs between residual risk and excess return for three levels of investor aversion to residual risk and two levels of manager skill.12 Here, the straight lines represent the hypothetical

11See Richard C. Grinold, “The Fundamental Law of Active Management,” Journal of Portfolio Management 15, no. 3 (1989): 30–37. 12See Bruce I. Jacobs and Kenneth N. Levy, “Residual Risk: How Much is Too Much?” Journal of Portfolio Management 22, no. 3 (1996): 10–16.

EXHIBIT 6.7 Risk and Return Change with Investor Risk and Manager Skill

10

9

8

7

6

5

4

3

2

1

0

E xc

es s

R et

ur n

(% )

0 1 2 3 4 5 6 7 8 9 10 Residual Risk (%)

P H.5

M.5

L.5

H1

M1

L1

IR = 1.0 IR = 0.5

An Architecture for Equity Portfolio Management 165

continuum of portfolios (defined by their residual risks and excess returns) that could be offered by a highly skilled manager with an IR of 1.0 and a good manager with an IR of 0.5. (In reality, no manager will offer a strategy for each possible risk–return combination. Furthermore, although IR is a linear function of residual risk when liquidity is unlimited and short sell- ing unrestricted, in the real world IR will begin to decline at high levels of residual risk.) The points H, M, and L represent the optimal portfolios for investors with high, medium, and low aversions to residual risk. The point at the origin, P, with zero excess return and zero residual risk, may be taken to be a passive strategy offering a return and a risk level identical to the benchmark’s.

Several important observations can be made from Exhibit 6.7. First, it is apparent that greater tolerance for risk (a lower risk-aversion level) allows the investor to choose a portfolio with a higher risk level that can offer a higher expected return. Second, the more highly skilled the manager, the higher the optimal level of portfolio residual risk, and the higher the port- folio’s expected excess return, whatever the investor’s risk-aversion level. In short, higher excess returns accrue to higher-risk portfolios and to higher-IR managers.

Within this framework, an investor who takes less than the optimal level of residual risk or who selects less than the best manager will sacrifice return. Exhibit 6.8, for example, shows the decrease in return and utility (U) that results when an investor overestimates risk aversion. Here, an investor with a highly skilled manager, who actually has a medium level of risk aversion (M1), chooses a portfolio suitable for an investor with a high level of risk aversion (H1). The investor give-up in return can be measured as the vertical distance between M1 and H1. In somewhat more sophisticated terms, the higher-risk portfolio corresponds to a certainty-equivalent return of 2.500% and the less risky portfolio to a certainty-equivalent return of 2.221%, so the investor who overestimates his or her level of risk aversion and therefore chooses a suboptimal portfolio sacrifices 0.279 percentage points.

Exhibit 6.9 illustrates the return give-up that results when an investor with medium risk aversion uses a less skilled manager (IR of 0.5) rather than a higher-skill manager (IR of 1.0). Here the give-up in certainty-equivalent return between portfolio M1 and portfolio M.5 amounts to 1.875 percentage points. Choice of manager can significantly affect portfolio return.

Suppose an investor finds a highly skilled manager (IR = 1), but that manager does not offer a portfolio with a risk level low enough to suit the investor’s high level of risk aversion. A less skilled (IR = 0.5) manager, how- ever, offers portfolios H.5 and M.5, which do provide about the right level of residual risk for this investor.

166 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 6.8 Sacrifice in Return from Overestimating Investor Risk Aversion

IR = 1.0 U = 2.500 U = 2.221

8

7

6

5

4

3

2

1

0 0 1 2 3 4 5 6 7 8

Residual Risk (%)

E xc

es s

R et

ur n

(% )

H1

M1

EXHIBIT 6.9 Sacrifice in Return from Using Less Skillful Manager

IR = 1.0 IR = 0.5 U = 2.500 U = 0.625

8

7

6

5

4

3

2

1

0 0 1 2 3 4 5 6 7 8

Residual Risk (%)

E xc

es s

R et

ur n

(% )

M.5

M1

An Architecture for Equity Portfolio Management 167

The investor might try to convince the IR = 1 manager to offer a lower- risk portfolio. If that fails, however, is the investor constrained to go with the less skilled manager? No. The investor can instead combine the highly skilled manager’s H1 portfolio with an investment in the passive benchmark portfolio P, reducing risk and return along the IR = 1 manager frontier. Such combination portfolios will offer a higher return than the portfolios of the less skilled manager, at a level of residual risk the investor can live with.

Finally, the manager’s investment approach may affect the investor’s optimal level of portfolio risk. Because engineered strategies control port- folio systematic and residual risk relative to the benchmark and take only compensated risks, they offer more assurance than traditional active strate- gies of achieving a return commensurate with the risk taken. Investors may feel more comfortable taking more risk with engineered portfolios, where risk and expected return are rigorously and explicitly assessed, than with traditional active portfolios.

THE ULTIMATE OBJECTIVE

The ultimate objective of investment management, of course, is to establish an investment structure that will, in the aggregate and over time, provide a return that compensates for the risk incurred, where the risk incurred is consistent with the investor’s risk tolerance. The objective may be the equity market’s return at the market’s risk level or the market return plus incre- mental returns commensurate with incremental risks incurred.

This may be accomplished by focusing on the core universe and a passive representation or by mixing universes (core and static subsets, for example) and approaches (e.g., passive with traditional active or engineered). What- ever the selection universe and investment approach chosen, success is more likely when investors start off knowing their risk-tolerance levels and their potential managers’ skill levels. The goal is to take no more risk than is compensated by expected return, but to take as much risk as risk-aversion level and manager skill allow.

Success is also more likely when equity architecture is taken into account. Without explicit ties between portfolios and the underlying mar- ket or market subsets (and thus between market subsets and the overall market), managers may be tempted to stray from their fold (core, value, or growth investing) in search of return. If value stocks are being punished, for example, an undisciplined value manager may be tempted to poach return from growth stock territory. An investor utilizing this manager can- not expect performance consistent with value stocks in general, nor can the investor combine this manager’s “value” portfolio with a growth portfolio

168 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

in the hopes of achieving an overall market return; the portfolio will instead be overweighted in growth stocks, and susceptible to the risk of growth stocks falling out of favor. The investor can mitigate the problem by balanc- ing non-benchmark-constrained, traditional portfolios with engineered or passive portfolios that offer benchmark accountability.

When investors set goals in terms of return only, with no regard to equity architecture, similar problems can arise. Consider an investor who hires active managers and instructs them to make money, with no regard to market sector or investment approach. Manager holdings may overlap to an extent that the overall portfolio becomes overdiversified and individual manager efforts are diluted. The investor may end up paying active fees and active transaction costs for essentially passive results.

Equity architecture provides a basic blueprint for relating equity invest- ment choices to their potential rewards and their risks. It can help investors construct portfolios that will meet their needs. First, however, the investor must determine what those needs are in terms of desire for return and tol- erance for risk. Then the investor can choose managers whose investment approaches and market focuses offer, overall, the greatest assurance of ful- filling those needs.

We believe that engineered management can provide the best match between client risk-return goals and investment results. An engineered approach that combines range with depth of inquiry can increase both the number and goodness of investment insights. As a result, engineered manage- ment offers better control of risk exposure than traditional active manage- ment and incremental returns relative to passive management, whether the selection universe is core equity, static style subsets, or dynamic style subsets.

KEY POINTS

■ The equity core and its constituent style subsets constitute the basic building blocks from which investors can construct their portfolios.

■ Investors must also decide between possible investment approaches— traditional, passive, and engineered—each of which can be character- ized by an underlying investment philosophy and a general level of risk.

■ Investment performance reflects both breadth of inquiry, the sheer num- ber of investment opportunities, and depth of analysis, the strength of investment insights.

■ Traditional management offers depth, but strikes out with lack of breadth, susceptibility to cognitive errors, and lack of portfolio integrity.

■ Passive management offers breadth, freedom from cognitive errors, and portfolio integrity, but no depth whatsoever.

An Architecture for Equity Portfolio Management 169

■ Engineered management has the ability to construct portfolios that benefit from both breadth and depth of analysis, are free of cognitive errors, and have structural integrity.

■ Breadth can be expanded with the use of short selling, either in market- neutral long-short or 120-20/130-30 enhanced active strategies.

■ The optimal level of residual risk for any investor will depend both on the investor’s level of risk aversion and on the given manager’s level of skill.

■ An investor who takes less than the optimal level of residual risk or who selects less than the best manager will needlessly sacrifice return.

QUESTIONS

1.  What is one advantage of viewing the market as an equity core com- prised of various style subsets?

2.  What are the advantages and disadvantages of a traditional active approach to investing?

3.  What are the advantages and disadvantages of a passive approach?

4.  What are the advantages and disadvantages of engineered approaches?

5.  Name some ways in which an engineered approach can be expanded.

6.  What factors might influence the optimal level of residual risk an inves- tor should take?

171

CHAPTER 7 Equity Analysis in a Complex Market

Bruce I. Jacobs, Ph.D. Principal

Jacobs Levy Equity Management

Kenneth N. Levy, CFA Principal

Jacobs Levy Equity Management

S cientists classify systems into three types—ordered, random, and com-plex. Ordered systems, such as the structure of diamond crystals or the dynamics of pendulums, are definable and predictable by relatively simple rules and can be modeled using a relatively small number of variables. Ran- dom systems like the Brownian motion of gas molecules or white noise (static) are unordered; they are the product of a large number of variables. Their behavior cannot be modeled and is inherently unpredictable.

Complex systems like the weather and the workings of DNA fall some- where between the domains of order and randomness. Their behavior can be at least partly comprehended and modeled, but only with great diffi- culty. The number of variables that must be modeled and their interactions are beyond the capacity of the human mind alone. Only with the aid of advanced computational science can the mysteries of complex systems be unraveled.1

The stock market is a complex system.2 Stock prices are not completely random, as the efficient market hypothesis and random walk theory would have it. Some price movements can be predicted, and with some consistency. But stock price behavior is not ordered. It cannot be successfully modeled

1See Heinz R. Pagels, The Dreams of Reason: The Computer and the Rise of the Sciences of Complexity (New York: Simon & Schuster, 1988); and Stephen Wolfram, A New Kind of Science (Champaign, IL: Wolfram Media Inc., 2002). 2See Bruce I. Jacobs and Kenneth N. Levy, “The Complexity of the Stock Market,” Journal of Portfolio Management 16, no. 1 (1989): 19–27.

172 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

by simple rules or screens such as low price–earnings ratios (P/Es) or even by elegant theories such as the capital asset pricing model or arbitrage pric- ing theory. Rather, stock price behavior is permeated by a complex web of interrelated return effects. A model of the market that is complex enough to disentangle these effects provides opportunities for modeling price behavior and predicting returns.

This chapter describes our approach to investing and its application to the stock selection, portfolio construction, and performance evalua- tion problems. We begin with the very basic question of how one should approach the equity market. Should one attempt to cover the broadest pos- sible range of stocks, or can greater analytical insights be garnered by focus- ing on a particular subset of the market or a limited number of stocks? Each approach has its advantages and disadvantages. However, combining the two may offer the best promise of finding the key to unlocking investment opportunity in a complex market.

While covering the broadest possible range of stocks, a complex approach recognizes that there are significant differences in the ways differ- ent types of stocks respond to changes in both fundamentals and investor behavior. This requires taking into account the interrelationships between numerous potential sources of price behavior. Multivariate analysis disen- tangles the web of return-predictor relationships that constitutes a complex market and provides independent, additive return predictions that are more robust than the predictions from univariate analyses.

AN INTEGRATED APPROACH TO A SEGMENTED MARKET

While one might think that U.S. equity markets are fluid and fully inte- grated, in reality there are barriers to the free flow of capital. Some of these barriers are self-imposed by investors. Others are imposed by regulatory and tax authorities or by client guidelines.

Some funds, for example, are prohibited by regulation or internal policy guidelines from buying certain types of stock—nondividend-paying stock, or stock below a given capitalization level. Tax laws, too, may effectively lock investors into positions they would otherwise trade. Such barriers to the free flow of capital foster market segmentation.

Other barriers are self-imposed. Traditionally, for example, manag- ers have focused (whether by design or default) on distinct approaches to stock selection. Value managers have concentrated on buying stocks selling at prices perceived to be low relative to the company’s assets or earnings. Growth managers have sought stocks with above-average earnings growth not fully reflected in price. Small-capitalization managers have searched for

Equity Analysis in a Complex Market 173

opportunity in stocks that have been overlooked by most investors. The stocks that constitute the natural selection pools for these managers tend to group into distinct market segments.

Client preferences encourage this balkanization of the market. Some investors, for example, prefer to buy value stocks, while others seek growth stocks; some invest in both, but hire separate managers for each segment. Both institutional and individual investors generally demonstrate a reluc- tance to upset the apple cart by changing allocations to previously selected style managers. Several periods of underperformance, however, may under- mine this loyalty and motivate a flow of capital from one segment of the market to another (often just as the out-of-favor segment begins to benefit from a reversion of returns back up to their historical mean).

The actions of investment consultants have formalized a market seg- mented into style groupings. Consultants design style indexes that define the constituent stocks of these segments and define managers in terms of their proclivity for one segment or another. As a manager’s performance is measured against the given style index, managers who stray too far from index territory are taking on extra risk. Consequently, managers tend to stick close to their style homes, reinforcing market segmentation.

An investment approach that focuses on individual market segments can have its advantages. Such an approach recognizes, for example, that the U.S. equity market is neither entirely homogeneous nor entirely hetero- geneous. All stocks do not react alike to a given impetus, but nor does each stock exhibit its own, totally idiosyncratic price behavior. Rather, stocks within a given style, or sector, or industry tend to behave similarly to each other and somewhat differently from stocks outside their group.

An approach to stock selection that specializes in one market segment can optimize the application of talent and maximize the potential for out- performance. This is most likely true for traditional, fundamental analysis. The in-depth, labor-intensive research undertaken by traditional analysts can become positively ungainly without some focusing lens.

An investment approach that focuses on the individual segments of the market, however, presents some theoretical and practical problems. Such an approach may be especially disadvantaged when it ignores the many forces that work to integrate, rather than segment, the market.

Many managers, for example, do not specialize in a particular market segment but are free to choose the most attractive securities from a broad universe of stocks. Others, such as style rotators, may focus on a particular type of stock, given current economic conditions, but be poised to change their focus should conditions change. Such managers make for capital flows and price arbitrage across the boundaries of particular segments.

174 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Furthermore, all stocks can be defined by the same fundamental param- eters—by market capitalization, P/E, dividend discount model ranking, and so on. All stocks can be found at some level on the continuum of values for each parameter. Thus, growth and value stocks inhabit the opposite ends of the continuums of P/E and dividend yield, and small and large stocks the opposite ends of the continuums of firm capitalization and analyst coverage.

As the values of the parameters for any individual stock change, so too does the stock’s position on the continuum. An out-of-favor growth stock may slip into value territory. A small-cap company may grow into the large- cap range.

Finally, while the values of these parameters vary across stocks belong- ing to different market segments—different styles, sectors, and industries— and while investors may favor certain values—low P/E, say, in preference to high P/E—arbitrage tends to counterbalance too pronounced a predilection on the part of investors for any one set of values. In equilibrium, all stocks must be owned. If too many investors want low P/E, low-P/E stocks will be bid up to higher P/E levels, and some investors will step in to sell them and buy other stocks deserving of higher P/Es. Arbitrage works toward market integration and a single pricing mechanism.

A market that is neither completely segmented nor completely integrated is a complex market. A complex market calls for an investment approach that is 180 degrees removed from the narrow, segment-oriented focus of traditional management. It requires a complex, unified approach that takes into account the behavior of stocks across the broadest possible selection universe, without losing sight of the significant differences in price behavior that distinguish particular market segments.

Such an approach offers three major advantages. First, it provides a coherent evaluation framework. Second, it can benefit from all the insights to be garnered from a wide and diverse range of securities. Third, because it has both breadth of coverage and depth of analysis, it is poised to take advantage of more profit opportunities than a more narrowly defined, seg- mented approach proffers.

A Coherent Framework

To the extent that the market is integrated, an investment approach that models each industry or style segment as if it were a universe unto itself is not the best approach. Consider, for example, a firm that offers both core and value strategies. Suppose the firm runs a model on its total universe of, say, 3,000 stocks. It then runs the same model or a different, segment- specific model on a 500-stock subset of large-cap value stocks.

Equity Analysis in a Complex Market 175

If different models are used for each strategy, the results will differ. Even if the same model is estimated separately for each strategy, its results will differ because the model coefficients are bound to differ between the broader universe and the narrower segment. What if the core model predicts GM will outperform Ford, while the value model shows the reverse? Should the investor start the day with multiple estimates of one stock’s alpha? This would violate what we call the law of one alpha.3

Of course, the firm could ensure coherence by using separate models for each market segment—growth, value, small-cap, linking the results via a single, overarching model that relates all the subsets. But the firm then runs into a second problem with segmented investment approaches: To the extent that the market is integrated, the pricing of securities in one segment may contain information relevant to pricing in other segments.

For example, within a generally well-integrated national economy, labor market conditions in the United States differ region by region. An economist attempting to model employment in the Northeast would probably consider economic expansion in the Southeast. Similarly, the investor who wants to model growth stocks should not ignore value stocks. The effects of inflation, say, on value stocks may have repercussions for growth stocks; after all, the two segments represent opposite ends of the same P/E continuum.

An investment approach that concentrates on a single market segment does not make use of all available information. A complex, unified approach considers all the stocks in the universe, value and growth, large and small. It thus benefits from all the information to be gleaned from a broad range of stock price behavior.

Of course, an increase in breadth of inquiry will not benefit the investor if it comes at the sacrifice of depth of inquiry. A complex approach does not ignore the significant differences across different types of stock, differences exploitable by specialized investing. What’s more, in examining similari- ties and differences across market segments, it considers numerous variables that may be considered to be defining.

For value, say, a complex approach does not confine itself to a dividend discount model measure of value, but examines also earnings, cash flow, sales, and yield value, among other attributes. Growth measurements to be considered include historical, expected, and sustainable growth, as well as the momentum and stability of earnings. Share price, volatility, and analyst coverage are among the elements to be considered along with market capi- talization as measures of size.

At a deeper level of analysis, one must also consider alternative ways of specifying such fundamental variables as earnings or cash flow. Over what 3See Bruce I. Jacobs and Kenneth N. Levy, “The Law of One Alpha,” Journal of Portfolio Management 21, no. 4 (1995): 78–79.

176 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

period does one measure earnings? If using analyst earnings expectations, which measure provides the best estimate of future real earnings? The con- sensus of all available estimates made over the past six months, or only the very latest earnings estimates? Are some analysts more accurate or more influential? What if a recent estimate is not available for a given company?4

Predictor variables are often closely correlated with each other. Small- cap stocks, for example, tend to have low P/Es; low P/E is correlated with high yield; both low P/E and high yield are correlated with dividend discount model (DDM) estimates of value. Furthermore, they may be correlated with a stock’s industry affiliation. A simple low-P/E screen, for example, will tend to select a large number of bank and utility stocks. Such correlations can distort naive attempts to relate returns to potentially relevant predictors. A true picture of the return-predictor relationship emerges only after disentan- gling the predictors.

DISENTANGLING

The effects of different sources of stock return can overlap. In Exhibit 7.1, the lines represent connections documented by academic studies; they may appear like a ball of yarn after the cat got to it. To unravel the connections between predictor variables and return, it is necessary to examine all the variables simultaneously.

For instance, the low P/E effect is widely recognized, as is the small-size effect. But stocks with low P/Es also tend to be of small size. Are P/E and size merely two ways of looking at the same effect? Or does each variable matter? Perhaps the excess returns to small-cap stocks are merely a January effect, reflecting the tendency of taxable investors to sell depressed stocks at year-end. Answering these questions requires disentangling return effects via multivariate regression.5

Common methods of measuring return effects (such as quintiling or uni- variate, single-variable, regression) are naive because they assume, naively, that prices are responding only to the single variable under consideration, low P/E, say. But a number of related variables may be affecting returns. As we have noted, small-cap stocks and banking and utility industry stocks tend to have low P/Es. A univariate regression of return on low P/E will capture,

4See Bruce I. Jacobs, Kenneth N. Levy, and Mitchell C. Krask, “Earnings Estimates, Predictor Specification, and Measurement Error,” Journal of Investing 6, no. 2 (1997): 29–46. 5See Bruce I. Jacobs and Kenneth N. Levy, “Disentangling Equity Return Regularities: New Insights and Investment Opportunities,” Financial Analysts Journal 44, no. 3 (1988): 18–44.

Equity Analysis in a Complex Market 177

along with the effect of P/E, a great deal of noise related to firm size, indus- try affiliation, and other variables.

Simultaneous analysis of all relevant variables via multivariate regres- sion takes into account and adjusts for such interrelationships. The result is the return to each variable separately, controlling for all related variables. A multivariate analysis for low P/E, for example, will provide a measure of the excess return to a portfolio that is market-like in all respects except for hav- ing a lower-than-average P/E ratio. Disentangled returns are pure returns.

Noise Reduction

Exhibit 7.2 plots naive and pure cumulative monthly excess (relative to a 3,000-stock universe) returns to high book–price ratio (B/P). (Conceptually, naive and pure returns come from a portfolio having a B/P that is one stan- dard deviation above the universe mean B/P; for the pure returns, the port- folio is also constrained to have universe-average exposures to all the other variables in the model, including fundamental characteristics and industry af- filiations.) The naive returns show a great deal of volatility; the pure returns,

EXHIBIT 7.1 Return Effects Form a Tangled Web

Small Size

Effect

Low Price Effect

Earnings Revision

Effect

Book–Price Effect

Yield Effect

Low P/E Effect

January Effect

Return Reversal

Effect

Neglected Firm Effect

Earnings Surprise Effect

178 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

by contrast, follow a much smoother path. There is a lot of noise in the naive returns. What causes it?

Notice the divergence between the naive and pure return series for the 12 months starting in March 1979. This date coincides with the crisis at Three Mile Island nuclear power plant. Utilities such as GPU, operator of the Three Mile Island power plant, tend to have high B/Ps, and naive B/P measures will reflect the performance of these utilities along with the per- formance of other high-B/P stocks. Electric utility prices plummeted 24% after the Three Mile Island crisis. The naive B/P measure reflects this decline.

But industry-related events such as Three Mile Island have no necessary bearing on the B/P variable. An investor could, for example, hold a high-B/P portfolio that does not overweight utilities, and such a portfolio would not have experienced the decline reflected in the naive B/P measure in Exhibit 7.2. The naive returns to B/P reflect noise from the inclusion of a utility industry effect. A pure B/P measure is not contaminated by such irrelevant variables.

Disentangling distinguishes real effects from mere proxies and thereby distinguishes between real and spurious investment opportunities. As it separates high B/P and industry affiliation, for example, it can also sepa- rate the effects of firm size from the effects of related variables. Disentan- gling shows that returns to small firms in January are not abnormal; the

EXHIBIT 7.2 Naive and Pure Returns to High Book-to-Price Ratio

80%

60%

40%

20%

0%

–20%

C um

ul at

iv e

E xc

es s

R et

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Naive Pure

Equity Analysis in a Complex Market 179

apparent January seasonal merely proxies for year-end tax-loss selling.6 Not all small firms will benefit from a January rebound; indiscriminately buying small firms at the turn of the year is not an optimal investment strategy. Ascertaining true causation leads to more profitable strategies.

Return Revelation

Disentangling can reveal hidden opportunities. Exhibit 7.3 plots the naively measured cumulative monthly excess returns (relative to the 3,000-stock universe) to portfolios that rank lower than average in market capitaliza- tion and price per share and higher than average in terms of analyst neglect. These results derive from monthly univariate regressions. The small-cap line thus represents the cumulative excess returns to a portfolio of stocks naively chosen on the basis of their size, with no attempt made to control for other variables.

All three return series move together. The similarity between the small- cap and neglect series is particularly striking. This is confirmed by the corre- lation coefficients in the first column of Exhibit 7.4. Furthermore, all series show a great deal of volatility within a broader up, down, up pattern.

6See Bruce I. Jacobs and Kenneth N. Levy, “Calendar Anomalies: Abnormal Returns at Calendar Turning Points,” Financial Analysts Journal 44, no. 6 (1988): 28–39.

EXHIBIT 7.3 Naive Returns Can Hide Opportunities: Three Size-Related Variables

40%

30%

20%

10%

0%

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–20%

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Small cap Neglect Low price

180 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 7.4 Correlations Between Monthly Returns to Size-Related Variablesa

Variable Naive Pure

Small cap/low price 0.82 −0.12

Small cap/neglect 0.87 −0.22

Neglect/low price 0.66 −0.11 aA coefficient of 0.14 is significant at the 5% level.

EXHIBIT 7.5 Pure Returns Can Reveal Opportunities: Three Size-Related Variables

40%

30%

20%

10%

0%

–10%

C um

ul at

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Small cap Neglect Low price

Exhibit 7.5 shows the pure cumulative monthly excess returns to each size-related attribute over the period. These disentangled returns adjust for correlations not only between the three size variables, but also between each size variable and industry affiliations and each variable and growth and value characteristics. Two findings are immediately apparent from Exhibit 7.5.

First, pure returns to the size variables do not appear to be nearly as closely correlated as the naive returns displayed in Exhibit 7.3. In fact, over the second half of the period, the three return series diverge substantially. This is confirmed by the correlation coefficients in the second column of Exhibit 7.4.

In particular, pure returns to small capitalization accumulate quite a gain over the period; they are up 30%, versus an only 20% gain for the naive returns to small cap. Purifying returns reveals a profit opportunity not apparent in the naive returns. Furthermore, pure returns to analyst neglect amount to a substantial loss over the period. Because disentangling controls

Equity Analysis in a Complex Market 181

for proxy effects, and thereby avoids redundancies, these pure return effects are additive. A portfolio could have aimed for superior returns by selecting small-cap stocks with a higher-than-average analyst following (that is, a negative exposure to analyst neglect).

Second, the pure returns appear to be much less volatile than the naive returns. The naive returns in Exhibit 7.3 display much month-to-month volatility within their more general trends. By contrast, the pure series in Exhibit 7.5 are much smoother and more consistent. This is confirmed by the standard deviations given in Exhibit 7.6.

The pure returns in Exhibit 7.5 are smoother and more consistent than the naive return responses in Exhibit 7.3 because the pure returns capture more signal and less noise. And because they are smoother and more consis- tent than naive returns, pure returns are also more predictive.

Predictive Power

Disentangling improves the predictive power of estimated returns by pro- viding a clearer picture of the relationships between investor behavior, fun- damental variables, and macroeconomic conditions. For example, investors often prefer value stocks in bearish market environments, because growth stocks are priced more on the basis of high expectations, which get dashed in more pessimistic eras. But the success of such a strategy will depend on the variables one has chosen to define value.

Exhibit 7.7 displays the results of regressing both naive and pure monthly returns to various value-related variables on market (S&P 500) returns over the 1978–1996 period. The results indicate that DDM value is a poor indicator of a stock’s ability to withstand a tide of receding market prices. The regression coefficient in the first column indicates that a portfo- lio with a one-standard-deviation exposure to DDM value will tend to out- perform by 0.06% when the market rises by 1.00% and to underperform by a similar margin when the market falls by 1.00%. The coefficient for

EXHIBIT 7.6 Pure Returns Are Less Volatile, More Predictable: Standard Deviations of Monthly Returns to Size-Related Variablesa

Variable Naive Pure

Small cap 0.87 0.60

Neglect 0.87 0.67

Low price 1.03 0.58

aAll differences between naive and pure return standard deviations are significant at the 1% level.

182 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

pure returns to DDM is similar. Whether their returns are measured in pure or naive form, stocks with high DDM values tend to behave procyclically.

High B/P appears to be a better indicator of a defensive stock. It has a regression coefficient of –0.10 in naive form. In pure form, however, B/P is virtually uncorrelated with market movements; pure B/P signals neither an aggressive nor a defensive stock. B/P as naively measured apparently picks up the effects of truly defensive variables, such as high yield.

The value investor in search of a defensive posture in uncertain market climates should consider moving toward high yield. The regression coef- ficients for both naive and pure returns to high yield indicate significant negative market sensitivities. Stocks with high yields may be expected to lag in up markets but to hold up relatively well during general market declines.

These results make broad intuitive sense. DDM is forward-looking, relying on estimates of future earnings. In bull markets, investors take a long-term outlook, so DDM explains security pricing behavior. In bear mar- kets, however, investors become myopic; they prefer today’s tangible income to tomorrow’s promise. Current yield is rewarded.

Pure returns respond in intuitively satisfying ways to macroeconomic events. Exhibit 7.8 illustrates, as an example, the estimated effects of changes in various macroeconomic variables on the pure returns to small size (as measured by market capitalization). Consistent with the capital constraints on small firms and their relatively greater sensitivity to the economy, pure returns to small size may be expected to be negative in the first four months following an unexpected increase in the Baa corporate rate and positive in the first month following an unexpected increase in industrial production.7 Investors can exploit such predictable behavior by moving into and out of the small-cap market segment as economic conditions evolve.8

These examples serve to illustrate that the use of numerous, finely defined fundamental variables can provide a rich representation of the com- plexity of security pricing. The model can be even more finely tuned, how- ever, by including variables that capture such subtleties as the effects of

7See Bruce I. Jacobs and Kenneth N. Levy, “Forecasting the Size Effect,” Financial Analysts Journal 45, no. 3 (1989): 38–54. 8See Bruce I. Jacobs and Kenneth N. Levy, “High-Definition Style Rotation,” Journal of Investing 6, no. 1 (1996): 14–23.

EXHIBIT 7.7 Market Sensitivities of Monthly Returns to Value-Related Variables

Variable Naive (t-stat.) Pure (t-stat.)

DDM 0.06 (5.4) 0.04 (5.6)

B/P −0.10 (−6.2) −0.01 (−0.8)

Yield −0.08 (−7.4) −0.03 (−3.5)

Equity Analysis in a Complex Market 183

investor psychology, possible nonlinearities in variable-return relationships, and security transaction costs.

Additional Complexities

In considering possible variables for inclusion in a model of stock price behav- ior, the investor should recognize that pure stock returns are driven by a com- bination of economic fundamentals and investor psychology. That is, economic fundamentals such as interest rates, industrial production, and inflation can explain much, but by no means all, of the systematic variation in returns. Psy- chology, including investors’ tendency to overreact, their desire to seek safety in numbers, and their selective memories, also plays a role in security pricing.

What’s more, the modeler should realize that the effects of different variables, fundamental and otherwise, can differ across different types of stocks. The value sector, for example, includes more financial stocks than the growth sector. Investors may thus expect value stocks in general to be more sensitive than growth stocks to changes in interest rate spreads.

Psychologically based variables such as short-term overreaction and price correction also seem to have a stronger effect on value than on

EXHIBIT 7.8 Forecast Response of Small Size to Macroeconomic Shocks

0.10 0.08 0.06 0.04 0.02 0.00

-0.02 -0.04 -0.06 -0.08

Pe rc

en t

1 2 3 4 5 6

Shock to Baa Corporate Bond Rate

Shock to Treasury Bond Rate

Shock to Treasury Bill Rate Shock to Industrial Production

Shock to Consumer Price Index

Shock to S&P 500 Return

0.10 0.08 0.06 0.04 0.02 0.00

-0.02 -0.04 -0.06 -0.08

Pe rc

en t

1 2 3 4 5 6

0.10 0.08 0.06 0.04 0.02 0.00

-0.02 -0.04 -0.06 -0.08

Pe rc

en t

1 2 3 4 5 6

0.10 0.08 0.06 0.04 0.02 0.00

-0.02 -0.04 -0.06 -0.08

Pe rc

en t

1 2 3 4 5 6

0.10 0.08 0.06 0.04 0.02 0.00

-0.02 -0.04 -0.06 -0.08

Pe rc

en t

1 2 3 4 5 6

0.10 0.08 0.06 0.04 0.02 0.00

-0.02 -0.04 -0.06 -0.08

Pe rc

en t

1 2 3 4 5 6

184 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

growth stocks. Earnings surprises and earnings estimate revisions, by con- trast, appear to be more important for growth than for value stocks. Thus, Google shares can take a nosedive when earnings come in a penny under expectations, whereas Duke Energy shares remain unmoved even by fairly substantial departures of actual earnings from expectations.

The relationship between stock returns and relevant variables may not be linear. The effects of positive earnings surprises, for instance, tend to be arbitraged away quickly; thus positive earnings surprises offer less oppor- tunity for the investor. The effects of negative earnings surprises, however, appear to be more long-lasting. This nonlinearity may reflect the fact that sales of stock are limited to those investors who already own the stock (and to a relatively small number of short sellers).9

Risk-variable relationships may also differ across different types of stock. In particular, small-cap stocks generally have more idiosyncratic risk than large-cap stocks. Diversification is thus more important for small-stock than for large-stock portfolios.

Return-variable relationships can also change over time. Recall the dif- ference between DDM and yield value measures: high-DDM stocks tend to have high returns in bull markets and low returns in bear markets; high- yield stocks experience the reverse. For consistency of performance, return modeling must consider the effects of market dynamics, the changing nature of the overall market.

The investor may also want to decipher the informational signals gener- ated by informed agents. Corporate decisions to issue or buy back shares, split stock, or initiate or suspend dividends, for example, may contain valu- able information about company prospects. So, too, may insiders’ (legal) trading in their own firms’ shares.

Finally, a complex model containing multiple variables is likely to turn up a number of promising return-variable relationships. But are these per- ceived profit opportunities translatable into real economic opportunities? Are some too ephemeral? Too small to survive frictions such as trading costs? Estimates of expected returns must be combined with estimates of the costs of trading to arrive at realistic returns net of trading costs.

CONSTRUCTING, TRADING, AND EVALUATING PORTFOLIOS

To maximize implementation of the model’s insights, the portfolio construc- tion process should consider exactly the same dimensions found relevant by

9See Bruce I. Jacobs and Kenneth N. Levy, “Long/Short Equity Investing,” Journal of Portfolio Management 20, no. 1 (1993): 52–63.

Equity Analysis in a Complex Market 185

the stock selection model. Failure to do so can lead to mismatches between model insights and portfolio exposures.

Consider a commercially available portfolio optimizer that recog- nizes only a subset of the variables in the valuation model. Risk reduction using such an optimizer will reduce the portfolio’s exposures only along the dimensions the optimizer recognizes. As a result, the portfolio is likely to wind up more exposed to those variables recognized by the model, but not the optimizer, and less exposed to those variables common to both the model and the optimizer.

Imagine an investor who seeks low-P/E stocks that analysts are recom- mending for purchase, but who uses a commercial optimizer that incorpo- rates a P/E factor but not analyst recommendations. The investor is likely to wind up with a portfolio that has a less-than-optimal level of exposure to low P/E and a greater-than-optimal level of exposure to analyst pur- chase recommendations. Optimization using all relevant variables ensures a portfolio whose risk and return opportunities are balanced in accordance with the model’s insights. Furthermore, the use of more numerous variables allows portfolio risk to be more finely tuned.

Insofar as the investment process, both stock selection and portfolio construction, is model-driven, it is more adaptable to electronic trading venues. This should benefit the investor in several ways. First, electronic trading is generally less costly, with lower commissions, market impact, and opportunity costs. Second, it allows real-time monitoring, which can further reduce trading costs. Third, an automated trading system can take account of more factors, including the urgency of a particular trade and market con- ditions, than individual traders can be expected to bear in mind.

Finally, the performance attribution process should be congruent with the dimensions of the selection model (and portfolio optimizer). Insofar as performance attribution identifies sources of return, a process that considers all the sources identified by the selection model will be more insightful than a commercial performance attribution system applied in a one-size-fits-all manner. Our investor who has sought exposure to low P/E and positive ana- lyst recommendations, for example, will want to know how each of these factors has paid off and will be less interested in the returns to factors that are not a part of the stock selection process.

A performance evaluation process tailored to the model also functions as a monitor of the model’s reliability. Has portfolio performance supported the model’s insights? Should some be reexamined? Equally important, does the model’s reliability hold up over time? A model that performs well in today’s economic and market environments may not necessarily perform well in the future. A feedback loop between the evaluation and the research or modeling processes can help ensure that the model retains robustness over time.

186 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

PROFITING FROM COMPLEXITY

H. L. Mencken is supposed to have noted, “For every complex problem, there is a simple solution, and it is almost always wrong.” Complex prob- lems more often than not require complex solutions.

A complex approach to stock selection, portfolio construction, and per- formance evaluation is needed to capture the complexities of the stock mar- ket. Such an approach combines the breadth of coverage and the depth of analysis needed to maximize investment opportunity and potential reward.

Grinold presents a formula that identifies the relationships between the depth and breadth of investment insights and investment performance:10

IR IC BR=

IR is the manager’s information ratio, a measure of the success of the invest- ment process. IR equals annualized excess return over annualized residual risk (e.g., 2% excess return with 4% tracking error provides 0.5 IR). IC, the information coefficient, or correlation between predicted and actual security returns, measures the goodness of the manager’s insights, or the manager’s skill. BR is the breadth of the strategy, measurable as the number of inde- pendent insights upon which investment decisions are made.

One can increase IR by increasing IC or BR. Increasing IC means com- ing up with some means of improving predictive accuracy. Increasing BR means coming up with more “investable” insights. A casino analogy may be apt even if it is anathema to prudent investors.

A gambler can seek to increase IC by card counting in blackjack or by building a computer model to predict probable roulette outcomes. Similarly, some investors seek to outperform by concentrating their research efforts on a few stocks: by learning all there is to know about Microsoft, for example, one may be able to outperform all the other investors who follow this stock. But a strategy that makes a few concentrated stock bets is likely to produce consistent performance only if it is based on a very high level of skill, or if it benefits from extraordinary luck.

Alternatively, an investor can place a larger number of smaller stock bets and settle for more modest returns from a greater number of investment decisions. That is, rather than behaving like a gambler in a casino, the inves- tor can behave like the casino. A casino has only a slight edge on any spin of the roulette wheel or roll of the dice, but many spins of many roulette wheels can result in a very consistent profit for the house. Over time, the odds will strongly favor the casino over the gambler.

10See Richard C. Grinold, “The Fundamental Law of Active Management,” Journal of Portfolio Management 15, no. 3 (1989): 30–37.

Equity Analysis in a Complex Market 187

A complex approach to the equity market, one that has both breadth of inquiry and depth of focus, can enhance the number and the goodness of investment insights. A complex approach to the equity market requires more time, effort, and ability, but it will be better positioned to capture the complexities of security pricing. The rewards are worth the effort.

KEY POINTS

■ Ordered systems are definable and predictable by relatively simple rules; random systems cannot be modeled and are inherently unpredictable; complex systems can be at least partly comprehended and modeled, but only with difficulty.

■ Stock price behavior is permeated by a complex web of interrelated return effects, and it requires a complex approach to stock selection, portfolio construction, and performance evaluation to capture this complexity.

■ A complex approach combines the breadth of coverage and the depth of analysis needed to maximize investment opportunity and potential reward.

■ Simple methods of measuring return effects (such as quintiling or uni- variate, single-variable regression) are naive because they assume that prices are responding only to the single variable under consideration.

■ Simultaneous analysis of all relevant variables via multivariate regres- sion takes into account and adjusts for interrelationships between effects, giving the return to each variable separately.

■ Disentangling distinguishes real effects from mere proxies and thereby distinguishes between real and spurious investment opportunities.

■ Because disentangling controls for proxy effects, pure return effects are additive, each having the potential to improve portfolio performance.

■ In general, disentangling enhances the predictive power of estimated returns by providing a clearer picture of the relationships between inves- tor behavior, fundamental variables, and macroeconomic conditions.

■ To maximize implementation of insights gained from disentangling the market’s complexity, the portfolio construction process should consider exactly the same dimensions found relevant by the stock selection process.

■ Performance attribution should be congruent with the stock selection and portfolio construction processes so that it can be used to moni- tor the reliability of the stock selection process and provide input for research.

188 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

QUESTIONS

1. In what ways is the stock market a complex system?

2. Is the stock market segmented or integrated?

3. What advantages does a complex, unified approach offer?

4. a. What is “disentangling”? b. What advantages does disentangling offer over simpler, univariate

analysis of return-related variables? c. Give an example of disentangling at work.

5. Why is it important to have portfolio construction and performance mea- surement processes that are congruent with the stock selection process?

6. How do the breadth of coverage and depth of analysis provided by a complex, unified approach improve the likelihood of successful invest- ment results?

189

CHAPTER 8 Survey Studies of the Use of

Quantitative Equity Management Frank J. Fabozzi, Ph.D., CFA, CPA

Professor of Finance EDHEC Business School

Sergio M. Focardi, Ph.D. Professor of Finance

EDHEC Business School and

Partner, The Intertek Group

Caroline L. Jonas Partner

The Intertek Group

In the other chapters of this book, the motivation for quantitative equity investing and actual quantitative equity models are covered. In this chap- ter, we discuss three studies on the use of quantitative equity management conducted by The Intertek Group. The studies are based on surveys and interviews of market participants.1 We conclude the chapter with a discus- sion of the challenges ahead.

2003 INTERTEK EUROPEAN STUDY

The 2003 Intertek European study deals with the use of financial modeling at European asset management firms.2 It is based on studies conducted by

1In the quotes from sources in these studies, we omit the usual practice of identifying the reference and page number. The study where the quote is obtained will be clear. 2The results of this study are reported in Frank J. Fabozzi, Sergio M. Focardi, and Caroline L. Jonas, “Trends in Quantitative Asset Management in Europe,” Journal of Portfolio Management 31, no. 4 (2004): 125–132 (Special European Section).

190 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

The Intertek Group to evaluate model performance following the fall of the markets from their peak in March 2000, and explores changes that have occurred since then. In total, 61 managers at European asset management firms in the Benelux countries, France, Germany, Italy, Scandinavia, Swit- zerland, and the United Kingdom were interviewed. (The study does not cover alternative investment firms such as hedge funds.) At least half of the firms interviewed are among the major players in their respective markets, with assets under management ranging from €50 to €300 billion.

The major findings are summarized next.

Greater Role for Models

In the two years following the March 2000 market highs, quantitative meth- ods in the investment decision-making process began to play a greater role. Almost 75% of the firms interviewed reported this to be the case, while roughly 15% reported that the role of models had remained stable. The remaining 10% noted that their processes were already essentially quantita- tive. The role of models had also grown in another sense; a higher percent- age of assets were being managed by funds run quantitatively. One firm reported that over the past two years assets in funds managed quantitatively grew by 50%.

Large European firms had been steadily catching up with their U.S. counterparts in terms of the breadth and depth of use of models. As the price of computers and computer software dropped, even small firms reported that they were beginning to adopt quantitative models. There were still dif- ferences between American and European firms, though. American firms tended to use relatively simple technology but on a large scale; Europeans tended to adopt sophisticated statistical methods but on a smaller scale.

Demand pull and management push were among the reasons cited for the growing role of models. On the demand side, asset managers were under pressure to produce returns while controlling risk; they were beginning to explore the potential of quantitative methods. On the push side, several sources remarked that, after tracking performance for several years, their management has made a positive evaluation of a model-driven approach against a judgment-driven decision-making process. In some cases, this led to a corporate switch to a quantitative decision-making process; in other instances, it led to shifting more assets into quantitatively managed funds.

Modeling was reported to have been extended over an ever greater uni- verse of assets under management. Besides bringing greater structure and discipline to the process, participants in the study remarked that models helped contain costs. Unable to increase revenues in the period immediately following the March 2000 market decline, many firms were cutting costs.

Survey Studies of the Use of Quantitative Equity Management 191

Modeling budgets, however, were reported as being largely spared. About 68% of the participants said that their investment in modeling had grown over the prior two years, while 50% expected their investments in modeling to continue to grow over the next year.

Client demand for risk control was another factor that drove the increased use of modeling. Pressure from institutional investors and consul- tants in particular continued to work in favor of modeling.

More generally, risk management was widely believed to be the key driving force behind the use of models.

Some firms mentioned they had recast the role of models in portfolio management. Rather than using models to screen and rank assets—which has been a typical application in Europe—they applied them after the asset man- ager had acted in order to measure the pertinence of fundamental analysis, characterize the portfolio style, eventually transform products through deriv- atives, optimize the portfolio, and track risk and performance.

Performance of Models Improves

Over one-half of the study’s participants responded that models performed better in 2002 than two years before. Some 20% evaluated 2002 model performance as stable with respect to two years ago, while another 20% considered that performance had worsened. Participants often noted that it was not models in general but specific models that had performed better or more poorly.

There are several explanations for the improved performance of mod- els. Every model is, ultimately, a statistical device trained and estimated on past data. When markets began to fall from their peak in March 2000, models had not been trained on data that would have allowed them to cap- ture the downturn—hence, the temporary poor performance of some mod- els. Even risk estimates, more stable than expected return estimates, were problematic. In many cases, it was difficult to distinguish between volatility and model risk. Models have since been trained on new sets of data and are reportedly performing better.

From a strictly scientific and economic theory point of view, the ques- tion of model performance overall is not easy to address. The basic question is how well a theory describes reality, with the additional complication that in economics uncertainty is part of the theory. We cannot object to financial modeling but we cannot pretend a priori that model performance be good. Modeling should reflect the objective amount of uncertainty present in a financial process. The statement that “models perform better” implies that the level of uncertainty has changed. To make this discussion meaningful, clearly somehow we have to restrict the universe of models under consideration.

192 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

In general, the uncertainty associated with forecasting within a given class of models is equated to market volatility. And as market volatility is not an observable quantity but a hidden one, it is model-dependent.3 In other words, the amount of uncertainty in financial markets depends on the accu- racy of models. For instance, an ARCH-GARCH model will give an esti- mate of volatility different from that of a model based on constant volatility. On top of volatility, however, there is another source of uncertainty, which is the risk that the model is misspecified. The latter uncertainty is generally referred to as model risk.

The problem experienced when markets began to fall was that models could not forecast volatility simply because they were grossly misspecified. A common belief is that markets are now highly volatile, which is another way of saying that models do not do a good job of predicting returns. Yet models are now more coherent; fluctuations of returns are synchronized with expectations regarding volatility. Model risk has been reduced substantially.

Overall, the global perception of European market participants who participated in the study was that models are now more dependable. This meant that model risk had been reduced; although their ability to predict returns had not substantially improved, models were better at predicting risk. Practitioners’ evaluation of model performance can be summarized as follows: (1) models will bring more and more insight to risk management; (2) in stock selection, we will see some improvement due essentially to better data, not better models; and (3) in asset allocation, the use of models will remain difficult as markets remain difficult to predict.

Despite the improved performance of models, the perception European market participants shared was one of uncertainty as regards the macroeco- nomic trends of the markets. Volatility, structural change, and unforecast- able events continue to challenge models. In addition to facing uncertainty related to a stream of unpleasant surprises as regards corporate accounting at large public firms, participants voiced the concern that there is consider- able fundamental uncertainty on the direction of financial flows.

A widely shared evaluation was that, independent of models them- selves, the understanding of models and their limits had improved. Most traders and portfolio managers had at least some training in statistics and finance theory; computer literacy was greatly increased. As a consequence, the majority of market participants understand at least elementary statisti- cal analyses of markets.

3This statement is not strictly true. With the availability of high-frequency data, there is a new strain of financial econometrics that considers volatility as an observ- able realized volatility.

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Use of Multiple Models on the Rise

According to the 2003 study’s findings, three major trends had emerged in Eu- rope over the prior few years: (1) a greater use of multiple models, (2) the mod- eling of additional new factors, and (3) an increased use of value-based models.

Let’s first comment on the use of multiple models from the point of view of modern financial econometrics and, in particular, from the point of view of the mitigation of model risk. The present landscape of financial modeling applied to investment management is vast and well articulated.4 Financial models are typically econometric models, they do not follow laws of nature but are approximate models with limited validity. Every model has an associated model risk, which can be roughly defined as the probability that the model does not forecast correctly. Note that it does not make sense to consider model risk in abstract terms and against every possible assump- tion; model risk can be meaningfully defined only by restricting the set of alternative assumptions. For instance, we might compute measures of the errors made by an option pricing model if the underlying follows a distribu- tion different from the one on which the model is based. Clearly, what must be specified are the families of alternative distributions.

Essentially every model is based on some assumption about the func- tional form of dependencies between variables and on the distribution of noise. Given the assumptions, models are estimated, and decisions made. The idea of estimating model risk is to estimate the distribution of errors that will be made if the model assumptions are violated. For instance, are there correlations or autocorrelations when it is assumed there are none? Are innovations fat-tailed when it is assumed that noise is white and nor- mal? From an econometric point of view, combining different models in this way means constructing a mixture of distributions. The result of this process is one single model that weights the individual models.

Some managers interviewed for the 2003 study reported they were using judgment on top of statistical analysis. This entails that models be reviewed when they begin to produce results that are below expectations. In practice, quantitative teams constantly evaluate the performance of different fami- lies of models and adopt those that perform better. Criteria for switching from one family of models to another are called for, though. This, in turn, requires large data samples.

Despite these difficulties, application of multiple models has gained wide acceptance in finance. In asset management, the main driver is the uncertainty related to estimating returns.

4For a discussion of the different families of financial models and modeling issues, see Sergio M. Focardi and Frank J. Fabozzi, The Mathematics of Financial Modeling and Investment Management (Hoboken, NJ: John Wiley & Sons, 2004).

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Focus on Factors, Correlation, Sentiment, and Momentum

Participants in the 2003 study also reported efforts to determine new factors that might help predict expected returns. Momentum and sentiment were the two most cited phenomena modeled in equities. Market sentiment, in particular, was receiving more attention.

The use of factor models is in itself a well-established practice in finan- cial modeling. Many different families of models are available, from the widely used classic static return factor analysis models to dynamic factor models. What remains a challenge is determination of the factors. Consider- able resources have been devoted to studying market correlations. Advanced techniques for the robust estimation of correlations are being applied at large firms as well as at boutiques.

According to study respondents, over the three years prior to 2001, quantitative teams at many asset management firms were working on deter- mining which factors are the best indicators of price movements. Senti- ment was often cited as a major innovation in terms of modeling strategies. Asset management firms typically modeled stock-specific sentiment, while sentiment as measured by business or consumer confidence was often the responsibility of the macroeconomic teams at the mother bank, at least in continental Europe. Market sentiment is generally defined by the distribu- tion of analyst revisions in earnings estimates. Other indicators of market confidence are flows, volume, turnover, and trading by corporate officers.

Factors that represent market momentum were also increasingly adopted according to the study. Momentum means that the entire market is moving in one direction with relatively little uncertainty. There are different ways to represent momentum phenomena. One might identify a specific factor that defines momentum, that is, a variable that gauges the state of the market in terms of momentum. This momentum variable then changes the form of mod- els. There are models for trending markets and models for uncertain markets.

Momentum can also be represented as a specific feature of models. A random walk model does not have any momentum, but an autoregressive model might have an intrinsic momentum feature.

Some participants also reported using market-timing models and style rota- tion for the active management of funds. Producing accurate timing signals is complex, given that financial markets are difficult to predict. One source of predictability is the presence of mean reversion and cointegration phenomena.

Back to Value-Based Models

At the time of the 2003 study, there was a widespread perception that value- based models were performing better in post-2000 markets. It was believed

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that markets were doing a better job valuing companies as a function of the value of the firm rather than price trends, notwithstanding our remarks on the growing use of factors such as market sentiment. From a methodologi- cal point of view, methodologies based on cash analysis had increased in popularity in Europe. A robust positive operating cash flow is considered to be a better indication of the health of a firm than earnings estimates, which can be more easily massaged.

Fundamental analysis was becoming highly quantitative and auto- mated. Several firms mentioned that they were developing proprietary meth- odologies for the automatic analysis of balance sheets. For these firms, with the information available on the Internet, fundamental analysis could be performed without actually going to visit firms. Some participants remarked that caution might be called for in attributing the good performance of value- tilted models to markets. One of the assumptions of value-based models is that there is no mechanism that conveys a large flow of funds through pre- ferred channels, but this was the case in the telecommunications, media, and technology (TMT) bubble, when value-based models performed so poorly. In the last bull run prior to the study, the major preoccupation was to not miss out on rising markets; investors who continued to focus on value suf- fered poor performance. European market participants reported that they are now watching both trend and value.

Risk Management

Much of the attention paid to quantitative methods in asset management prior to the study had been focused on risk management. According to 83% of the participants, the role of risk management had evolved significantly over the prior two years to extend across portfolios and across processes.

One topic that has received a lot of attention, both in academia and at financial institutions, is the application of extreme value theory (EVT) to financial risk management. The RiskLab in Zurich, headed by Paul Embre- chts, advanced the use of EVT and copula functions in risk management. At the corporate level, universal banks such as HSBC CCF have produced theo- retical and empirical work on the applicability of EVT to risk management.5 European firms were also paying considerable attention to risk measures.

For participants in the Intertek study, risk management was the area where quantitative methods had made their biggest contribution. Since the pioneering work of Harry Markowitz in the 1950s, the objective of invest- ment management has been defined as determining the optimal risk-return trade-off in an investor’s profile. Prior to the diffusion of modeling techniques, 5François Longin, “Stock Market Crashes: Some Quantitative Results Based on Extreme Value Theory.” Derivatives Use, Trading and Regulation 7, no. 3 (2001): 197–205.

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though, evaluation of the risk-return trade-off was left to the judgment of individual asset managers. Modeling brought to the forefront the question of ex ante risk-return optimization. An asset management firm that uses quan- titative methods and optimization techniques manages risk at the source. In this case, the only risk that needs to be monitored and managed is model risk.6

Purely quantitative managers with a fully automated management process were still rare according to the study. Most managers, although quantitatively oriented, used a hybrid approach calling for models to give evaluations that managers translate into decisions. In such situations, risk is not completely controlled at the origin.

Most firms interviewed for the study had created a separate risk manage- ment unit as a supervisory entity that controls the risk of different portfolios and eventually—although still only rarely—aggregated risk at the firm-wide level. In most cases, the tools of choice for controlling risk were multifactor models. Models of this type have become standard when it comes to making risk evaluations for institutional investors. For internal use, however, many firms reported that they made risk evaluations based on proprietary models, EVT, and scenario analysis.

Integrating Qualitative and Quantitative Information

More than 60% of the firms interviewed for the 2003 Intertek study reported they had formalized procedures for integrating quantitative and qualitative input, although half of these mentioned that the process had not gone very far; 30% of the participants reported no formalization at all. Some firms mentioned they had developed a theoretical framework to integrate results from quantitative models and fundamental views. Assigning weights to the various inputs was handled differently from firm to firm; some firms reported establishing a weight limit in the range of 50% to 80% for quantitative input.

A few quantitative-oriented firms reported that they completely formal- ized the integration of qualitative and quantitative information. In these cases, everything relevant was built into the system. Firms that both quan- titatively managed and traditionally managed funds typically reported that formalization was implemented in the former but not in the latter.

Virtually all firms reported at least a partial automation in the handling of qualitative information. For the most part, a first level of automation—includ- ing automatic screening and delivery, classification, and search—is provided by suppliers of sell-side research, consensus data, and news. These suppliers are automating the delivery of news, research reports, and other information.

6Asset management firms are subject to other risks, namely, the risk of not fulfilling a client mandate or operational risk. Although important, these risks were outside the scope of the survey.

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About 30% of the respondents note they have added functionality over and above that provided by third-party information suppliers, typically starting with areas easy to quantify such as earnings announcements or ana- lysts’ recommendations. Some have coupled this with quantitative signals that alert recipients to changes or programs that automatically perform an initial analysis.

Only the braver will be tackling difficult tasks such as automated news summary and analysis. For the most part, news analysis was still considered the domain of judgment. A few firms interviewed for this study reported that they attempted to tackle the problem of automatic news analysis, but aban- doned their efforts. The difficulty of forecasting price movements related to new information was cited as a motivation.

2006 INTERTEK STUDY

The next study we discuss is based on survey responses and conversations with industry representatives in 2006.7 Although this predates the subprime mortgage crisis and the resulting impact on the performance of quantitative asset managers, the insights provided by this study are still useful. In all, managers at 38 asset management firms managing a total of $4.3 trillion in equities participated in the study. Participants included individuals respon- sible for quantitative equity management and quantitative equity research at large- and medium-sized firms in North America and Europe.8 Sixty-three percent of the participating firms were among the largest asset managers in their respective countries; they clearly represented the way a large part of the industry was going with respect to the use of quantitative methods in equity portfolio management.9

The findings of the 2006 study suggested that the skepticism relative to the future of quantitative management at the end of the 1990s had given way by 2006 and quantitative methods were playing a large role in equity portfolio management. Of the 38 survey participants, 11 (29%) reported that more than 75% of their equity assets were being managed quantita- tively. This includes a wide spectrum of firms, with from $6.5 billion to over

7The results of this study are reported in Frank J. Fabozzi, Sergio M. Focardi, and Caroline Jonas, “Trends in Quantitative Equity Management: Survey Results,” Quantitative Finance 7, no. 2 (2007): 115–122. 8The home market of participating firms was a follows: 15 from North America (14 from the United States, 1 from Canada) and 23 from Europe (7 from United King- dom, 5 from Germany, 4 from Switzerland, 3 from Benelux, 2 from France, and 2 from Italy). 9Of the 38 participants in this survey, two responded only partially to the question- naire. Therefore, for some questions, there are 36 (not 38) responses.

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$650 billion in equity assets under management. Another 22 firms (58%) reported that they have some equities under quantitative management, though for 15 of these 22 firms the percentage of equities under quantitative management was less than 25%—often under 5%—of total equities under management. Five of the 38 participants in the survey (13%) reported no equities under quantitative management.

Relative to the period 2004–2005, the amount of equities under quanti- tative management was reported to have grown at most firms participating in the survey (84%). One reason given by respondents to explain the growth in equity assets under quantitative management was the flows into existing quantitative funds. A source at a large U.S. asset management firm with more than half of its equities under quantitative management said in 2006 “The firm has three distinct equity products: value, growth, and quant. Quant is the biggest and is growing the fastest.”

According to survey respondents, the most important factor contribut- ing to a wider use of quantitative methods in equity portfolio management was the positive result obtained with these methods. Half of the participants rated positive results as the single most important factor contributing to the widespread use of quantitative methods. Other factors contributing to a wider use of quantitative methods in equity portfolio management were, in order of importance attributed to them by participants, (1) the computa- tional power now available on the desk top, (2) more and better data, and (3) the availability of third-party analytical software and visualization tools.

Survey participants identified the prevailing in-house culture as the most important factor holding back a wider use of quantitative methods (this evaluation obviously does not hold for firms that can be described as quantitative): more than one third (10/27) of the respondents at other than quant-oriented firms considered this the major blocking factor. This posi- tive evaluation of models in equity portfolio management in 2006 was in contrast with the skepticism of some 10 years early. A number of changes have occurred. First, expectations at the time of the study had become more realistic. In the 1980s and 1990s, traders were experimenting with method- ologies from advanced science in the hope of making huge excess returns. Experience of the prior 10 years has shown that models were capable of delivering but that their performance must be compatible with a well- functioning market.

More realistic expectations have brought more perseverance in model testing and design and have favored the adoption of intrinsically safer mod- els. Funds that were using hundred fold leverage had become unpalatable following the collapse of LTCM (Long-Term Capital Management). This, per se, has reduced the number of headline failures and had a beneficial

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impact on the perception of performance results. We can say that models worked better in 2006 because model risk had been reduced: simpler, more robust models delivered what was expected. Other technical reasons that explained improved model performance included a manifold increase in computing power and more and better data. Modelers by 2006 had avail- able on their desk top computing power that, at the end of the 1980s, could be got only from multimillion-dollar supercomputers. Cleaner, more com- plete data, including intraday data and data on corporate actions and divi- dends, could be obtained. In addition, investment firms (and institutional clients) have learned how to use models throughout the investment man- agement process. Models had become part of an articulated process that, especially in the case of institutional investors, involved satisfying a number of different objectives, such as superior information ratios.

Changing Role for Models in Equity Portfolio

The 2006 study revealed that quantitative models were now used in active management to find sources of excess returns (i.e., alphas), either relative to a benchmark or absolute. This was a considerable change with respect to the 2003 Intertek European study where quantitative models were reported as being used primarily to manage risk and to select parsimonious portfolios for passive management.

Another finding of the study was the growing amount of funds man- aged automatically by computer programs. The once futuristic vision of machines running funds automatically without the intervention of a port- folio manager was becoming a reality on a large scale: 55% (21/38) of the respondents reported that at least part of their equity assets were being managed automatically with quantitative methods; another three planned to automate at least a portion of their equity portfolios within the next 12 months. The growing automation of the equity investment process suggests that there was no missing link in the technology chain that leads to auto- matic quantitative management. From return forecasting to portfolio forma- tion and optimization, all the needed elements were in place. Until recently, optimization represented the missing technology link in the automation of portfolio engineering. Considered too brittle to be safely deployed, many firms eschewed optimization, limiting the use of modeling to stock ranking or risk control functions. Advances in robust estimation methodologies and in optimization now allow an asset manager to construct portfolios of hun- dreds of stocks chosen in universes of thousands of stocks with little or no human intervention outside of supervising the models.

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Modeling Methodologies and the Industry’s Evaluation

At the end of the 1980s, academics and researchers at specialized quant boutiques experimented with many sophisticated modeling methodologies including chaos theory, fractals and multifractals, adaptive programming, learning theory, complexity theory, complex nonlinear stochastic models, data mining, and artificial intelligence. Most of these efforts failed to live up to expectations. Perhaps expectations were too high. Or perhaps the re- sources or commitment required were lacking. Emanuel Derman provides a lucid analysis of the difficulties that a quantitative analyst has to overcome. As he observed, though modern quantitative finance uses some of the tech- niques of physics, a wide gap remains between the two disciplines.10

The modeling landscape revealed by the 2006 study is simpler and more uniform. Regression analysis and momentum modeling are the most widely used techniques: respectively, 100% and 78% of the survey respondents said that these techniques were being used at their firms. With respect to regression models used today, the survey suggests that they have undergone a substantial change since the first multifactor models such as Arbitrage Pricing Theory (APT) were introduced. Classical multifactor models such as APT are static models embodied in linear regression between returns and factors at the same time. Static models are forecasting models insofar as the factors at time t are predictors of returns at time behavior t + 1. In these static models, individual return processes might exhibit zero autocorrelation but still be forecastable from other variables. Predictors might include financial and macroeconomic factors as well as company specific parameters such as financial ratios. Predic- tors might also include human judgment, for example, analyst estimates, or technical factors that capture phenomena such as momentum. A source at a quant shop using regression to forecast returns said,

Regression on factors is the foundation of our model building. Ratios derived from financial statements serve as one of the most important components for predicting future stock returns. We use these ratios extensively in our bottom-up equity model and catego- rize them into five general categories: operating efficiency, financial strength, earnings quality (accruals), capital expenditures, and ex- ternal financing activities.

Momentum and reversals were the second most widely diffused modeling technique among survey participants. In general, momentum and reversals were being used as a strategy, not as a model of asset returns. Momentum strategies are based on forming portfolios choosing the highest or lowest

10Emanuel Derman, “A Guide for the Perplexed Quant,” Quantitative Finance 1, no. 5 (2001): 476–480.

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returns, where returns are estimated on specific time windows. Survey par- ticipants gave these strategies overall good marks but noted that (1) they do not always perform so well; (2) they can result in high turnover (though some were using constraints/penalties to deal with this problem); and (3) identifying the timing of reversals was tricky.

Momentum was first reported in 1993 by Jegadeesh and Titman in the U.S. market.11 Nine years later, they confirmed that momentum continued to exist in the 1990s in the U.S. market.12 Two years later, Karolyi and Kho examined different models for explaining momentum and concluded that no random walk or autoregressive model is able to explain the magnitude of momentum empirically found13; they suggested that models with time varying expected returns come closer to explaining empirical magnitude of momentum. Momentum and reversals are presently explained in the context of local models updated in real time. For example, momentum as described in the original Jegadeesh and Titman study is based on the fact that stock prices can be represented as independent random walks when considering periods of the length of one year. However, it is fair to say that there is no complete agreement on the econometrics of asset returns that justifies momentum and reversals and stylized facts on a global scale, and not as local models. It would be beneficial to know more about the econometrics of asset returns that sustain momentum and reversals.

Other modeling methods that were widely used by participants in the 2006 study included cash flow analysis and behavioral modeling. Seventeen of the 36 participating firms said that they modeled cash flows; behavioral modeling was reported as being used by 16 of the 36 participating firms.14 Considered to play an important role in asset predictability, 44% of the

11Narasimhan Jegadeesh and Sheridan Titman, “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency,” Journal of Finance 48, no. 1 (1993): 65–92. 12Narasimhan Jegadeesh and Sheridan Titman, “Cross-Sectional and Time-Series Determinants of Momentum Returns,” Review of Financial Studies 15, no. 1 (2002): 143–158. 13George A. Karolyi and Bong-Chan Kho, “Momentum Strategies: Some Bootstrap Tests,” Journal of Empirical Finance 11 (2004): 509–536. 14The term behavioral modeling is often used rather loosely. Full-fledged behavioral modeling exploits a knowledge of human psychology to identify situations where investors are prone to show behavior that leads to market inefficiencies. The ten- dency now is to call behavioral any model that exploits market inefficiency. How- ever, implementing true behavioral modeling is a serious challenge; even firms with very large, powerful quant teams who participated in the survey reported that there is considerable work needed to translate departures from rationality into a set of rules for identifying stocks as well as entry and exit points for a quantitative stock selection process.

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survey respondents said that they use behavioral modeling to try to cap- ture phenomena such as departures from rationality on the part of inves- tors (e.g., belief persistence), patterns in analyst estimates, and corporate executive investment/disinvestment behavior. Behavioral finance is related to momentum in that the latter is often attributed to various phenomena of persistence in analyst estimates and investor perceptions. A source at a large investment firm that has incorporated behavioral modeling into its active equity strategies commented,

The attraction of behavioral finance is now much stronger than it was just five years ago. Everyone now acknowledges that markets are not efficient, that there are behavioral anomalies. In the past, there was the theory that was saying that markets are efficient while market participants such as the proprietary trading desks ignored the theory and tried to profit from the anomalies. We are now see- ing a fusion of theory and practice.

As for other methodologies used in return forecasting, sources cited nonlinear methods and cointegration. Nonlinear methods are being used to model return processes at 19% (7/36) of the responding firms. The non- linear method most widely used among survey participants is classification and regression trees (CART). The advantage of CART is its simplicity and the ability of CART methods to be cast in an intuitive framework. A source in the survey that reported using CART as a central part of the portfolio construction process in enhanced index and longer-term value-based port- folios said,

CART compresses a large volume of data into a form that identi- fies its essential characteristics, so the output is easy to understand. CART is nonparametric—which means that it can handle an in- finitely wide range of statistical distributions—and nonlinear—so as a variable selection technique it is particularly good at handling higher-order interactions between variables.

Only 11% (4/36) of the respondents reported using nonlinear regime- shifting models; at most firms, judgment was being used to assess regime change. Participants identified the difficulty in detecting the precise timing of a regime switch and the very long time series required to estimate shifts as obstacles to modeling regime shifts. A survey participant at a firm where regime-shifting models have been experimented with commented,

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Everyone knows that returns are conditioned by market regimes, but the potential for overfitting when implementing regime-switching models is great. If you could go back with fifty years of data—but we have only some ten years of data and this is not enough to build a decent model.

Cointegration was being used by 19% (7/36) of the respondents. Coin- tegration models the short-term dynamics (direction) and long-run equi- librium (fair value). A perceived plus of cointegration is the transparency that it provides: The models are based on economic and finance theory and calculated from economic data.

Optimization

Another area where much change was revealed by the 2006 study was opti- mization. According to sources, optimization was being performed at 92% (33/36) of the participating firms, albeit in some cases only rarely. Mean variance was the most widely used technique among survey participants: it was being used by 83% (30/36) of the respondents. It was followed by util- ity optimization (42% or 15/36) and, robust optimization (25% or 9/36). Only one firm mentioned that it is using stochastic optimization.

The wider use of optimization was a significant development compared to the 2003 study when many sources had reported that they eschewed opti- mization: The difficulty of identifying the forecasting error was behind the then widely held opinion that optimization techniques were too brittle and prone to error maximization. The greater use of optimization was attributed to advances in large-scale optimization coupled with the ability to include constraints and robust methods for both estimation and optimization. This result is significant as portfolio formation strategies rely on optimiza- tion. With optimization feasible, the door was open to a fully automated investment process. In this context, it is noteworthy that 55% of the survey respondents in the 2006 study reported that at least a portion of their equity assets is being managed by a fully automated process.

Optimization is the engineering part of portfolio construction. Most portfolio construction problems can be cast in an optimization framework, where optimization is applied to obtain the desired optimal risk-return pro- file. Optimization is the technology behind the current offering of products with specially engineered returns, such as guaranteed returns. However, the offering of products with particular risk-return profiles requires optimiza- tion methodologies that go well beyond classical mean-variance optimiza- tion. In particular, one must be able to (1) work with real-world utility functions and (2) apply constraints to the optimization process.

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Challenges

The growing diffusion of models is not without challenges. The 2006 survey participants noted three: (1) increasing difficulty in differentiating products; (2) difficulty in marketing quant funds, especially to noninstitutional inves- tors; and (3) performance decay.

Quantitative equity management has now become so wide spread that a source at a long-established quantitative investment firm remarked:

There is now a lot of competition from new firms entering the space [of quantitative investment management]. The challenge is to continue to distinguish ourselves from competition in the minds of clients.

With quantitative funds based on the same methodologies and using the same data, the risk is to construct products with the same risk-return profile. The head of active equities at a large quantitative firm with more than a decade of experience in quantitative management remarked in the survey, “Everyone is using the same data and reading the same articles: It’s tough to differentiate.”

While sources in the survey reported that client demand was behind the growth of (new) pure quantitative funds, some mentioned that quantitative funds might be something of a hard sell. A source at a medium-sized asset management firm servicing both institutional clients and high-net worth individuals said:

Though clearly the trend towards quantitative funds is up, quant approaches remain difficult to sell to private clients: They remain too complex to explain, there are too few stories to tell, and they often have low alpha. Private clients do not care about high infor- mation ratios.

Markets are also affecting the performance of quantitative strategies. A 2006 report by the Bank for International Settlements noted that this is a period of historically low volatility. What is exceptional about this period, observes the report, is the simultaneous drop in volatility in all variables: stock returns, bond spreads, rates, and so on. While the role of models in reducing volatility is unclear, what is clear is that models immediately trans- late this situation into a rather uniform behavior. Quantitative funds try to differentiate themselves either finding new unexploited sources of return forecastability, for example, novel ways of looking at financial statements, or using optimization creatively to engineer special risk-return profiles.

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A potentially more serious problem is performance decay. Survey par- ticipants remarked that model performance was not so stable. Firms are tackling these problems in two ways. First, they are protecting themselves from model breakdown with model risk mitigation techniques, namely by averaging results obtained with different models. It is unlikely that all mod- els break down in the same way in the same moment, so that averaging with different models allows asset managers to diversify risk. Second, there is an ongoing quest for new factors, new predictors, and new aggregations of fac- tors and predictors. In the long run, however, something more substantial might be required.

2007 INTERTEK STUDY

The 2007 Intertek study, sponsored by the Research Foundation of the CFA Institute (now the Chartered Financial Analysts Institute), is based on con- versations with asset managers, investment consultants, and fund-rating agencies as well as survey responses from 31 asset managers in the United States and Europe.15 In total, 12 asset managers and eight consultants and fund-rating agencies were interviewed and 31 managers with a total of $2.2 trillion in equities under management participated in the survey. Half of the participating firms were based in the United States; half of the participating firms were among the largest asset managers in their countries. Survey par- ticipants included chief investment officers of equities and heads of quanti- tative management and/or quantitative research.

A major question in asset management that this study focused on was if the diffusion of quantitative strategies was making markets more efficient, thereby reducing profit opportunities. The events of the summer of 2007, which saw many quantitatively managed funds realize large losses, brought an immediacy to the question. The classical view of financial markets holds that market speculators make markets efficient, hence the absence of profit opportunities after compensating for risk. This view had formed the basis of academic thinking for several decades starting from the 1960s. However, practitioners had long held the more pragmatic view that a market formed by fallible human agents (as market speculators also are) offers profit oppor- tunities due to the many small residual imperfections that ultimately result in delayed or distorted responses to news.

15The results of this study are reported in Frank J. Fabozzi, Sergio M. Focardi, and Caroline Jonas, Challenges in Quantitative Equity Management (Charlottesville, VA: CFA Institute Research Foundation, 2008); and Frank J. Fabozzi, Sergio M. Focardi, and Caroline L. Jonas, “On the Challenges in Quantitative Equity Manage- ment.” Quantitative Finance 8, no. 7 (2008): 649–655.

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A summary of the findings of this study are provided next.

Are Model-Driven Investment Strategies Impacting Market Efficiency and Price Processes?

The empirical question of the changing nature of markets is now receiving much academic attention. For example, using empirical data from 1927 to 2005, Hwang and Rubesam16 argued that momentum phenomena disap- peared during the period 2000–2005, while Figelman,17 analyzing the S&P 500 over the period 1970–2004, found new evidence of momentum and reversal phenomena previously not described. Khandani and Lo18 show how a mean-reversion strategy that they used to analyze market behavior lost profitability in the 12-year period from 1995 to 2007.

Intuition suggests that models will have an impact on price processes but whether models will make markets more efficient or less efficient will depend on the type of models widely adopted. Consider that there are two categories of models, those based on fundamentals and those based on the analysis of time series of past prices and returns. Models based on funda- mentals make forecasts based on fundamental characteristics of firms and, at least in principle, tend to make markets more efficient. Models based on time series of prices and returns are subject to self-referentiality and might actually lead to mispricings. A source at a large financial firm that has both fundamental and quant processes said:

The impact of models on markets and price processes is asymmet- rical. [Technical] model-driven strategies have a less good impact than fundamental-driven strategies as the former are often based on trend following.

Another source commented:

Overall quants have brought greater efficiency to the market, but there are poor models out there that people get sucked into. Take momentum. I believe in earnings momentum, not in price momen- tum: It is a fool buying under the assumption that a bigger fool will buy in the future. Anyone who uses price momentum assumes that

16Soosung Hwang and Alexandre Rubesam, “The Disappearance of Momentum” (November 7, 2008). Available at SSRN: http://ssrn.com/abstract=968176. 17Ilya Figelman, “Stock Return Momentum and Reversal,” Journal of Portfolio Management 34, no. 1 (2007): 51–69. 18Amir E. Khandani and Andrew W. Lo, “What Happened to the Quants in August 2007,” Journal of Investment Management 5, no. 4 (2007): 29–78.

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there will always be someone to take the asset off your hands—a fool’s theory. Studies have shown how it is possible to get into a mo- mentum-type market in which asset prices get bid up, with every- one on the collective belief wagon.

The question of how models impact the markets—making them more or less efficient—depends on the population of specific models. As long as models based on past time series of prices and returns (i.e., models that are trend followers) are being used, it will not be possible to assume that models make markets more efficient. Consider that it is not only a question of how models compete with each other but also how models react to exogenous events and how models themselves evolve. For example, a prolonged period of growth will produce a breed of models different from models used in low-growth periods.

Performance Issues

When the 2006 Intertek study was conducted on equity portfolio modeling in early 2006, quantitative managers were very heady about performance. By mid-2007, much of that headiness was gone. By July–August 2007, there was much perplexity.

Many participants in the 2007 Intertek study attributed the recent poor performance of many quant equity funds to structural changes in the mar- ket. A source at a large financial firm with both fundamental and quantita- tive processes said:

The problem with the performance of quant funds [since 2006] is that there was rotation in the marketplace. Most quants have a strong value bias so they do better in a value market. The period 1998–1999 was not so good for quants as it was a growth market; in 2001–2005, we had a value market so value-tilted styles such as the quants were doing very well. In 2006, we were back to a growth market. In addition, in 2007, spreads compressed. The edge quants had has eroded.

One might conclude that if markets are cyclical, quant outperformance will also be cyclical. A leading investment consultant who participated in the survey remarked:

What is most successful in terms of producing returns—quant or fun- damental—is highly contextual: there is no best process, quant or fundamental. Quants are looking for an earnings-quality component

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that has dissipated in time. I hate to say it, but any manager has to have the wind behind its strategies, favoring the factors.

Speaking in August 2007, the head of active quantitative research at a large international firm said:

It has been challenging since the beginning of the year. The problem is that fundamental quants are stressing some quality—be it value or growth—but at the beginning of the year there was a lot of activ- ity of hedge funds, much junk value, much froth. In addition, there was a lot of value-growth style rotation, which is typical when there is macro insecurity and interest rates go up and down. The growth factor is better when rates are down, the value factor better when rates are up. Fundamental quants could not get a consistent expo- sure to factors they wanted to be exposed to.

Another source said, “We tried to be balanced value-growth but the biggest danger is rotation risk. One needs a longer-term view to get through mar- ket cycles.” The CIO of equities at a large asset management firm added, “Growth and value markets are cyclical and it is hard to get the timing right.”

The problem of style rotation (e.g., value versus growth) is part of the global problem of adapting models to changing market conditions. Value and growth represent two sets of factors, both of which are captured, for example, in the Fama-French three-factor model.19 But arguably there are many more factors. So factor rotation is more than just a question of value and growth markets. Other factors, such as momentum, are subject to the same problem; that is to say, one factor prevails in one market situation and loses importance in another and is replaced by yet another factor(s).

Other reasons were cited to explain why the performance of quantita- tive products as a group has been down since 2006. Among these is the fact that there were now more quantitative managers using the same data, similar models, and implementing similar strategies. A source at a firm that has both quant and fundamental processes said:

Why is performance down? One reason is because many more peo- ple are using quant today than three, five years ago. Ten years ago the obstacles to entry were higher: data were more difficult to ob- tain, models were proprietary. Now we have third-party suppliers of data feeds, analytics, and backtesting capability.

19Eugene F. Fama and Kenneth R. French, “Common Risk Factors and the Returns on Stocks and Bonds,” Journal of Financial Economics, 47, no. 2 (1993): 427–465.

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A consultant concurred:

The next 12 to 24 months will be tough for quants for several rea- sons. One problem is…the ease with which people can now buy and manipulate data. The problem is too many people are running similar models so performance decays and it becomes hard to stay ahead. Performance is a genuine concern.

Still another source said:

Quant performance depends on cycles and the secular trend but success breeds its own problems. By some estimates there are $4 trillion in quantitative equity management if we include passive, active, hedge funds, and proprietary desks. There is a downside to the success of quants. Because quants have been so successful, if a proprietary desk or a hedge fund needs to get out of a risk, they can’t. Then you get trampled on as others have more to sell than you have to buy. The business is more erratic because of the sheer size and needs of proprietary desks and hedge funds whose clients hold 6 to 12 months against six years for asset managers.

However, not all sources agreed that quantitative managers using the same data or similar models entails a loss of performance. One source said:

Though all quants use the same data sources, I believe that there is a difference in models and in signals. There are details behind the signals and in how you put them together. Portfolio construction is one very big thing.

Another source added:

All quants use similar data but even minor differences can lead to nontrivial changes in valuation. If you have 15 pieces of informa- tion, different sums are not trivial. Plus if you combine small differ- ences in analytics and optimization, the end result can be large dif- ferences. There is not one metric but many metrics and all are noisy.

Investment consultants identified risk management as among the big- gest pluses for a quantitative process. According to one source:

Quantitative managers have a much greater awareness of risk. They are attuned to risk in relation to the benchmark as well as to systemic

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risk. Fundamental managers are often not aware of concentration in, for example, factors or exposure.

In view of the performance issues, survey participants were asked if they believed that quantitative managers were finding it increasingly difficult to generate excess returns as market inefficiencies were exploited. Just over half agreed, while 32% disagreed and 16% expressed no opinion. When the question was turned around, 73% of the survey participants agreed that, though profit opportunities would not disappear, quantitative managers would find it increasingly hard to exploit them. One source remarked:

Performance is getting harder to wring out not because everyone is using the same data and similar models, but because markets are more efficient. So we will see Sharpe ratios shrink for active returns. Managers will have to use more leverage to get returns. The prob- lem is more acute for quant managers as all quant positions are highly correlated as they all use book to price; fundamental manag- ers, on the other hand, differ on the evaluation of future returns.

When asked what market conditions were posing the most serious challenge to a quantitative approach in equity portfolio management, sur- vey respondents ranked in order of importance on a scale from one to five the rising correlation level, style rotation, and insufficient liquidity. Other market conditions rated important were a fundamental market shift, high (cross sector) volatility and low (cross) volatility. Felt less important were the impact of the dissipation of earnings and nontrending markets.

In their paper on the likely causes of the summer 2007 events, Khandani and Lo20 note the sharp rise in correlations over the period 1998–2007. They observe that this rise in correlations reflects a much higher level of interdependence in financial markets. This interdependence is one of the factors responsible for the contagion from the subprime mortgage crisis to the equity markets in July–August 2007. When problems began to affect equity markets, the liquidity crisis started. Note that liquidity is a word that assumes different meanings in different contexts. In the study, liquidity refers to the possibility of finding buyers and thus to the possibility of dele- veraging without sustaining heavy losses. One CIO commented:

Everyone in the quant industry is using the same factors [thus creat- ing highly correlated portfolios prone to severe contagion effects]. When you need to unwind, there is no one there to take the trade:

20Khandani and Lo, “What Happened to the Quants in August 2007?”

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Quants are all children of Fama and French. Lots of people are us- ing earnings revision models.

Another source remarked, “Because quants have been so successful, if you need to get out of a risk for whatever reason, you can’t get out. This leads to a liquidity sell-off.”

Specific to recent market turmoil, participants identified the unwinding of long-short positions by hedge funds as by far the most important factor contributing to the losses incurred by some quant equity finds in the sum- mer of 2007. One source said wryly, “Everyone is blaming the quants; they should be blaming the leverage.”

Improving Performance

As it was becoming increasingly difficult to deliver excess returns, many quant managers had turned to using leverage in an attempt to boost perfor- mance—a strategy most sources agreed was quite risky. The events of the summer of 2007 were to prove them right. Given the performance issues, survey participants were asked what they were likely to do to try to improve performance.

The search to identify new and unique factors was the most frequently cited strategy and complementary to it, the intention to employ new models. A CIO of equities said:

Through the crisis of July–August 2007, quant managers have learned which of their factors are unique and will be focusing on what is unique. There will be a drive towards using more propri- etary models, doing more unique conceptual work. But it will be hard to get away from fundamental concepts: you want to hold companies that are doing well and do not want to pay too much for them.

As for the need to employ new models, the global head of quantitative strategies at a large financial group remarked:

Regression is the art of today’s tool kit. To get better performance, we will have to enlarge the tool kit and add information and dy- namic and static models. People are always changing things; maybe we will be changing things just a bit quicker.

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Other strategies to improve performance given by the 2007 survey par- ticipants included attempts to diversify sources of business information and data. As one investment consultant said:

All quant managers rely on the same set of data but one cannot rely on the same data and have an analytical edge; it is a tough sell. Quant managers need an informational edge, information no one else has or uses. It might be coming out of academia or might be information in the footnotes of balance sheet data or other infor- mation in the marketplace that no one else is using.

Just over 60% of the survey participants agreed that, given that every- one is using the same data and similar models, quantitative managers need a proprietary informational edge to outperform. Sources mentioned that some hedge fund managers now have people in-house on the phone, doing proprietary market research on firms.

Opinions among survey respondents diverged as to the benefits to be derived from using high-frequency (up to tick-by-tick) data. Thirty-eight percent of the participants believed that high-frequency data can give an informational edge in equity portfolio management while 27% disagreed and 35% expressed no opinion. It is true that there was still only limited experience with using high-frequency data in equity portfolio management at the time of the survey. One source remarked, “Asset managers now have more frequent updates, what was once monthly is now daily with services such as WorldScope, Compustat, Market QA, Bloomberg, or Factset. But the use of intraday data is still limited to the trading desk.”

Fund Flows

Estimates of how much was under management in active quant strategies in 2007 vary from a few hundred million dollars to over $1 trillion. In a study that compared cumulative net flows in U.S. large-cap quantitative and “oth- er” products as a percentage of total assets during the 36-month period that coincided with the 2001–2005 value market, Casey, Quirk and Associates21 found that assets grew 25% at quantitative funds and remained almost flat for other funds. A coauthor of that study commented:

What we have seen in our studies, which looked at U.S. large-cap funds, is that since 2004 investors have withdrawn money from

21Casey, Quirk and Associates, “The Geeks Shall Inherit the Earth?” November 2005.

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the U.S. large-cap segment under fundamental managers but active quants have held on to their assets or seen them go up slightly.

Addressing the question of net flows into quantitatively managed equity funds before July–August 2007, a source at a leading investment consul- tancy said:

There has been secular growth for quant equity funds over the past 20 or so years, first into passive quant and, over the past 12–36 months, into active quant given their success in the past value mar- ket. Right now there is about an 80/20 market split between funda- mental and active quant management. If active quants can continue their strong performance in a growth market that I think we are now in, I can see the percentage shift over the next three years to 75/25 with active quant gaining a few points every year.

Despite the high-profile problems at some long-short quantitative man- aged funds during the summer of 2007, 63% of the respondents indicated that they were optimistic that, overall, quantitatively managed equity funds will continue to increase their market share relative to traditionally man- aged funds, as more firms introduce quantitative products and exchange- traded funds (ETFs) give the retail investor access to active quant prod- ucts. However, when the question was reformulated, that optimism was somewhat dampened. Thirty-nine percent of the survey participants agreed that overall quantitatively managed funds would not be able to increase their market share relative to traditionally managed funds for the year 2007 while 42% disagreed.

Many consultants who were interviewed for the study just before the July–August 2007 market turmoil were skeptical that quantitative managers could continue their strong performance. These sources cited performance problems dating back to the year 2006.

Lipper tracks flows of quantitative and nonquantitative funds in four equity universes: large cap, enhanced index funds, market neutral, and long-short funds. The Lipper data covering the performance of quantita- tively and nonquantitatively driven funds in the three-year period 2005– 2007 showed that quant funds underperformed in 2007 in all categories except large cap—a reversal of performance from 2005 and 2006 when quant managers were outperforming nonquantitative managers in all four categories. However, Lipper data are neither risk adjusted nor fee adjusted and the sampling of quant funds in some categories is small. For the period January 2005–June 2008, according to the Lipper data, long-only funds— both quant and nonquant—experienced a net outflow while all other

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categories experienced net inflows—albeit at different rates—with the exception of nonquant market neutral funds. The differences (as percent- ages) between quant and nonquant funds were not very large but quant funds exhibited more negative results.

In view of the preceding, the survey participants were asked if, given the poor performance of some quant funds in the year 2007, they thought that traditional asset management firms that have diversified into quanti- tative management would be reexamining their commitment. Nearly one third agreed while 52% disagreed (16% expressed no opinion). Those that agreed tended to come from firms at which equity assets under management represent less than 5% of all equities under management or where there is a substantial fundamental overlay to the quantitative process.

The head of quantitative equity at a large traditional manager said:

When the firm decided back in the year 2000 to build a quant business as a diversifier, quant was not seen as a competitor to fundamental analysis. The initial role of quant managers was one of being a problem solver, for 130-30-like strategies or whereever there is complexity in portfolio construction. If quant performance is down, the firm might reconsider its quant products. Should they do so, I would expect that the firm would keep on board some quants as a support to their fundamental business.

Quantitative Processes, Oversight, and Overlay

Let’s define what we mean by a quantitative process. Many traditionally managed asset management firms now use some computer-based, statistical decision-support tool and do some risk modeling. The study referred to an investment process as fundamental (or traditional) if it is performed by a human asset manager using information and judgment, and quantitative if the value-added decisions are made primarily in terms of quantitative out- puts generated by computer-driven models following fixed rules. The study referred to a process as being hybrid if it uses a combination of the two. An example of the latter is a fundamental manager using a computer-driven stock-screening system to narrow his or her portfolio choices.

Among participants in the study, two-thirds had model-driven pro- cesses allowing only minimum (5%–10%) discretion or oversight, typi- cally to make sure that numbers made sense and that buy orders were not issued for firms that were the subject of news or rumors not accounted for by the models. Model oversight was considered a control function. This oversight was typically exercised when large positions were involved. A head of quantitative equity said, “Decision making is 95% model-driven,

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but we will look at a trader’s list and do a sanity check to pull a trade if necessary.”

Some firms indicated that they had automated the process of checking if there are exogenous events that might affect the investment decisions. One source said:

Our process is model driven with about 5% oversight. We ask our- selves: “Do the numbers make sense?” and do news scanning and flagging using in-house software as well as software from a pro- vider of business information.

This comment underlines one of the key functions of judgmental overlays: the consideration of information with a bearing on forecasts that does not appear yet in the predictors. This information might include, for example, rumors about important events that are not yet confirmed, or facts hidden in reporting or news releases that escape the attention of most investors.

Fundamental analysts and managers might have sources of information that can add to the information that is publicly available. However, there are drawbacks to a judgmental approach to information gathering. As one source said, “An analyst might fall in love with the Chief Financial Officer of a firm, and lose his objectivity.”

Other sources mentioned using oversight in the case of rare events such as those of July–August 2007. The head of quantitative management at a large firm said:

In situations of extreme market events, portfolio managers talk more to traders. We use Bayesian learning to learn from past events but, in general, dislocations in the market are hard to model.

Bayesian priors are a disciplined way to integrate historical data and a man- ager’s judgment in the model.

Another instance of exercising oversight is in the area of risk. One source said, “The only overlay we exercise is on risk, where we allow our- selves a small degree of freedom, not on the model.”

The key question is: Is there a best way to comingle judgment and models? Each of these presents pitfalls. Opinions among participants in the 2007 Intertek study differed as to the advantage of commingling models and judgment and ways that it might be done. More than two-thirds of the survey participants (68%) disagreed with the statement that the most effec- tive equity portfolio management process combines quantitative tools and a fundamental overlay; only 26% considered that a fundamental overlay adds value. Interestingly, most investment consultants and fund-rating firms

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interviewed for the study shared the appraisal that adding a fundamental overlay to a quantitative investment process did not add value.

A source at a large consultancy said:

Once you believe that a model is stable, effective over a long time, it is preferable not to use human overlay as it introduces emotion, judgment. The better alternative to human intervention is to arrive at an understanding of how to improve model performance and implement changes to the model.

Some sources believed that a fundamental overlay had value in extreme situations, but not everyone agreed. One source said:

Overlay is additive and can be detrimental, oversight is neither. It does not alter the quantitative forecast but implements a reality check. In market situations such as of July–August 2007, overlay would have been disastrous. The market goes too fast and takes on a crisis aspect. It is a question of intervals.

Among the 26% who believed that a fundamental overlay does add value, sources cited the difficulty of putting all information in the models. A source that used models for asset managers said:

In using quant models, there can be data issues. With a fundamen- tal overlay, you get more information. It is difficult to convert all fundamental data, especially macro information such as the yen/ dollar exchange rate, into quant models.

A source at a firm that is using a fundamental overlay systematically said:

The question is how you interpret quantitative outputs. We do a fundamental overlay, reading the 10-Qs and the 10-Ks and the footnotes, plus looking at, for example, increases in daily sales in- voices. I expect that we will continue to use a fundamental overlay: it provides a common-sense check. You cannot ignore real-world situations.

In summary, overlays and human oversight in model-driven strategies can be implemented in different ways. First, as a control function, oversight allows managers to exercise judgment in specific situations. Second, human judgment might be commingled with a model’s forecasts.

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Implementing a Quant Process

The 2007 survey participants were asked how they managed the model build- ing and backtesting process. One-fourth of the participants said that their firms admitted several processes. For example, at 65% of the sources, quan- titative models are personally built and backtested by the asset manager; at 39%, quantitative models are built and backtested by the firm’s central re- search center. More rarely, at 23% models might also be built by the corpo- rate research center to the specifications of the asset manager, while at 16% models might also be built by the asset manager but are backtested by the research center. (The percentages do not add to 100 because events overlap.)

Some sources also cited a coming together of quantitative research and portfolio management. Certainly this is already the case at some of the larg- est quantitative players that began in the passive quantitative arena, where, as one source put it, “the portfolio manager has Unix programming skills as a second nature.”

The need to continuously update models was identified by sources as one of the major challenges to a quantitative investment process. A consul- tant to the industry remarked:

The specifics of which model each manager uses is not so important as long as management has a process to ensure that the model is al- ways current, that as a prism for looking at the universe the model is relevant, that it is not missing anything. One problem in the U.S. in the 1980s–’90s was that models produced spectacular results for a short period of time and then results decayed. The math behind the models was static, simplistic, able to capture only one trend. Today, quants have learned their lesson; they are paranoid about the need to do a constant evaluation to understand what’s working this year and might not work next year. The problem is one of cap- turing the right signals and correctly weighting them when things are constantly changing.

The need to sustain an ongoing effort in research was cited by invest- ment consultants as determinant in manager choices. One consultant said:

When quant performance decays it is often because the manager has grown complacent and then things stop working. When we look at a quant manager, we ask: Can they continue to keep doing research?

One way to ensure that models adapt to the changing environment is to use adaptive modeling techniques. One quantitative manager said:

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You cannot use one situation, one data set in perpetuity. For consis- tently good performance, you need new strategies, new factors. We use various processes in our organization, including regime-shifting adaptive models. The adaptive model draws factors from a pool and selects variables that change over time.

The use of adaptive models and of strategies that can self-adapt to changing market conditions is an important research topic. From a math- ematical point of view, there are many tools that can be used to adapt mod- els. Among these is a class of well-known models with hidden variables, including state-space models, hidden Markov models, or regime-shifting models. These models have one or more variables that represent different market conditions. The key challenge is estimation: the ability to identify regime shifts sufficiently early calls for a rich regime structure. Estimating a rich regime shifting model, however, calls for a very large data sample— something we rarely have in finance.

The survey participants were asked if they thought that quantitative- driven equity investment processes were moving towards full automation. By a fully automated quant investment process we intend a process where investment decisions are made by computers with little or no human inter- vention. An automated process includes the input of data, production of forecasts, optimization and portfolio formation, oversight, and trading. Among those expressing an opinion, as many believed that quantitative managers are moving toward full automation (38%) as not (38%). Industry observers and consultants also had difficulty identifying a trend. One source remarked, “There are all degrees of automation among quants and we see no obvious trend either towards or away from automation.” It would appear that we will continue to see a diversity in management models. This diversity is due to the fact that there is no hard science behind quantita- tive equity investment management; business models reflect the personalities and skill sets inside an organization.

Obstacles to full automation are not due to technical shortcomings. As noted earlier, there are presently no missing links in the automation chain going from forecasting to optimization. Full automation is doable, but suc- cessful implementation depends on the ability to link seamlessly a return forecasting tool with a portfolio formation strategy. Portfolio formation strategies can take the form of full optimization or be based on some heu- ristics with constraints.

The progress of full automation will ultimately depend on performance and investor acceptance. Consultants that interviewed for this study were divided in their evaluation of the advisability of full automation. One source said, “All things being equal, I actually prefer a fully automated process

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once you believe that a model is stable, effective over a long time.” How- ever, in a divergent view, another consultant said, “I am not keen on fully automated processes. I like to see human intervention, interaction before and after optimization, and especially before trading.”

Risk Management

The events of July–August 2007 highlighted once more that quantitative- ly managed funds can be exposed to the risk of extreme events (i.e., rare large—often adverse—events). Fundamentally, managed funds are also ex- posed to the risk of extreme events, typically of a more familiar nature, such as a market crash or a large drop in value of single firms or sectors. A head of quantitative management remarked, “There are idiosyncratic risks and systemic risks. Fundamental managers take idiosyncratic risk while the quants look at the marginal moves, sometimes adding leverage.”

There seems to be a gap between state-of-the-art risk management and the practice of finance. At least, this is what appears in a number of state- ments made after the summer of 2007 that attributed losses to multisigma events in a Gaussian world. It is now well known that financial phenomena do not follow normal distributions and that the likelihood of extreme events is much larger than if they were normally distributed. Financial phenomena are governed by fat-tailed distributions. The fat-tailed nature of financial phenomena has been at the forefront of research in financial econometrics since the 1990s. Empirical research has shown that returns are not normal and most likely can be represented as fat-tailed processes.

Facts like this have an important bearing on the distribution of returns of dynamic portfolios. Consequently, the 2007 study asked survey participants if they believed that the current generation of risk models had pitfalls that do not allow one to properly anticipate risks such as those of July–August 2007. Just over two-thirds of the survey respondents evaluated agreed that, because today’s risk models do not take into consideration global systemic risk factors, they cannot predict events such as those of July–August 2007. One source commented:

Risk management models work only under benign conditions and are useless when needed. We use two risk methods, principal com- ponent analysis and rare (six-sigma) events, and risk models from MSCI Barra and Northfield. But the risk models are misspecified: most pairs of stocks have high correlations.

Another source added:

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There are estimation errors in everything, including in risk models. You know that they will fail, so we add heuristics to our models. Risk models do not cover downside risk but they do help control it. Stud- ies have shown that risk models do improve the information ratio.

The growing use of derivatives in equity portfolio management is add- ing a new type of risk. One source commented:

The derivatives markets are susceptible to chaos; they overheat compared to normal markets. Derivatives contracts are complex and no one knows how they will behave in various scenarios. In ad- dition, there is credit risk or counterparty risk dealing with entities such as Sentinel—not a Wall Street firm—that can go with a puff of smoke. Their going under was blamed on the subprime crisis but it was fraud.

Sixty-three percent of the survey participants agreed that the deriva- tive market is a market driven by its own supply and demand schedule and might present risk that is not entirely explained in terms of the underlying.

Why Implement a Quant Process?

According to survey respondents, three main objectives were behind the decision to adopt (at least partially) a quantitative-based equity investment process: tighter risk control, more stable returns, and better overall per- formance. The profile of a firm’s founder(s) and/or the prevailing in-house culture were correlated in that they provided the requisite environment.

Other major objectives reported behind the decision to implement a quantitative equity investment process include diversification in general or in terms of new products such as 130-30-type strategies and scalability, including the ability to scale to different universes. Relative to the diversi- fication in a global sense, a source at a large asset management firm with a small quant group said:

An important motivating factor is diversification of the overall product lineup performance. Management believes that quant and fundamental products will not move in synch.

As for the ability to offer new products such as the long-short strategies, a source at a sell-side firm modeling for the buy side remarked:

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We are seeing a lot of interest by firms known for being fundamen- tal and that now want to introduce quant processes in the form of screens or other. These firms are trying to get into the quant space and it is the 130-30-type product that is pushing into this direction.

It was generally believed that quantitatively managed funds outperform fundamental managers in the 130-30-type arena. The ability to backtest the strategy was cited as giving quantitatively managed funds the edge. A manager at a firm that offers both fundamental and quantitative products said, “Potential clients have told us that new products such as the 130-30 strategies are more believable with extensive quant processes and testing behind them.”

More generally, sources believed that quantitative processes give an edge whenever there is a complex problem to solve. An investment consul- tant remarked:

Quant has an advantage when there is an element of financial en- gineering. The investment process is the same but quant adds value when it comes to picking components and coming up with products such as the 130-30.

Another source added:

A quant process brings the ability to create structured products. In the U.S., institutional investors are using structured products in especially fixed income and hedge funds. Given the problem of ag- ing, I would expect more demand in the future from private inves- tors who want a product that will give them an income plus act as an investment vehicle, such as a combination of an insurance-type payout and the ability to decompose and build up.

As for scalability, a consultant to the industry remarked:

One benefit a quantitative process brings to the management firms is the ability to apply a model quickly to a different set of stocks. For example, a firm that had been applying quant models to U.S. large cap also tested these models on 12–15 other major markets in the backroom. Once they saw that the models had a successful in-house track record in different universes, they began to commer- cialize these funds.

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Among survey participants, the desire to stabilize costs, revenues, and performance or to improve the cost–revenues ratio were rated relatively low as motivating factors to introduce quantitative processes. But one source at a large asset management firm said that stabilizing costs, revenues, and performance was an important factor in the firm’s decision to embrace a quantitative process. According to this source, “Over the years, the firm has seen great consistency in a quant process: Fees, revenues, and costs are all more stable, more consistent than with a fundamental process.”

Bringing management costs down was rated by participants as the weakest factor behind the drive to implement a quantitative-driven equity investment process. A source at a large asset management firm with a small quantitative group said:

Has management done a cost–benefit analysis of quant versus fundamental equity investment management process? Not to my knowledge. I was hired a few years ago to start up a quant process. But even if management had done a cost–benefit analysis and found quant attractive, it would not have been able to move into a quant process quickly. The average institutional investor has a seven-man team on the fund. If you were to switch to a two-man quant team, 80% of the clients would go away. Management has to be very careful; clients do not like to see change.

Barriers to Entry

The 2007 study concluded with an investigation of the barriers to entry in the business. Seventy-seven percent of the survey respondents believed that the active quantitative arena will continue to be characterized by the domi- nance of a few large players and a large number of small quant boutiques. Only 10% disagreed.

Participants were asked to rate a number of factors as barriers to new entrants into the quant equity investment space. The most important barrier remained the prevailing in-house culture. While one source at a fundamental- oriented firm said that very few firms are seriously opposed to trying to add discipline and improve performance by applying some quant techniques, the problem is that it is not so easy to change an organization.

A source at a large international investment consultancy commented:

For a firm that is not quant-endowed, it is difficult to make the shift from individual judgment to a quant process. Those that have been most successful in terms of size in the active quant arena are those that began in passive quant. They chose passive because they

Survey Studies of the Use of Quantitative Equity Management 223

understood it would be easier for a quantitative process to perform well in passive as opposed to active management. Most of these firms have been successful in their move to active quant management.

A source at a large firm with fundamental and quant management styles said:

Can a firm with a fundamental culture go quant? It is doable but the odds of success are slim. Fundamental managers have a differ- ent outlook and these are difficult times for quants.

Difficulty in recruiting qualified persons was rated the second most important barrier while the cost of qualified persons was considered less of a barrier. Next was the difficulty in gaining investor confidence and the entrenched position of market leaders. An industry observer remarked:

What matters most is the investment culture and market credibility. If an investor does not believe that the manager has quant as a core skill, the manager will not be credible in the arena of quant products. There is the risk that the effort is perceived by the investor as a back- room effort with three persons, understaffed, and undercommitted.

Among the selling points, participants (unsurprisingly) identified alpha generation as the strongest selling point for quant funds, followed by the disciplined approach and better risk management. Lower management and trading costs and a statistics-based stock selection process were rated lowest among the suggested selling points.

Survey participants were also asked to rate factors holding back invest- ment in active quant equity products. A lack of understanding of quant pro- cesses by investors and consultants was perceived to be the most important factor holding back investments in active quant products. As one quantita- tive manager at an essentially fundamental firm noted, “Quant products are unglamorous. There are no ‘story’ stocks to tell, so it makes it a hard sell for consultants to their clients.”

The need to educate consultants and investors alike, in an effort to gain their confidence, was cited by several sources as a major challenge going forward. Educating investors might require more disclosure about quant processes. At least that was what just under half of the survey participants believed, while one-fourth disagree and one-fourth have no opinion.

One CIO of equities who believes that greater disclosure will be required remarked:

224 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Following events of this summer [i.e., July–August 2007], quants will need to be better on explaining what they do and why it ought to work. They will need to come up with a rationale for what they are doing. They will have to provide more proof-of-concept statements.

However, among the sources that disagreed, the CIO of equities at another firm said:

One lesson from the events of July–August 2007 is that we will be more circumspect when describing what we are doing. Disclosing what one is doing can lead to others replicating the process and thus a reduction of profit opportunities.

Lack of stellar performance was rated a moderately important factor in holding back investments in quantitative funds. Lack of stellar performance is balanced by a greater consistency in performance. A source at a fund rat- ing service said, “Because quant funds are broadly diversified, returns are watered down. Quants do not hit the ball out of the park, but they deliver stable performance.” The ability to deliver stable if not stellar performance can, of course, be turned into a major selling point.

Quantitative managers cite how Oakland Athletics’ manager Billy Beane improved his team’s performance using sabermetrics, the analysis of base- ball through objective (i.e., statistical) evidence. Beane’s analysis led him to shifting the accent from acquiring players who hit the most home runs to acquiring players with the most consistent records of getting on base.22 Interestingly, Beane is credited with having made the Oakland Athletics the most cost-effective team in baseball though winning the American League Championship Series has proved more elusive.

CHALLENGES FOR QUANTITATIVE EQUITY INVESTING

The studies we have just discussed suggested challenges that participants see in implementing quantitative strategies. We can see a number of ad- ditional challenges. Robust optimization, robust estimation, and the in- tegration of the two are probably on the research agenda of many firms. As asset management firms strive to propose innovative products, robust and flexible optimization methods will be high on the R&D agenda. In addition, as asset management firms try to offer investment strategies to meet a stream of liabilities (i.e., measured against liability benchmarking),

22As reported in Michael Lewis, Moneyball: The Art of Winning an Unfair Game (New York: Norton, 2003).

Survey Studies of the Use of Quantitative Equity Management 225

multistage stochastic optimization methods will become a priority for firms wanting to compete in this arena. Pan, Sornette, and Kortanek call “Intel- ligent Finance” the new field of theoretical finance at the confluence of dif- ferent scientific disciplines.23 According to them, the theoretical framework of intelligent finance consists of four major components: (1) financial infor- mation fusion, (2) multilevel stochastic dynamic process models, (3) active portfolio and total risk management, and (4) financial strategic analysis.

Modelers are facing the problem of performance decay that is the con- sequence of a wider use of models. Classical financial theory assumes that agents are perfect forecasters in the sense that they know the stochastic processes of prices and returns. Agents do not make systematic predict- able mistakes: their action keeps the market efficient. This is the basic idea underlying rational expectations and the intertemporal models of Merton.24

Practitioners (and now also academics) have relaxed the hypothesis of the universal validity of market efficiency; indeed, practitioners have always been looking for asset mispricings that could produce alpha. As we have seen, it is widely believed that mispricings are due to behavioral phenomena, such as belief persistence. This behavior creates biases in agent evaluations— biases that models attempt to exploit in applications such as momentum strategies. However, the action of models tends to destroy the same sources of profit that they are trying to exploit. This fact receives specific attention in applications such as measuring the impact of trades. In almost all cur- rent implementations, measuring the impact of trades means measuring the speed at which models constrain markets to return to an unprofitable effi- ciency. To our knowledge, no market impact model attempts to measure the opposite effect, that is, the eventual momentum induced by a trade.

It is reasonable to assume that the diffusion of models will reduce the mispricings due to behavioral phenomena. However, one might reasonably ask whether the impact of models on prices will ultimately make markets more efficient, destroying any residual profitability in excess of market returns, or if the action of implementing models will create new opportuni- ties that can be exploited by other models, eventually by a new generation of models based on an accurate analysis of model biases. It is far from being obvious that markets populated by agents embodied in computerized pro- grams tend to be efficient. In fact, models might create biases of their own. For example, momentum strategies (buy winners, sell losers) are a cata- lyst for increased momentum, further increasing the price of winners and depressing the price of losers.

23Heping Pan, Dider Sornette, and Kenneth Kortanek, “Intelligent Finance—An Emerging Direction.” Quantitative Finance 6, no. 4 (2006): 273–277. 24Robert C. Merton, “An Intertemporal Capital Asset Pricing Model,” Economet- rica 41, no. 5 (1973): 867–887.

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This subject has received much attention in the past as researchers stud- ied the behavior of markets populated by boundedly rational agents. While it is basically impossible, or at least impractical, to code the behavior of human agents, models belong to a number of well-defined categories that process past data to form forecasts. Several studies, based either on theory or on simulation, have attempted to analyze the behavior of markets popu- lated by agents that have bounded rationality, that is, filter past data to form forecasts.25 One challenge going forward is to study what type of ineffi- ciencies are produced by markets populated by automated decision-makers whose decisions are based on past data. It is foreseeable that simulation and artificial markets will play a greater role as discovery devices.

MODELING AFTER THE 2007–2009 GLOBAL FINANCIAL CRISIS

The period following the 2007–2009 global financial crisis has witnessed the acceleration of a number of modeling trends identified in previous re- search by Fabozzi, Focardi, and Jonas. In particular, the growing awareness of the nonnormal nature of returns is fueling efforts to adopt models and risk measures able to cope with nonlinearity. Among these are conditional value-at-risk (CVaR) to measure risk and copula functions to measure co- movements. Regime shifting models, which are in principle able to capture transitions from one regime to another, for example from stable to volatile market states, are increasingly being considered as a modeling option. Mod- elers also sought to find new factors and new predictors (hopefully unique), using new data sources, in particular from the derivatives market. However, as equity markets began to rebound in 2010, modeling strategies that essen- tially work in growth markets were back in favor. This includes strategies such as equal-weighted portfolios that benefit from both mean reversion and upward market valuations.

The 2007–2009 global financial crisis underlined the importance of asset allocation in explaining returns. The renewed awareness of the overwhelming

25For the theoretical underpinning of bounded rationality from a statistical point of view, see Thomas J. Sargent, Bounded Rationality in Macroeconomics (New York: Oxford University Press, 1994). For the theoretical underpinning of bounded ra- tionality from a behavioral finance perspective, see Daniel Kahneman, “Maps of Bounded Rationality: Psychology for Behavioral Economics,” American Economic Review 93, no. 5 (2003): 1449–1475. For a survey of research on computational finance with boundedly rational agents, see Blake LeBaron, “Agent-Based Computa- tional Finance,” in Handbook of Computational Economics, edited by Leigh Tesfat- sion and Kenneth L. Judd (Amsterdam: North-Holland, 2006).

Survey Studies of the Use of Quantitative Equity Management 227

importance of asset allocation, compared to, for example, stock selection or execution, has accelerated the adoption of dynamic asset allocation. According to the paradigm of dynamic asset allocation, investors switch into and out of asset classes, or at least dynamically change the weighting of different asset classes, as a function of the their forecast of the average return of each class. While traditional asset allocation is reviewed at time horizons of one to three years, the time horizon of dynamic asset allocation is typically of the order of months.

The execution process has also undergone important changes since about 2004. The increasing availability of intraday (or high frequency) data and modeling techniques based on optimizing the market impact of trades are behind the diffusion of program trading and high-frequency trading. Program trading, which utilizes computer programs to reduce the market impact of large trades by subdividing a large trade into many small trades with optimal rules, created a flow of high-frequency trades that has, in turn, created trading opportunities for those able to make, at a very low cost, many small trades with very short holding periods. Holding periods for high-frequency trades are generally less than one day and can be as short as a few milliseconds.

The diffusion of high-frequency trading, which is now estimated to rep- resent more than half of all trading activity on major U.S and European exchanges, has fundamentally changed the characteristics of exchanges and created a new generation of models. High-frequency trading is a form of trading that leverages high-speed computing, high-speed communications, tick-by-tick data, and technological advances to execute trades in as little as milliseconds. A typical objective of high-frequency trading is to identify and capture (small) price discrepancies present in the market. This is done using computer algorithms to automatically capture and read market data in real- time, transmit thousands of order messages per second to an exchange, and execute, cancel or replace orders based on new information on prices or demand.26

Lastly, awareness of systemic risk has created a new area of research whose objective is to measure market connectivity. This research is based on a fundamental property of all random networks, namely that random networks exhibit connectivity thresholds. Below the connectivity thresh- olds, clusters remain small, with an exponential distribution; however, when approaching the connectivity threshold, very large clusters can be formed. This fact has an important bearing on risk management because connected

26For a review of the issues and opportunities associated with high-frequency trad- ing, see Frank J. Fabozzi, Sergio M. Focardi, and Caroline Jonas, “High-Frequen- cy Trading: Methodologies and Market Impact,” Review of Futures Markets, 19 (2011): 7–38.

228 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

clusters might propagate large losses. An example from the 2007–2009 cri- sis is the propagation of losses due to the subprime mortgage crisis. Focardi and Fabozzi suggest the use of a connectivity parameter based on percola- tion theory to improve the measurement of credit risk.27 More recently, and in the wake of the 2007–2009 global financial crisis, the Bank of England’s executive director of financial stability Andrew Haldane, suggested the use of connectivity parameters to measure the risk of widespread contagion and propagation of losses.28

KEY POINTS

■ The first decade of the twentieth century witnessed an increasing use of quantitative models in investment management.

■ Initially used primarily in passive management and risk management, models are increasingly used in active management and to engineer innovative investment strategies such as the use of optimized indexes and dynamic asset allocation. One reason many investment firms built up quantitative teams was to have the ability to extend the product offering to new products for which there is demand, such as exchange- traded funds.

■ The performance of models has improved; this improved performance has been particularly effective in active strategies, where it has helped reduce risk.

■ Factor models are the primary methodology of financial modeling in investment management; they are used to forecast returns and to com- pute exposure to risk factors. Momentum and reversal models, cash flow-based models, and behavioral models are also widely used. It is likely that multiple models suitable for different market conditions are needed and we begin to see the deployment of adaptive models able to adapt to changing market conditions.

■ Thanks to progress in robust estimation techniques and robust opti- mization methods, portfolio optimization is now being used in asset management.

■ Execution has been impacted by the availability of tick-by-tick data and fast computer and communications technology, making program trading and subsequently high-speed trading the new “best execution.”

27Sergio M. Focardi and Frank J. Fabozzi, “A Percolation Approach to Modeling Credit Loss Distribution Under Contagion,” Journal of Risk 7, no. 1 (2004): 75–94. 28Andrew G. Haldane, “Rethinking the Financial Network,” Speech to the Financial Student Association in Amsterdam (April 28, 2009).

Survey Studies of the Use of Quantitative Equity Management 229

■ While much progress has been made in modeling, many economic and financial phenomena are still being handled by humans. Macroeco- nomic issues, such as the understanding of what conditions lead to a crisis are an example. However, new modeling techniques such as Mar- kov switching models are beginning to tackle these areas.

■ Looking forward a major use of methods to handle nonlinearities and fat-tailed distributions, the use of risk measures suitable for nonlinear distributions such as conditional VaR, and methods to measure the complexity of the financial system is expected.

QUESTIONS

1. What is the purpose of estimating model risk?

2. How is behavioral modeling used?

3. What are some of the reasons for the greater use of optimization techniques?

4. What are meant by a fundamental, quantitative, and hybrid investment processes?

5. a. Why are adaptive modeling techniques used by quantitative equity managers?

b. Describe several examples of adaptive modeling techniques and the challenge in using them.

6. What is meant by “performance decay”?

7. How has the execution process undergone important changes in recent years?

231

CHAPTER 9 Implementable Quantitative

Equity Research* Frank J. Fabozzi, Ph.D., CFA, CPA

Professor of Finance EDHEC Business School

Sergio M. Focardi, Ph.D. Professor of Finance

EDHEC Business School and

Partner, The Intertek Group

K. C. Ma, Ph.D., CFA KCM Asset Management, Inc.

and Roland George Chair of Applied Investments

Stetson University

F inance is by nature quantitative like economics but it is subject to a large level of risk. It is the measurement of risk and the implementation of decision-making processes based on risk that makes finance a quantitative science and not simply accounting. Equity investing is one of the most fun- damental processes of finance. With the diffusion of affordable fast comput- ers and with progress made in understanding financial processes, financial modeling has become a determinant of investment decision-making pro- cesses. Despite the growing diffusion of financial modeling, objections to its use are often raised.

*Parts of this chapter are adapted from Frank J. Fabozzi, Sergio M. Focardi, and K. C. Ma, “Implementable Quantitative Research and Investment Strategies,” Journal of Alternative Investments 8, no. 2 (2005): 71–79.

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In the second half of the 1990s, there was so much skepticism about quan- titative equity investing that David Leinweber, a pioneer in applying advanced techniques borrowed from the world of physics to fund management, wrote an article entitled: “Is quantitative investment dead?”1 In the article, Leinwe- ber defended quantitative fund management and maintained that in an era of ever faster computers and ever larger databases, quantitative investment was here to stay. The skepticism toward quantitative fund management, pro- voked by the failure of some high-profile quantitative funds at that time, was related to the fact that investment professionals felt that capturing market inefficiencies could best be done by exercising human judgment.

Despite mainstream academic opinion that held that equity markets are efficient and unpredictable, the asset managers’ job is to capture market inefficiencies and translate them into enhanced returns for their clients. At the academic level, the notion of efficient markets has been progressively relaxed. Empirical evidence led to the acceptance of the notion that financial markets are somewhat predictable and that systematic market inefficiencies can be detected. There has been a growing body of evidence that there are market anomalies that can be systematically exploited to earn excess profits after considering risk and transaction costs.2 In the face of this evidence, Andrew Lo proposed replacing the efficient market hypothesis with the adaptive market hypothesis as market inefficiencies appear as the market adapts to changes in a competitive environment.3

In this scenario, a quantitative equity investment management process is characterized by the use of computerized rules as the primary source of decisions. In a quantitative process, human intervention is limited to a con- trol function that intervenes only exceptionally to modify decisions made by computers. We can say that a quantitative process is a process that quantifies things. The notion of quantifying things is central to any modern science, including the dismal science of economics. Note that everything related to accounting—balance sheet/income statement data, and even accounting at the national level—is by nature quantitative. So, in a narrow sense, finance has always been quantitative. The novelty is that we are now quantifying things that are not directly observed, such as risk, or things that are not quantitative per se, such as market sentiment and that we seek simple rules to link these quantities.

1David Leinweber, “Is Quantitative Investing Dead?” Pensions & Investments, Feb- ruary 8, 1999. 2For a modern presentation of the status of market efficiency, see M. Hashem Pesa- ran, “Market Efficiency Today,” Working Paper 05.41, Institute of Economic Policy Research, 2005. 3Andrew Lo, “The Adaptive Markets Hypothesis: Market Efficiency from an Evolu- tionary Perspective,” Journal of Portfolio Management 30 (2004): 15–29.

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The gradual move of replacing traditional human judgments with machine calculations is based on the assumption that computers outper- form most humans. Since a quantitative process is capable of systematically handling a large amount of information quickly and consistently, ambiguity and unpredictability that are often associated with subjective choices during decision making can be kept to a minimum. For fact or fancy, most mod- ern portfolio managers include some form of quantitative approach in their overall investment process.

However, “quants” are often too anxious and overzealous to prove their points. This attitude leads to several side effects that offset some of the advantages of quantitative analysis. First, cards can be unintentionally stacked toward locating some significant pattern that they are eager to show. Finding a way to do this is much easier than conventional subjective reason- ing, due to fast computing power that allows numerous trials and errors. Second, using the conventional criterion of significance at some statistical level, researchers who are superstitious of its power often quickly jump to the wrong conclusion. What they sometimes fail to realize is that statistical significance is neither a necessary nor sufficient condition for implementable excess returns because trading strategies often work only on portions of the data. For example, a return reversal strategy might be profitable even if the information coefficient is very low at a good confidence level. Third, humans have a tendency to only look at the unusual. Do you notice an event because it is interesting or is it interesting because you notice it? The resulting bias is that theories are established or tests are performed more easily on extraor- dinary events, and seemingly correlations are easily mistaken for causalities. This bias is further reinforced by high-speed computing, since quantitative tools are very efficient in locating outliers and finding correlations.

In this chapter, we explain the process of performing quantitative equity research and converting that research into implementable trading strategies. We begin by comparing the discovery process in the physical sciences and in economics.

THE RISE OF ECONOPHYSICS

Before outlining a general framework for quantitative equity research, let’s briefly compare the discovery process in the physical sciences and in econom- ics. The classical view of scientific discovery (albeit grossly oversimplified) is one of empirical observations plus human genius. Vast amounts of data are collected and then a theoretical synthesis is made. The end result is a mathematical model that explains the data and allows accurate predictions. In modern science, this process forces us to make model revisions when even very small discrepancies occur between prediction and observation.

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Let’s mention a few points that have become pivotal to modern scien- tific methodology and that are important as well to economics:

1. “Observation” is far from being an obvious term. Any observation pre- supposes some theory. In the parlance of the modern philosophy of sci- ence, we say that observations are “theory laden.” Thus we see a strati- fication of science, where advanced theories live on the back of simpler theories. For example, the so called “stylized facts” are an example of first level theories. They are empirical observations that presuppose a significant amount of theory.

2. There is an ongoing debate as to whether science actually “describes” an objective reality or simply provides recipes for predicting the out- come of observations without any descriptive pretension. In economics, the latter point of view was forcefully made by Milton Friedman.4

3. In general, different (infinite) models can explain the same data. The criterion of choice between different theories is often “aesthetic” in the sense of mathematical simplicity and elegance. Theories can always be mended to accommodate new facts: eventually they are replaced by simpler and more elegant theories.

4. It is questionable whether the process of discovery is an unexplicable product of human genius or if there is some compelling logic that inevi- tably leads to discoveries.

We do not want to discuss these points here, but only to point out that the above considerations have become important in economics and financial theories. There is one point of departure from economics and the physical sciences: in the physical sciences theories are constructed and validated on empirical data with a high level of accuracy. One makes experiments and tests different empirical settings. However, the level of statistical significance of theories in the physical sciences is extremely high

Methodologies used in economics5 are different from those used in the physical sciences in three key ways:

1. Economic laws are never validated with a high level of precision: There is ample room for ambiguity.

2. The economy is a human artifact as well as an intelligent processor of information: One cannot think of the economy as a permanent physical

4Milton Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1953). 5The same considerations apply to other scientific domains ranging from biology, medicine, ecological studies, and so on. Our focus here is economics.

Implementable Quantitative Equity Research 235

object. In today’s parlance, economies are evolving, self-reflecting, com- plex systems.

3. With the advent of computers, human creativity is complemented and even replaced by a learning approach based on statistics and data mining.

The field of “econophysics,” a term used by Mantegna and Stanley,6 has tried to bridge the gap between the two worlds, drawing attention to the need for strict scientific validation of laws and results. Still it is important to realize that true differences exist, to avoid the forcing upon economics of an impossible scientific paradigm. We have to ask on what genuine knowledge implementable strategies are based.

The level of significance of economic theories is low: No economic model fits data with a very high level of significance. Many different models fit data and it is often impossible to distinguish them on the basis of signifi- cance. The financial literature is full of bona fide defenses of contradictory facts. As a consequence, in economics it is very difficult to generalize and integrate theories. This happens because every theory or model is somehow misspecified and passes tests only within a given level of approximations and significance. When different models are integrated and generalized, approximations no longer hold.

For these reasons, two principles are fundamental in economic analysis: (1) model simplicity and (2) out-of-sample validation. We can place a higher level of confidence on a simple model validated on data different from those on which it has been built. These principles apply in particular when a “learning” approach is deployed. A learning approach is based on models of unbounded complexity able to perfectly fit any set of data. For example, an autoregressive model can have an arbitrary number of lags, a neural net- work can have an arbitrary number of nodes, and so on. Models of this type can describe any set of data with arbitrary precision. For example, provided that a sufficient number of lags is allowed, an autoregressive model can describe any time series with zero error. Forecasting performance, however, would be extremely bad as the model fits noise.

A GENERAL FRAMEWORK

The common objective of a quantitative process is to identify any per- sistent pattern in the data and, in finance, convert it into implementable

6Rosario N. Mantegna and H. Eugene Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge: Cambridge University Press, 2000).

236 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

and profitable investment strategies. Given the relatively young life of its application to investment management, we find that there is a need to explore the general process of a quantitative procedure, and identify some of the commonly induced biases in this process. Specifically, in Ex- hibit 9.1, we provide a flowchart that demonstrates the process of how quantitative research is performed and converted into implementable trading strategies. Generally, it includes developing underlying economic theories, explaining actual returns, estimating expected returns, and for- mulating corresponding portfolios. We discuss each step in the following sections.

EXHIBIT 9.1 Process of Quantitative Research and Investment Strategy

Develop an ex ante Hypothesis

Select a Survivorship-Free Sample

Estimate a Parameter-Free Model

No Yes

Quantitative Research

Investment Strategy

Estimate Expected Returns

Independent Risk Control

No Yes

No Yes

Implementable Quantitative Equity Research 237

Develop a Truly Ex Ante Economic Justification

Sound economic hypothesis is a necessary condition for the birth of an im- plementable and replicable investment strategy. True economics, however, can only be motivated with creative intuitions and scrutinized by strict logi- cal reasoning, but it does not come from hindsight or prior experience. This requirement is critical since scientific conclusions can easily be contaminat- ed by the process of data snooping, especially when a truly independent economic theory is not established first.

Data snooping (or data mining) is identifying seemingly significant but in fact spurious patterns in the data.7 All empirical tests are at risk for this problem, especially if a large number of studies have been performed on the same data sets. Given enough time and trials, people who are convinced of the existence of a pattern will eventually manage to find that pattern, real or imagined. Furthermore, there is an identical life cycle of experience in data snooping. Researchers are often confronted with exactly the same issues and will have to make the same types of choices in the process.

The process of data snooping comes in several forms. At some basic but subtle level, an economic hypothesis is founded by the knowledge of past patterns in data. Researchers may establish their “prior” from their knowledge, learning, experience, or simply what others have said. A good example for a classic yet wrong way to model the excess return is “market capitalization should be included in the model because there is evidence of a size effect.”

From then on, the problem can only get worse as long as there is more room for choices. A researcher may choose to design the same statistical tests because of what others have done using similar data. The choices in these tests include, but are not limited to, the selection of explanatory vari- ables, how to measure them, the functional form of the model, the length of the time period, the underlying probability distribution, and test statistics. The difference in each of these artificial choices by itself may be small, but its resulting investment performance impact is often significant.

Ideally, there should be no need to make artificial selections since all of the tests should have been dictated by the underlying economic theo- ries. However, even the best economic concept, being abstract and simpli- fied, does not always fully specify its application in reality. There are ample opportunities that decision makers have to find proxies and instruments to complete the process.

7See, for example, Stephen A. Ross, “Survivorship Bias in Performance Studies,” and Andrew Lo, “Data-Snooping Biases in Financial Analysis,” both appearing in Pro- ceedings of Blending Quantitative and Traditional Equity Analysis (Charlottesville, VA: Association for Investment Management and Research, 1994).

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Always Start from the Beginning!

A common fallacy, however, is that researchers tend to go back to the most immediate prior step in searching for solutions when the result is not what they expect to see. Of course, this attitude reflects the general human ten- dency to overweight the information in the most recent period in their deci- sion making. This could easily lead to the mindless trial of numerous alter- natives, which are most likely not justified.

Therefore, a direct way to control for data snooping at all levels is that the entire process will have to be reconstructed right from the beginning whenever the output at any step cannot pass the quality test. If the estimated model cannot explain the variation of excess returns to some satisfactory degree, the process needs to be stopped and abandoned. We need to go back to Step 1 and develop a new theory. If the predicted model does not produce acceptable excess returns, go back to Step 1. Finally, if the level of the actual risk-adjusted excess return found from following the strategy “does not cut the muster”—go back to Step 1. This “trial-and-error” process may correct for most, but not all, of the data snooping problem. As we throw away the obvious, “bad” models through testing, we learn from the experience of trial and error. This experience itself inevitably affects the seemingly “inde- pendent” creation of the economic intuition of next generation.

Of course, most of us would agree that there is almost no way to com- pletely eliminate some form of data snooping since even the most rigorous scientific process is no more than a sequence of choices, subjective or not. As suggested by Andrew Lo,8 like someone suffering from substance abuse, the first sign of recovery is the recognition of the problem. The next step is to facilitate a research environment that avoids the temptations of making choices. (This reluctance is probably the single most important reason for the recently developed machine learning techniques.) What this conclusion also means is that researchers should be extremely disciplined at every step of the process in making choices, with the explicit understanding of the problem and bias induced from data snooping.

SELECT A SAMPLE FREE FROM SURVIVORSHIP BIAS

Since all backtest research is performed on a data set that looks back in time, the entire history of an observation will not be available if it does not survive the present. The sample that researchers can work with is a set of observations that have been preselected through time by some common de- nominators. A sample of a sample should not pose a problem if the subset

8Lo, “Data-Snooping Biases in Financial Analysis.”

Implementable Quantitative Equity Research 239

is selected randomly. But this is not the case for most samples, which suffer from survivorship bias. The bias becomes relevant if the common bond to survive the observation is related to the pattern for which we are looking. A finding of a statistically significant pattern merely reflects the underlying common bond that was used to construct the testing sample.

One typical point of interest, which is severely affected by the survivor- ship bias, is performance comparison. By only looking at the portfolios cur- rently outstanding, it is obvious that portfolios that did not survive through time due to poor performance are excluded from the sample. By design, the sample only contains good portfolios. How can the true factors that have caused the bad performance ever be identified?

Commercial data vendors are not helping on this issue. Because of cost consideration, most data sets are only provided on a live basis. That is, for a currently non-existent sample observation, the common practice is to delete its entire history from the data set. To simulate the true historical situation, it is the researchers’ responsibility to bring these observations back to the sample. The sample collection procedure should be reversed in time. Cases that existed at the beginning of the sample period should be included and tracked through time.

SELECT A METHODOLOGY TO ESTIMATE THE MODEL

The selection of a certain methodology should pass the same quality tests as developing economic theories and selecting samples. Without strong intuition, researchers should choose the methodology that needs the least amount of human inputs. A good example is the machine-learning method that uses computerized algorithms to discover the knowledge (pattern or rule) inherent in data. Advances in modeling technology such as artificial intelligence, neural network, and genetic algorithms fit in this category. The beauty of this approach is its vast degree of freedom. There are none of the restrictions, which are often explicitly specified in traditional, linear, station- ary models.

Of course, researchers should not rely excessively on the power of the method itself. Learning is impossible without knowledge. Even if you want to simply throw data into an algorithm and expect it to spit out the answer, you need to provide some background knowledge, such as the justification and types of input variables. There are still numerous occasions that require researchers to make justifiable decisions. For example, a typical way of modeling stock returns is using the following linear form,

ER it = a + b1tF1it-1 + b2tF2it-1 + ... bntFnit-1 (9.1)

240 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

where

ER it

= excess return for the ith security in period t Fj

it-1 = jth factor value for the ith security at the beginning of period t bkt = the market-wide payoff for factor k in period t

Trade-Off between Better Estimations and Prediction Errors

Undoubtedly, in testing and estimating equation (9.1), the first task is to decide which and how many explanatory variables should be included. This decision should not be a question whether the test is justified by a truly ex ante economic hypothesis. Economic theories, however, are often developed with abstract concepts that need to be measured by alternative proxies. The choice of proper proxies, while getting dangerously close to data snooping, makes the determination of both the type and the number of explanatory variables an art rather than a science. The choice of a particular proxy based on the rationale “Because it works!” is not sufficient unless it is first backed up by the theory.

One rule of thumb is to be parsimonious. A big model is not neces- sarily better, especially in the context of predictable risk-adjusted excess return. While the total power of explanation increases with the number of variables (size) in the model, the marginal increase of explanatory power drops quickly after some threshold. Whenever a new variable is intro- duced, what comes with the benefit of the additional description is the increase of estimation error of an additional parameter. In Exhibit 9.2, we demonstrate the explanatory power of a typical multifactor model for stock returns by including one additional variable at a time from a study conducted by Ma in 2010.9 The second and the third columns clearly show that although by design the R-square increases with the number of the variables, the adjusted R-square, which also reflects the impact of the additional estimation error, levels off and starts decreasing after some point. This example suggests that in the process of estimation, the cost of estimation error is even compounded when new prediction is further extended into the forecast period. In Exhibit 9.2, we also perform out-of- sample prediction based on the estimated multifactor model in each stage. Columns 4 and 5 in the exhibit show a more striking pattern that the risk- adjusted excess return, in the form of information ratio, deteriorates even more quickly when the model becomes large.

9Christopher K. Ma, “How Many Factors Do You Need?” Research Paper #96-4, KCM Asset Management, Inc. (2005 and 2010).

Implementable Quantitative Equity Research 241

Animal Spirits

It is the exact same objectivity that quantitative analysts are proud of re- garding their procedures that often leads to the question, “If everyone has the algorithms, will they not get the same answers?” The “overmining” on the same data set using simple linear models almost eliminates the possibil- ity of gaining economic profit.

Pessimism resulting from the competition of quantitative research also justifies the need to include some form of “animal spirit” in the deci- sion process. Being able to do so is also probably the single most impor- tant advantage that traditional security analysis can claim over quantita- tive approach. Casual observations provide ample examples that investor behavior determining market pricing follows neither symmetric nor linear patterns: investors tend to react to bad news much differently than to good news;10 information in more recent periods is overweighed in the decision

10See Keith Brown, W. Van Harlow, and Seha.M. Tinic, “Risk Aversion, Uncertain Information, and Market Efficiency,” Journal of Financial Economics 22, no. 2 (1988): 355–386.

EXHIBIT 9.2 Marginal Contribution of Additional Explanatory Variables

In Sample Out of Sample

Additional Explanatory

Variable

Explanatory Power (R2)

Explanatory Power

(Adj. R2)

Annualized Excess Return

(%)

Annualized Standard Deviation

(%) Information

Ratio

1st 0.086 0.082 2.52 7.15 0.352

2nd 0.132 0.105 2.98 7.10 0.420

3rd 0.175 0.117 3.61 6.97 0.518

4th 0.188 0.165 3.82 6.82 0.560

5th 0.202 0.174 4.05 6.12 0.662

6th 0.251 0.239 3.99 6.08 0.656

7th 0.272 0.221 3.76 6.19 0.607

8th 0.282 0.217 3.71 6.22 0.596

9th 0.291 0.209 3.64 6.37 0.571

10th 0.292 0.177 3.53 6.58 0.536

Source: K. C. Ma, “How Many Factors Do You Need?” Research Paper #96-4, KCM Asset Management, Inc. (2010).

242 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

process;11 investors ignore the probability of the event but emphasize the magnitude of the event;12 stocks are purchased for their glamour but not for intrinsic value;13 and, low PE stocks paying high returns do not imply that high price–earnings stocks pay low returns.14 We are not proposing that a quantitative model should include all these phenomenon, but the modeling methodology should be flexible enough to entertain such possibilities if they are warranted by the theory.

Statistical Significance Does Not Guarantee Economic Profits

As a result, staunch defenders of quantitative research argue that profitable strategies cannot be commercialized by quantitative analysis;15 the produc- tion of excess returns will stay idiosyncratic and proprietary. Profits will originate in those proprietary algorithms that outperform commercially standardized packages for data analysis. In other words, researchers will have to learn to gain confidence even if there is no statistical significance, while statistical significance does not guarantee economic profit.

Since quantitative market strategists often start with the identification of a pattern that is defined by statistical standards, it is easy to assume eco- nomic profit from conventional statistical significance. To show that there is not necessarily a link, we perform a typical momentum trading strategy that is solely based on the predictability of future returns from past returns. A simplified version of the return-generating process under this framework follows:

E t-1(Rt) = a + bt-1Rt-1

where E t-1(Rt) is the expected return for the period t, estimated at point t –

1, a is time-invariant return, and b t-1 is the momentum coefficient observed

at time t-1. When b t-1 is (statistically) significantly positive, the time-series

returns are said to exhibit persistence and positive momentum. To imple- ment the trading strategy using the information in correlations, stocks with

11See Werner F. DeBondt and Richard Thaler,” Does the Stock Market Overreact?” Journal of Finance 40, no. 1 (1985): 793–805. 12See K. C. Ma, “Preference Reversal in Futures Markets,” working paper, Stetson University, 2010. 13See Josef Lakonishok, Andrei Shleifer, and Robert W. Vishny, “Contrarian Invest- ment, Extrapolation, and Risk,” Journal of Finance 49, no. 5 (1994): 1541–1578. 14See K. C. Ma, “How Many Factors Do You Need?” Stetson University, 2005 and 2010. 15See, for example, Russell H. Fogler, “Investment Analysis and New Quantitative Tools,” Journal of Portfolio Management (1995): 39–47.

Implementable Quantitative Equity Research 243

at least a certain level of correlation are included in portfolios at the begin- ning of each month, and their returns are tracked. The performance of these portfolios apparently reflects the statistical significance (or lack of) in cor- relation between successive returns. In Exhibit 9.3, we summarize the per- formance of some of the representative portfolios from a study conducted and updated by Ma in 2005 and 2010.16

It is not surprising that higher excess returns are generally associated with higher correlation between successive returns. More importantly, higher risk seems to be also related to higher statistical significance of the relationship (correlation). The bottom line is that an acceptable level of risk-adjusted excess return, in the form of information ratio (e.g., 1), can- not always be achieved by statistical significance alone. A more striking observation, however, is that, sometime without conventional statistical sig- nificance, the portfolio was able to deliver superior risk-adjusted economic profit. While the driving force may yet be known, evidence is provided for the disconnection between statistical significance and economic profit.

A Model to Estimate Expected Returns

The estimation for the model to explain past returns from Step 3, by itself, is not enough, since the objective of the process is to predict future returns. A good model for expected return is much harder to come by since we simply don’t have enough data. As pointed out by Fischer Black, people are often confused between a model to explain average returns and a model to predict

16Ma, “How Many Factors Do You Need?” 2005 and 2010.

EXHIBIT 9.3 Statistical Significance and Economic Profits

Correlation Coefficienta t-Valueb

Annual Excess Return (%)

Annual Standard Deviation (%)

Information Ratio

0.10 2.10b 0.50 2.17 0.230

0.25 3.78b 1.82 4.06 0.448

0.50 7.15b 3.71 4.25 0.873

0.15 1.20 0.58 1.10 0.527

0.35 2.93b 1.98 4.55 0.435

0.60 2.75b 3.80 4.55 0.835

aSignificant at the 1% level. bt-value is for the significance of correlation coefficient. Source: K. C. Ma, “How Many Factors Do You Need?” Research Paper #96-4, KCM Asset Management, Inc., 2010.

244 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

expected returns.17 While the former can be tested on a large number of historical data points, the latter requires such a long time period (sometimes decades) to cover various conditions to predict the expected return. Since we do not have that time to wait, one common shortcut is to simply as- sume that the model to explain average returns will be the model to predict expected returns. Of course, such prediction is highly inaccurate, given the assumption of constant expected returns.

We can easily find evidence to show it is a bad assumption. For exam- ple, if one can look at the actual model that explains the cross-sections of short-term stock returns, even the most naive researcher can easily conclude that there is little resemblance between the models from one period to the next. This would in turn suggest, at least in the short term, the model to explain past returns cannot be used to predict expected returns.

We are calling for brand new efforts to establish an ex ante expected return model. The process has to pass the same strict tests for quality that are required for any good modeling, as discussed earlier. These tests would include the independent formulation of the hypothesis for expected return and a methodology and sample period free from data snooping and survi- vorship bias. While they are not necessarily related, the process of develop- ing hypotheses for conditional expected return models can greatly benefit from the insights from numerous models of past returns estimated over a long time period.

Largest Value Added

Apparently, the final risk-adjusted returns from a strategy can be attributed to the proper execution of each step described in Exhibit 9.1. The entire process can be generally described in a three-step procedure consisting of economic hypothesis, model estimation, and prediction. It is only natural for researchers to ask how to allocate their efforts among the three steps to maximize the return contribution.

To answer this question, we examine the return contribution from model estimation and prediction. For this purpose, we use a typical multi- factor model to explain the return for all stocks in the Standard & Poor’s 500 Index. Assume that at the beginning of each period, the best model actually describing the return in the period is known to the portfolio man- ager. Using this information, a portfolio consisting of the predicted top quartile is formed. The excess return from this portfolio generated with perfect information would suggest the extent of return contribution from

17Fischer Black, “Estimating Expected Return,” Financial Analysts Journal 49, no. 5 (1993): 36–38.

Implementable Quantitative Equity Research 245

model estimation. Accordingly, based on a 2010 study by Ma18 reported in Exhibit 9.4, the annual mean excess return of the top predicted quartile is between 12% and 26%, depending on the length of the investment horizon.

In contrast, the annual mean excess return of the actual top quartile in the S&P 500 Index is between 42% and 121%. The difference in excess return between the actual top quartile portfolio and the predicted top quar- tile portfolio, between 30% and 95%, would suggest the extent of the return contribution from model prediction. It is clear then that for all investment horizons, the return contribution from model prediction is on average two to five times the excess returns from model estimation.

Therefore, for all practical purposes, the step of identifying a predict- able model is responsible for the largest potential value added in generating predictable excess returns. The implication is that resources allocated to research should be placed disproportionally toward the effort of out-of- sample prediction.

Test the Prediction Again!

Another safeguard against data snooping is to scrutinize the model once more through time. That is, the conditional model to estimate expected re- turn needs to be tested again in a “fresh” data period. As it requires multiple

18K. C. Ma, “Nonlinear Factor Payoffs?” Research Paper #97-5, KCM Asset Man- agement, Inc., 2010.

EXHIBIT 9.4 Potential Returns for Perfect Estimation and Prediction: S&P 500 Stocks, 1975–2010

Annualized Excess Returns if Perfect Foresight

Best Modela for S&P 500 Actualb S&P 500 Quartiles

Top Quartile

Bottom Quartile

Top Quartile

Bottom Quartile

Monthly periodc 19.3% –21.4% 121.7% –97.5%

Quarterly period 25.7 –26.1 91.2 –82.1

Annual period 11.8 –13.6 42.5 –26.7

aThe parameters of the actual model to explain S&P 500 performance is known beforehand. bThe performance of each stock, in terms of the actual quartile, is known beforehand. cThe length of investment horizon for each portfolio is rebalanced based on the perfect information.

Source: K. C. Ma, “Nonlinear Factor Payoffs?” Research Paper #97-5, KCM Asset Management, Inc., 2010.

246 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

time periods to observe the conditional model for expected returns, the pre- diction model derived under a single condition has to be confirmed again. In Exhibit 9.5, we specify the relationship in time periods among estimation, testing, and confirmation.

The sequential testing of the prediction model in the forecast period would affirm the condition that converts the model of actual returns to the model of expected returns still produces an acceptable level of performance. As the conditioning factor varies from one period to anther, the consistent performance of the three-period process suggests that it is not driven by a constant set of artificial rules introduced by data snooping.

Test against a Random Walk

After completing the modeling exercise it is always wise to test the model against an artificial data set formed from independent and identically dis- tributed returns. Any trading strategy applied to purely random data should yield no average profit. Of course, purely random fluctuations will produce profits and losses. However, because we can simulate very long sequences of data, we can test with high accuracy that our models do not actually intro- duce artefacts that will not live up to a real life test.

RISK CONTROL

Even if the expected return is modeled properly at the individual stock level, the bottom line of implementable investment strategies is evaluated by an acceptable level of risk-adjusted portfolio excess returns. As most institu- tional portfolios are benchmarked, the goal is to minimize tracking error (standard deviation of excess returns), given some level of portfolio excess return. Consequently, risk control becomes technically much more complex than the conventional efficient portfolio concept. As shown by Richard Roll, an optimal portfolio that minimizes tracking error subject to a level of excess return is not a mean-variance efficient portfolio.19 It should be noted that, due to the objective and competitive nature of the quantita- tive approach in its strong form, most models produce similar rankings in

19Richard R. Roll, “A Mean/Variance Analysis of Tracking Error,” Journal of Port- folio Management 18, no. 4 (1992): 13–23.

EXHIBIT 9.5 The Sample Period

Estimation Testing Forecast Estimation Testing Forecast

Period I Period I Period I Period II Period II Period II . . . Now

Implementable Quantitative Equity Research 247

expected returns. The variation in performance among quantitative portfo- lios is mainly attributed to a superior risk control technology.

One commonly used, but less preferred practice in risk management is often performed right at the stage of identifying the model for expected returns. It involves revising the estimates from the model to explain the actual return. The purpose is to control the risk by attempting to reduce the estimation error for the model of expected returns. This approach has several flaws. First, in most cases, the procedure of revising the parameter estimates (from the model of actual returns) so they can be used in the model of expected returns is often performed on an ad hoc basis, and vul- nerable to data snooping. Second, in revising the parameter estimates, the task of building a relevant expected model with low prediction errors is mis- taken for risk control on portfolio returns. Finally, there is a lesser degree of freedom in that estimates are made based on the estimates of previous steps. The “risk control” procedure becomes dependent to the process of estimating expected returns. Consequently, an independent risk control pro- cedure, usually through an optimization process, should be performed as an overlay on the stock selections that are determined initially by the predicted expected returns.

For computing efficiency, the iterations can be significantly reduced if several other conditions are simultaneously imposed. For example, it has been shown that the largest source of tracking error is the deviation of port- folio sector weights from its benchmark sector weights.20 Consequently, most optimal benchmarked portfolios are “sector neutral,” that is, port- folios do not make sector bets against the benchmark. This consideration would indicate the need to include a constraint that sets maximum accept- able deviations of portfolio sector weights from benchmark sector weights.

Along the same line, tracking error can be further controlled when the individual stock weight is constrained to conform to its corresponding weight in the benchmark. It is also accomplished by setting a maximum allowed deviation of stock weight in the portfolio from the weight in the benchmark.

Additional realistic portfolio constraints may be considered. Examples would include specification of a (1) minimum level of market liquidity for individual stocks, (2) maximum absolute weight in which any stock is allowed to invest, (3) minimum total number of stocks held, (4) minimum number of stocks held in each sector, and (5) maximum level of portfolio turnover allowed.

20See Ma, “Nonlinear Factor Payoffs?”

248 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

KEY POINTS

■ Despite mainstream academic opinion equity markets are efficient, there is a growing body of evidence that there are market anomalies that can be systematically exploited to earn excess profits after considering risk and transaction costs.

■ The technological advances in computing power have tempted investors to use machines to make investment decisions. In the process of doing so, it is easy to lose sight of the essence of human knowledge required in any good decision making process.

■ In evaluating models for potential implementation of investment strat- egies, two guiding principles are model simplicity and out-of-sample validation. We can place a higher level of confidence on a simple model validated on data different from those on which it has been built.

■ In the quantitative process the identification of any persistent pattern in the data is sought and must then be converted it into implementable and prof- itable investment strategies. How this is done requires the development of underlying economic theories, an explanation of actual returns, estimation of expected returns, and construction of corresponding portfolios.

■ For backtesting proposed strategies, the sample used can be a set of observations that have been preselected through time by some com- mon denominators. Although a sample of a sample should not pose a problem in backtesting if the subset is selected randomly, this is not the case for most samples that suffer from survivorship bias. A statistically significant pattern found for a strategy may merely reflect the underly- ing common bond that was used to construct the testing sample.

■ The selection of a methodology for estimating a model should satisfy the same quality tests as developing economic theories and selecting samples. In the absence of strong intuition, the methodology that needs the least amount of human inputs should be employed for estimating a model.

■ For both testing and model estimation, the first task is to decide which and how many explanatory variables should be included. Economic theories underlying a model typically involve abstract concepts that need to be measured by alternative proxies. Selection of the appropriate proxies, while getting dangerously close to data snooping, makes the determination of both the type and the number of explanatory variables an art rather than a science. One rule of thumb is to be parsimonious.

■ To safeguard against data snooping there should be a sequential testing of the prediction model in the forecast period in order to affirm that the condition that converts the model of actual returns to the model of expected returns still produces an acceptable level of performance.

Implementable Quantitative Equity Research 249

■ Even if the expected return is modeled properly at the individual stock level, the bottom line of implementable investment strategies is evalu- ated by an acceptable level of risk-adjusted portfolio excess returns. Because most institutional portfolios are benchmarked, the objective is to minimize tracking error given some level of portfolio excess return. For this purpose, risk control becomes technically much more complex than the conventional efficient portfolio concept.

QUESTIONS

1. What is the extent and purpose of human intervention in a quantitative investment management process?

2. How are the methodologies utilized in economics different from those employed in the physical sciences?

3. What is the common objective of all quantitative processes?

4. What are the steps in the process for converting quantitative research into an implementable trading process?

5. What is meant by “data snooping”?

6. Why would it be prudent to test a quantitative model before it is imple- mented against an artificial data set formed from independent and iden- tically distributed returns?

251

CHAPTER 10 Tracking Error and Common Stock

Portfolio Management Raman Vardharaj, CFA

Portfolio Manager OppenheimerFunds

Frank J. Fabozzi, Ph.D., CFA, CPA Professor of Finance

EDHEC Business School

Frank J. Jones, Ph.D. Professor of Finance

San Jose State University

In this chapter, we describe the concept of tracking error, how it is com-puted, and identify some of the factors that affect tracking error for an equity portfolio.

DEFINITION OF TRACKING ERROR

The risk of a portfolio can be measured by the standard deviation of port- folio returns. This statistical measure provides a range around the average return of a portfolio within which the actual return over a period is likely to fall with some specific probability. The mean return and standard deviation (or volatility) of a portfolio can be calculated over a period of time.

The standard deviation or volatility of a portfolio or a market index is an absolute number. A portfolio manager or client can also ask what the variation of the return of a portfolio is relative to a specified benchmark. Such variation is called the portfolio’s tracking error.

252 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Specifically, tracking error measures the dispersion of a portfolio’s returns relative to the returns of its benchmark. That is, tracking error is the standard deviation of the portfolio’s active return where active return is defined as:

Active return Portfolio actual return Benchmar= − kk actual return

A portfolio created to match the benchmark index (i.e., an index fund) that regularly has zero active returns (i.e., always matches its benchmark’s actual return) would have a tracking error of zero. But a portfolio that is actively managed that takes positions substantially different from the bench- mark would likely have large active returns, both positive and negative, and thus would have an annual tracking error of, say, 5% to 10%.

To find the tracking error of a portfolio, it is first necessary to specify the benchmark. The tracking error of a portfolio, as indicated, is its stan- dard deviation relative to the benchmark, not its total standard deviation. Exhibit 10.1 presents the information used to calculate the tracking error for a hypothetical portfolio and benchmark using 30 weekly observations. The fourth column in the exhibit shows the active return for the week. It is from the data in this column that the tracking error is computed. As reported in the exhibit, the standard deviation of the weekly active returns is 0.54%. This value is then annualized by multiplying by the square root of 52—52 representing the number of weeks in a year. This gives a value of 3.89%. If the observations were monthly rather than weekly, the monthly tracking error would be annualized by multiplying by the square root of 12.

Given the tracking error, a range for the possible portfolio active return and corresponding range for the portfolio can be estimated assuming that the active returns are normally distributed. For example, assume the following:

Benchmark = S&P 500 Expected return on S&P 500 = 20% Tracking error relative to S&P 500 = 2%

Then, the range for portfolio returns and associated probabilities are as follows:

Number of Standard Deviations

Range for Portfolio Active Return

Corresponding Range for Portfolio Return Probability

1 ±2% 18%–22% 67%

2 ±4% 16%–24% 95%

3 ±6% 14%–26% 99%

Tracking Error and Common Stock Portfolio Management 253

EXHIBIT 10.1 Data and Calculation for Active Return, Alpha, and Information Ratio

Weekly Returns (%)

Week Portfolio Benchmark Active

1 3.69% 3.72% −0.03% 2 −0.56 −1.09 0.53 3 −1.41 −1.35 −0.06 4 0.96 0.34 0.62 5 −4.07 −4.00 −0.07 6 1.27 0.91 0.37 7 −0.39 −0.08 −0.31 8 −3.31 −2.76 −0.55 9 2.19 2.11 0.09

10 −0.02 −0.40 0.37 11 −0.46 −0.42 −0.05 12 0.09 0.71 −0.62 13 −1.93 −1.99 0.06 14 −1.91 −2.37 0.46 15 1.89 1.98 −0.09 16 −3.75 −4.33 0.58 17 −3.38 −4.22 0.84 18 0.60 0.62 −0.02 19 −10.81 −11.60 0.79 20 6.63 7.78 −1.15 21 3.52 2.92 0.59 22 1.24 1.89 −0.66 23 −0.63 −1.66 1.03 24 3.04 2.90 0.14 25 −1.73 −1.58 −0.15 26 2.81 3.05 −0.23 27 0.40 1.64 −1.23 28 1.03 1.03 0.01 29 −0.94 −0.95 0.00 30 1.45 1.66 −0.21

Average of active returns = 0.04% Standard deviation of active returns = 0.54%

Annualizing: Annual average = Weekly average × 52 Annual variance = Weekly variance × 52 Annual std dev = Weekly std dev × (520.5)

Therefore, on an annual basis: Alpha = 1.83% (= 0.04% × 52 = Annualized average of weekly active returns) Tracking error = 3.89% (= 0.54% × [520.5] = Annualized std dev of weekly active returns) Information ratio = Alpha/Tracking error = 1.83%/3.89%= 0.47

254 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Tracking Error for an Active/Passive Portfolio

A manager can pursue a blend of an active and a passive (i.e., indexing) strategy. That is, a manager can construct a portfolio such that a certain percentage of the portfolio is indexed to some benchmark index and the bal- ance actively managed. Assume that the passively managed portion (i.e., the indexed portion) has a zero tracking error relative to the index. For such a strategy, we can show (after some algebraic manipulation) that the tracking error for the overall portfolio would be as follows:

Portfolio tracking error relative to index = (Percent of portfolio actively managed) × (Tracking error of the actively managed portion relative to index)

An enhanced index fund differs from an index fund in that it deviates from the index holdings in small amounts and hopes to slightly outper- form the index through those small deviations. In terms of an active/passive strategy, the manager allocates a small percentage of the portfolio to be actively managed. The reason is that in case the bets prove detrimental, then the underperformance would be small. Thus, realized returns would always deviate from index returns only by small amounts. There are many enhanc- ing strategies. Suppose that a manager whose benchmark is the S&P 500 pursues an enhanced indexing strategy allocating only 5% of the portfolio to be actively managed and 95% indexed. Assume further that the tracking error of the actively managed portion is 15% with respect to the S&P 500. The portfolio would then have a tracking error calculated as follows:

Percent of portfolio actively managed relative to S&P 500 = 5% Tracking error relative to S&P 500 = 15% Portfolio’s tracking error relative to S&P 500 = 5% × 15% = 0.75%

COMPONENTS OF TRACKING ERROR

There are two distinct approaches to portfolio selection. The first is a top- down approach. Here the manager tries to pick broad economic themes, such as sectors, style, size, and the like, which are likely to outperform in the coming periods and holds stocks that are consistent with the chosen theme. The second is a bottom-up approach, where the manager picks each individual stock in the portfolio on its own merit.

Insofar as the themes or stocks emphasized in the portfolio differ from those in the benchmark (through overweights and underweights), there will

Tracking Error and Common Stock Portfolio Management 255

be a tracking error. We can then view the tracking error as arising partly from the theme-picking and partly from the stock-picking.

Since top-down managers believe they can add value mainly through discerning trends in returns associated with broad themes, they may want to reduce the portion of their portfolio’s tracking error that arises from stock- specific reasons.

Bottom-up managers believe it is difficult, if not impossible, to forecast trends in themes. Returns associated with such broad themes tend to be volatile and this can amplify mistakes. Such managers believe it is more prudent to place a lot of small bets via stock selection than to place a few large bets via theme selection. Bottom-up managers would, therefore, seek to reduce the portion of the tracking error of their portfolios that comes from theme-specific reasons.

To answer the needs of these two types of managers, it would be useful to decompose a portfolio’s tracking error along these lines. Fortunately, this can be done using multifactor risk models.

FORWARD-LOOKING VS. BACKWARD-LOOKING TRACKING ERROR

In Exhibit 10.1 the tracking error of the hypothetical portfolio is shown based on the active returns reported. However, the performance shown is the result of the portfolio manager’s decisions during those 30 weeks with respect to portfolio positioning issues such as beta, sector allocations, style tilt (that is, value versus growth), stock selections, and the like. Hence, we can call the tracking error calculated from these trailing active returns a backward-looking tracking error. It is also called the ex post tracking error.

One problem with a backward-looking tracking error is that it does not reflect the effect of current decisions by the portfolio manager on the future active returns and hence the future tracking error that may be realized. If, for example, the manager significantly changes the portfolio beta or sector allocations today, then the backward-looking tracking error that is calcu- lated using data from prior periods would not accurately reflect the current portfolio risks going forward. That is, the backward-looking tracking error will have little predictive value and can be misleading regarding portfolio risks going forward.

The portfolio manager needs a forward-looking estimate of tracking error to accurately reflect the portfolio risk going forward. The way this is done in practice is by using the services of a commercial vendor that has a model, called a multifactor risk model, that has defined the risks associated with a benchmark index. Statistical analysis of the historical return data of the stocks

256 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

in the benchmark index are used to obtain the factors and quantify their risks. (This involves the use of variances and correlations.) Using the manager’s cur- rent portfolio holdings, the portfolio’s current exposure to the various factors can be calculated and compared to the benchmark’s exposures to the factors. Using the differential factor exposures and the risks of the factors, a forward- looking tracking error for the portfolio can be computed. This tracking error is also referred to as the predicted tracking error or ex ante tracking error.

There is no guarantee that the forward-looking tracking error at the start of, say, a year would exactly match the backward-looking tracking error calculated at the end of the year. There are two reasons for this. The first is that as the year progresses and changes are made to the portfolio, the forward-looking tracking error estimate would change to reflect the new exposures. The second is that the accuracy of the forward-looking tracking error depends on the extent of the stability in the variances and correlations that were used in the analysis. These problems notwithstanding, the average of forward-looking tracking error estimates obtained at different times dur- ing the year will be reasonably close to the backward-looking tracking error estimate obtained at the end of the year.

Each of these estimates has its use. The forward-looking tracking error is useful in risk control and portfolio construction. The manager can imme- diately see the likely effect on tracking error of any intended change in the portfolio. Thus, she can do a what-if analysis of various portfolio strategies and eliminate those that would result in tracking errors beyond her tolerance for risk. The backward-looking tracking error can be useful for assessing actual performance analysis, such as the information ratio discussed next. Evaluating the factors that caused past portfolio performance, called attribu- tion analysis, is an important use.

INFORMATION RATIO

Alpha is the average active return over a time period. Since backward-look- ing tracking error measures the standard deviation of a portfolio’s active return, it is different from alpha. A portfolio does not have backward-look- ing tracking error simply because of outperformance or underperformance. For instance, consider a portfolio that outperforms (or underperforms) its benchmark by exactly 10 basis points every month. This portfolio would have a backward-looking tracking error of zero and a positive (negative) alpha of 10 basis points. In contrast, consider a portfolio that outperforms its benchmark by 10 basis points during half the months and underperforms by 10 basis points during the other months. This portfolio would have a backward-looking tracking error that is positive but an alpha equal to zero.

Tracking Error and Common Stock Portfolio Management 257

(Note that in some texts, alpha and tracking error are calculated respec- tively as the average and the standard deviation of the beta-adjusted active return, instead of the total active return.)

The information ratio combines alpha and tracking error as follows:

Information ratio Alpha

Backward-looking track =

iing error

The information ratio is essentially a reward-to-risk ratio. The reward is the average of the active return, that is, alpha. The risk is the standard deviation of the active return, the tracking error, and, more specifically, backward- looking tracking error. The higher the information ratio, the better the man- ager performed relative to the risk assumed.

To illustrate the calculation of the information ratio, consider the active returns for the hypothetical portfolio shown in Exhibit 10.1. The weekly average active return is 0.04%. Annualizing the weekly average active return by multiplying by 52 gives an alpha of 1.83%. Since the backward- tracking error is 3.89%, the information ratio is 0.47 (1.83%/3.89%).

DETERMINANTS OF TRACKING ERROR

Several factors affect the level of tracking error. The major factors include:

■ Number of stocks in the portfolio ■ Portfolio market capitalization and style difference relative to the

benchmark ■ Sector deviation from the benchmark ■ Market volatility ■ Portfolio beta

The impact of each of these factors is investigated in Vardharaj, Fabozzi, and Jones.1

Number of Stocks in the Portfolio

Tracking error decreases as the portfolio progressively includes more of the stocks that are in the benchmark index. This general effect is illustrated in Exhibit 10.2 that shows the effect of portfolio size for a large-cap portfolio benchmarked to the S&P 500. Notice that an optimally chosen portfolio of just 50 stocks can track the S&P 500 within 1.6%. For midcap and

1Raman Vardharaj, Frank J. Fabozzi, and Frank J. Jones, “Determinants of Tracking Error For Equity Portfolios,” Journal of Investing 13, no. 2 (2004): 37–47.

258 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

small-cap stocks, Vardharaj, Fabozzi, and Jones found that the tracking er- rors are 3.5% and 4.3%, respectively.2 In contrast, tracking error increases as the portfolio progressively includes more stocks that are not in the bench- mark. This effect is illustrated in Exhibit 10.3. In this case, the benchmark index is the S&P 100 and the portfolio progressively includes more and more stocks from the S&P 500 that are not in the S&P 100. The result is that the tracking error with respect to the S&P 100 rises.

Portfolio Market Cap and Style Difference Relative to the Benchmark

Vardharaj, Fabozzi, and Jones found tracking error increases as the aver- age market cap of the portfolio deviates from that of the benchmark in- dex.3 Tracking error also increases as the overall style (growth/value) of the portfolio deviates from that of the benchmark index. First, holding style constant, they find that tracking error rises when the cap size difference increases. For example, a midcap blend portfolio has a tracking error of 7.07% while a small-cap blend portfolio has a tracking error of 8.55% with respect to the S&P 500, which is a large-cap blend portfolio. Second, for a given cap size, tracking error is greater when the style is either growth or value than when it is the blend. 2Ibid. 3Ibid.

EXHIBIT 10.2 Typical Tracking Error vs. the Number of Benchmark Stocks in the Portfolio for the S&P 500

8%

7%

6%

5%

4%

3%

2%

1%

0%

T ra

ck in

g E

rr or

Large Cap Benchmark: S&P 500

Number of Benchmark (S&P 500) Stocks in the Portfolio

50 100 150 200 250 300 350 400 450 500

Tracking Error and Common Stock Portfolio Management 259

EXHIBIT 10.3 Tracking Error vs. the Number of Nonbenchmark Stocks in the Portfolio

4%

3%

2%

1%

0%

T ra

ck in

g E

rr or

Benchmark: S&P 100

Portfolio Universe: S&P 500

400350300250200150100500 Number of Stocks in the Portfolio that are not

Present in the Benchmark (S&P 100)

Vardharaj, Fabozzi, and Jones examine portfolios that deviate from the S&P 500 either in cap size or in style and have the same tracking error. They find that the farther a portfolio is from the center of the Morningstar equity fund box for large-cap blend stocks (proxied by S&P 500), the greater is its tracking error.

Sector Deviation from the Benchmark

When a portfolio’s allocations to various economic sectors differ from those of its benchmark, it results in tracking error. In general, when the differ- ences in sector allocation increase, the tracking error increases. Vardharaj, Fabozzi, and Jones found that in general, the tracking error increased as the level of sector bets increased.

Market Volatility

Managed portfolios generally hold only a fraction of the assets in their benchmark. Given this, a highly volatile benchmark index (as measured in terms of standard deviation) would be harder to track closely than a gener- ally less volatile benchmark index. As market volatility rises, the portfolio tracking error increases. This correspondingly increases the probability of

260 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

“dramatic underperformance,” by which we mean an underperformance of 10% or more. This can be seen in Exhibit 10.4. On the horizontal axis of the exhibit is the tracking error and on the vertical axis is the probability of a shortfall of 10% or more from the benchmark index. (In this calculation, we assumed normal distribution of active returns and an alpha of zero.)

As the tracking error rises, the probability of dramatic outperformance increases just as much as the probability of dramatic underperformance. But, the portfolio management consequences of these two types of extreme relative performances are not symmetric—dramatic underperformance can cause a manager to be terminated. Another implication is that since an increase in market volatility increases tracking error and, thereby, the chances of dramatic underperformance, there is an increased need for man- agers to monitor the portfolio tracking error more frequently and closely during periods of high market volatility.

Portfolio Beta

The beta for the market portfolio is 1 and beta for the risk-free portfolio (cash) is zero. Suppose an investor holds a combination of cash and the market portfolio. Then, the portfolio beta falls below 1. The managed port- folio is less sensitive to systematic risk than the market, and is therefore less risky than the market. Conversely, when the investor holds a leveraged market portfolio, by borrowing at the risk-free rate and investing in the market portfolio, the beta is above 1, and the portfolio is more risky than the market.

EXHIBIT 10.4 Tracking Error and Dramatic Shortfall

40%

35%

30%

25%

20%

15%

10%

5%

0%

C ha

nc es

o f

D ra

m at

ic S

ho rt

fa ll

0% 5% 10% 15% 20% 25% Tracking Error

Tracking Error and Common Stock Portfolio Management 261

EXHIBIT 10.5 Tracking Error and Beta

T ra

ck in

g E

rr or

0.00 0.50 1.00 1.50 2.00 Beta

It can be demonstrated that the portfolio tracking error with respect to the market portfolio, increases both when the beta falls below 1 and when the beta rises above 1. So, as the portfolio increases the proportion of cash held, even though its absolute risk falls, its tracking error risk rises. As shown in Exhibit 10.5, tracking error rises linearly as the beta deviates from 1.

In the above example, we make the simplistic assumption that the man- ager only chooses between holding the market portfolio and cash when making changes to its beta. In the more general case where the fund can hold any number of stocks in any proportion, its beta can differ from 1 due to other reasons. But, even in this general case, the tracking error increases when the portfolio beta deviates from the market beta.

MARGINAL CONTRIBUTION TO TRACKING ERROR

Since tracking error arises from various bets (some intentional and some un- intentional) placed by the manager through overweights and underweights relative to the benchmark index, it would be useful to understand how sen- sitive the tracking error is to small changes in each of these bets.

Suppose, for example, a portfolio initially has an overweight of 3% in the semiconductor industry relative to its benchmark index, and that the tracking error is 6%. Suppose that the tracking error subsequently increases to 6.1% due to the semiconductor industry weight in the portfolio increas- ing by 1% (and hence the overweight goes to 4%). Then, it can be said that this industry adds 0.1% to tracking error for every 1% increase in its weight. That is, its marginal contribution to tracking error is 0.1%. This would hold only at the margin, that is, for a small change, and not for large changes.

262 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Marginal contributions can be also calculated for individual stocks. If the risk analysis employs a multifactor risk model, then similar marginal contribution estimates can be obtained for the risk factors also.

Generally, marginal contributions would be positive for overweighted industries (or stocks) and negative for underweighted ones. The reason is as follows. If a portfolio already holds an excess weight in an industry, then increasing this weight would cause the portfolio to diverge further from the benchmark index. This increased divergence adds to tracking error, leading to a positive marginal contribution for this industry. Suppose, however, the portfolio has an underweight in an industry. Then, increasing the portfo- lio weight in this industry would make the portfolio converge towards the benchmark, thus reducing tracking error. This leads to a negative marginal contribution for this industry.

An analysis of the marginal contributions can be useful for a manager who seeks to alter the portfolio tracking error. Suppose a manager wishes to reduce the tracking error, then she should reduce portfolio overweights in industries (or stocks) with the highest positive marginal contributions. Alternatively, she can reduce the underweights (that is, increase the overall weights) in industries (or stocks) with the most negative marginal contribu- tions. Such changes would be most effective in reducing the tracking error while minimizing the necessary turnover and the associated expenses.

KEY POINTS

■ Tracking error is a key concept in understanding the potential perfor- mance of a common stock portfolio relative to a benchmark index and the actual performance of a common stock portfolio relative to a bench- mark index.

■ Tracking error can be used to measure the degree of active management by a portfolio manager.

■ Tracking error measures the variation of a portfolio’s active return (i.e., the difference between the portfolio return and the benchmark return).

■ Backward-looking tracking error or ex post tracking error is tracking error calculated from historical active returns; it will have little predic- tive value and can be misleading regarding portfolio risks going forward.

■ A portfolio manager used forward-looking tracking error to estimate portfolio risk going forward.

■ The information ratio, found by dividing alpha (i.e., the average active return over a time period) by the backward tracking error, is a reward- to-risk ratio.

Tracking Error and Common Stock Portfolio Management 263

■ As the portfolio differs from its benchmark index in terms of the number of stocks held, their average market caps, sector allocations, and beta, its tracking error rises. Tracking error also rises in volatile markets.

■ For a portfolio manager, the risk of heavily underperforming or out- performing the benchmark rises as the tracking error increases. Thus tracking error is an important indicator of portfolio performance and should be monitored frequently.

QUESTIONS

1. Calculate the annualized alpha, tracking error, and information ratio based on the 12 monthly returns below:

Month Active Return (%)

1 0.37

2 –0.31

3 –0.55

4 0.09

5 0.37

6 –0.05

7 –0.62

8 0.06

9 0.46

10 –0.09

11 0.58

12 0.84

2. Assuming active returns are normally distributed, calculate the expected returns about the benchmark at various at the 67%, 95%, and 99% confidence levels assuming the following data:

Expected active return (%) 2%

Tracking error (%) 3%

Benchmark expected return 8%

3. Suppose that a manager whose benchmark is the S&P 500 pursues an enhanced indexing strategy allocating 10% of the portfolio to be actively managed and 90% indexed. Assume further that the tracking

264 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

error of the actively managed portion is 12% with respect to the S&P 500. What is the portfolio’s tracking error?

4. Why is backward-looking tracking error not a good indicator of future risk?

5. In practice, how is forward-looking tracking error calculated?

6. Why is there no guarantee that the forward-looking tracking error at the start of a quarter will exactly match the backward-looking tracking error calculated at the end of that quarter?

7. a. What does the marginal contribution to tracking error mean? b. Suppose that the marginal contribution to tracking error for some

factor is negative. What does that mean? c. Why is the marginal contribution to tracking error a useful measure

for a portfolio manager?

265

CHAPTER 11 Factor-Based Equity Portfolio

Construction and Analysis Petter N. Kolm, Ph.D.

Deputy Director of the Mathematics in Finance Masters Program and Clinical Associate Professor

Courant Institute of Mathematical Sciences, New York University

Joseph A. Cerniglia Visiting Researcher

Courant Institute of Mathematical Sciences, New York University

Frank J. Fabozzi, Ph.D., CFA, CPA Professor of Finance

EDHEC Business School

Common stock investment strategies can be broadly classified into the fol-lowing categories: (1) factor-based trading strategies (also called stock selection or alpha models), (2) statistical arbitrage, (3) high-frequency strat- egies, and (4) event studies. Factors and factor-based models form the core of a major part of today’s quantitative trading strategies. The focus of this and the companion chapter that follows is on developing trading strategies based on factors constructed from common (cross-sectional) characteris- tics of stocks. For this purpose, first we provide a definition of factors. We then examine the major sources of risk associated with trading strategies, and demonstrate how factors are constructed from company characteristics and market data. The quality of the data used in this process is critical. We examine several data cleaning and adjustment techniques to account for problems occurring with backfilling and restatements of data, missing data, inconsistently reported data, as well as survivorship and look-ahead biases. In the last section of this chapter, we discuss the analysis of the statistical properties of factors. In the companion chapter, we extend this analysis to

266 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

include multiple factors and cover techniques used to implement multifactor trading strategies.

In a series of examples throughout both chapters, we show the indi- vidual steps for developing a basic trading strategy. The purpose of these examples is not to provide yet another profitable trading strategy, but rather to illustrate the process an analyst may follow when performing research. In fact, the factors that we use for this purpose are well known and have for years been exploited by industry practitioners. We think that the value added of these examples is in the concrete illustration of the research and development process of a factor-based trading model.

FACTOR-BASED TRADING

Since the first version of the classic text on security analysis by Benjamin Graham and David Dodd1—considered to be the Bible on the fundamen- tal approach to security analysis—was published in 1934, equity portfolio management and trading strategies have developed considerably. Graham and Dodd were early contributors to factor-based strategies because they extended traditional valuation approaches by using information throughout the financial statements2 and by presenting concrete rules of thumb to be used to determine the attractiveness of securities.3

Today’s quantitative managers use factors as fundamental building blocks for trading strategies. Within a trading strategy, factors determine when to buy and sell securities. We define a factor as a common character- istic among a group of assets. In the equities market, it could be a particu- lar financial ratio such as the price–earnings (P/E) or the book–price (B/P) ratios. Some of the most well-known factors and their underlying basic eco- nomic rationale references are provided in Exhibit 11.1.

Most often this basic definition is expanded to include additional objec- tives. First, factors frequently are intended to capture some economic intu- ition. For instance, a factor may help understand the prices of assets by reference to their exposure to sources of macroeconomic risk, fundamental characteristics, or basic market behavior. Second, we should recognize that assets with similar factors (characteristics) tend to behave in similar ways. This attribute is critical to the success of a factor. Third, we would like

1Benjamin Graham and David Dodd, Security Analysis (New York: McGraw-Hill, 1962). 2Benjamin Graham, The Intelligent Investor (1949; reprint New York: Harper & Row, 1973). 3Peter L. Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street (New York: The Free Press, 1992).

Factor-Based Trading Strategies I: Factor Construction and Analysis 267

EXHIBIT 11.1 Summary of Well-Known Factors and Their Underlying Economic Rationale

Factor Economic Rationale

Dividend yield Investors prefer to immediately receive receipt of their investment returns.

Value Investors prefer stocks with low valuations.

Size (market capitalization) Smaller companies tend to outperform larger companies.

Asset turnover This measure evaluates the productivity of assets employed by a firm. Investors be- lieve higher turnover correlates with higher future return.

Earnings revisions Positive analysts’ revisions indicate stronger business prospects and earnings for a firm.

Growth of fiscal year 1 and fiscal year 2 earnings estimates

Investors are attracted to companies with growing earnings.

Momentum Investors prefer stocks that have had good past performance.

Return reversal Investors overreact to information, that is, stocks with the highest returns in the cur- rent month tend to earn lower returns the following month.

Idiosyncratic risk Stocks with high idiosyncratic risk in the current month tend to have lower returns the following month.

Earnings surprises Investors like positive earnings surprises and dislike negative earnings surprises

Accounting accruals Companies with earnings that have a large cash component tend to have higher future returns.

Corporate governance Firms with better corporate governance tend to have higher firm value, higher profits, higher sales growth, lower capital expendi- tures, and fewer corporate acquisitions.

Executive compensation factors Firms that align compensation with share- holders interest tend to outperform.

Accounting risk factors Companies with lower accounting risk tend to have higher future returns.

268 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

our factor to be able to differentiate across different markets and samples. Fourth, we want our factor to be robust across different time periods.

Factors fall into three categories—macroeconomic influences, cross- sectional characteristics, and statistical factors. Macroeconomic influences are time series that measure observable economic activity. Examples include interest rate levels, gross domestic production, and industrial production. Cross-sectional characteristics are observable asset specifics or firm character- istics. Examples include, dividend yield, book value, and volatility. Statistical factors are unobservable or latent factors common across a group of assets. These factors make no explicit assumptions about the asset characteristics that drive commonality in returns. Statistical factors, also referred to as latent factors, are not derived using exogenous data but are extracted from other variables such as returns. These factors are calculated using various statistical techniques such as principal components analysis or factor analysis.

Within asset management firms, factors and forecasting models are used for a number of purposes. Those purposes could be central to managing portfolios. For example, a portfolio manager can directly send the model output to the trading desk to be executed. In other uses, models provide ana- lytical support to analysts and portfolio management teams. For instance, models are used as a way to reduce the investable universe to a manageable number of securities so that a team of analysts can perform fundamental analysis on a smaller group of securities.

Factors are employed in other areas of financial theory, such as asset pricing, risk management, and performance attribution. In asset pricing, researchers use factors as proxies for common, undiversifiable sources of risk in the economy to understand the prices or values of securities to uncer- tain payments. Examples include the dividend yield of the market or the yield spread between a long-term bond yield and a short-term bond yield.4 In risk management, risk managers use factors in risk models to explain and to decompose variability of returns from securities, while portfolio managers rely on risk models for covariance construction, portfolio construction, and risk measurement. In performance attribution, portfolio managers explain past portfolio returns based on the portfolio’s exposure to various factors. Within these areas, the role of factors continues to expand. Recent research presents a methodology for attributing active return, tracking error, and the information ratio to a set of custom factors.5

The focus in this and the companion chapter is on using factors to build equity forecasting models, also referred to as alpha or stock selection models.

4Eugene F. Fama and Kenneth R. French, “Dividend Yields and Expected Stock Re- turns,” Journal of Financial Economics 22, no. 1 (1988): 3–25. 5Jose Menchero and Vijay Poduri, “Custom Factor Attribution,” Financial Analysts Journal 62, no. 2 (2008): 81–92.

Factor-Based Trading Strategies I: Factor Construction and Analysis 269

The models serve as mathematical representations of trading strategies. The mathematical representation uses future returns as dependent variables and factors as independent variables.

DEVELOPING FACTOR-BASED TRADING STRATEGIES

The development of a trading strategy has many similarities with an engi- neering project. We begin by designing a framework that is flexible enough so that the components can be easily modified, yet structured enough that we remain focused on our end goal of designing a profitable trading strategy.

Basic Framework and Building Blocks

The typical steps in the development of a trading strategy are:

■ Defining a trading idea or investment strategy. ■ Developing factors. ■ Acquiring and processing data. ■ Analyzing the factors. ■ Building the strategy. ■ Evaluating the strategy. ■ Backtesting the strategy. ■ Implementing the strategy.

In what follows, we take a closer look at each step.

Defining a Trading Idea or Investment Strategy

A successful trading strategy often starts as an idea based on sound econom- ic intuition, market insight, or the discovery of an anomaly. Background research can be helpful in order to understand what others have tried or implemented in the past.

We distinguish between a trading idea and trading strategy based on the underlying economic motivation. A trading idea has a more short-term horizon often associated with an event or mispricing. A trading strategy has a longer horizon and is frequently based on the exploitation of a premium associated with an anomaly or a characteristic.

Developing Factors

Factors provide building blocks of the model used to build an investment strategy. We introduced a general definition of factors earlier in this chapter.

270 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

After having established the trading strategy, we move from the economic concepts to the construction of factors that may be able to capture our intu- ition. In this chapter, we provide a number of examples of factors based on the cross-sectional characteristics of stocks.

Acquiring and Processing Data

A trading strategy relies on accurate and clean data to build factors. There are a number of third-party solutions and databases available for this pur- pose such as Thomson MarketQA,6 Factset Research Systems,7 and Com- pustat Xpressfeed.8

Analyzing the Factors

A variety of statistical and econometric techniques must be performed on the data to evaluate the empirical properties of factors. This empirical re- search is used to understand the risk and return potential of a factor. The analysis is the starting point for building a model of a trading strategy.

Building the Strategy

The model represents a mathematical specification of the trading strategy. There are two important considerations in this specification: The selection of which factors and how these factors are combined. Both considerations need to be motivated by the economic intuition behind the trading strategy. We advise against model specification being strictly data driven because that approach often results in overfitting the model and consequently overesti- mating forecasting quality of the model.

Evaluating, Backtesting, and Implementing the Strategy

The final step involves assessing the estimation, specification, and forecast quality of the model. This analysis includes examining the goodness of fit (often done in sample), forecasting ability (often done out of sample), and sensitivity and risk characteristics of the model.

We cover the last two steps in greater detail in the companion chapter that follows.

6Thomson MarketQA, http://thomsonreuters.com/products_services/financial/financial_ products/quantitative_analysis/quantitative_analytics. 7Factset Research Systems, http://www.factset.com. 8Compustat Xpressfeed, http://www.compustat.com.

Factor-Based Trading Strategies I: Factor Construction and Analysis 271

RISK TO TRADING STRATEGIES

In investment management, risk is a primary concern. The majority of trad- ing strategies are not risk free but rather subject to various risks. It is im- portant to be familiar with the most common risks in trading strategies. By understanding the risks in advance, we can structure our empirical research to identify how risks will affect our strategies. Also, we can develop tech- niques to avoid these risks in the model construction stage when building the strategy.

We describe the various risks that are common to factor trading strate- gies as well as other trading strategies such as risk arbitrage. Many of these risks have been categorized in the behavioral finance literature.9 The risks discussed include fundamental risk, noise trader risk, horizon risk, model risk, implementation risk, and liquidity risk.

Fundamental risk is the risk of suffering adverse fundamental news. For example, say our trading strategy focuses on purchasing stocks with high earnings-to-price ratios. Suppose that the model shows a pharmaceuti- cal stock maintains a high score. After purchasing the stock, the company releases a news report that states it faces class-action litigation because one of its drugs has undocumented adverse side effects. While during this period other stocks with high earnings-to-price ratio may perform well, this par- ticular pharmaceutical stock will perform poorly despite its attractive char- acteristic. We can minimize the exposure to fundamental risk within a trad- ing strategy by diversifying across many companies. Fundamental risk may not always be company specific, sometimes this risk can be systemic. Some examples include the exogenous market shocks of the stock market crash in 1987, the Asian financial crisis in 1997, and the tech bubble in 2000. In these cases, diversification was not that helpful. Instead, portfolio managers that were sector or market neutral in general fared better.

Noise trader risk is the risk that a mispricing may worsen in the short run. The typical example includes companies that clearly are undervalued (and should therefore trade at a higher price). However, because noise trad- ers may trade in the opposite direction, this mispricing can persist for a long time. Closely related to noise trader risk is horizon risk. The idea here is that the premium or value takes too long to be realized, resulting in a realized return lower than a target rate of return.

Model risk, also referred to as misspecification risk, refers to the risk asso- ciated with making wrong modeling assumptions and decisions. This includes the choice of variables, methodology, and context the model operates in.

9See Nicholas Barberis and Richard Thaler, “A Survey of Behavioral Finance,” in Handbook of the Economics of Finance, edited by George M. Constantinides, M. Harris, and Rene M. Stulz (Amsterdam: Elsevier Science, 2003).

272 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

There are different sources that may result in model misspecification and there are several remedies based on information theory, Bayesian methods, shrinkage, and random coefficient models.10

Implementation risk is another risk faced by investors implementing trading strategies. This risk category includes transaction costs and funding risk. Transaction costs such as commissions, bid-ask spreads and market impact can adversely affect the results from a trading strategy. If the strategy involves shorting, other implementation costs arise such as the ability to locate securities to short and the costs to borrow the securities. Funding risk occurs when the portfolio manager is no longer able to get the funding nec- essary to implement a trading strategy. For example, many statistical arbi- trage funds use leverage to increase the returns of their funds. If the amount of leverage is constrained then the strategy will not earn attractive returns. Khandani and Lo confirm this example by showing that greater competition and reduced profitability of quantitative strategies today require more lever- age to maintain the same level of expected return.11

Liquidity risk is a concern for investors. Liquidity is defined as the abil- ity to (1) trade quickly without significant price changes, and (2) the abil- ity to trade large volumes without significant price changes. Cerniglia and Kolm discuss the effects of liquidity risk during the “quant crisis” in August 2007. 12 They show how the rapid liquidation of quantitative funds affected the trading characteristics and price impact of trading individual securities as well as various factor-based trading strategies.

These risks can detract or contribute to the success of a trading strategy. It is obvious how these risks can detract from a strategy. What is not always clear is when any one of these unintentional risks contributes to a strategy. That is, sometimes when we build a trading strategy we take on a bias that is not obvious. If there is a premium associated with this unintended risk then a strategy will earn additional return. Later the premium to this unintended risk may disappear. For example, a trading strategy that focuses on price momentum performed strongly in the calendar years of 1998 and 1999. What an investor might not notice is that during this period the port- folio became increasingly weighted toward technology stocks, particularly Internet-related stocks. During 2000, these stocks severely underperformed.

10For a discussion of the sources of model misspecification and remedies, see Frank J. Fabozzi, Sergio Focardi, and Petter N. Kolm, Quantitative Equity Investing (Hobo- ken, NJ: John Wiley & Sons, 2010). 11Amir E. Khandani and Andrew W. Lo, “What Happened to the Quants in August 2007?” Journal of Investment Management 5, no. 4 (2007): 5–54. 12Joseph A. Cerniglia and Petter N. Kolm,“The Information Content of Order Im- balances: A Tick-by-Tick Analysis of the Equity Market in August 2007,” working paper, Courant Institute, New York University, 2009.

Factor-Based Trading Strategies I: Factor Construction and Analysis 273

DESIRABLE PROPERTIES OF FACTORS

Factors should be founded on sound economic intuition, market insight, or an anomaly. In addition to the underlying economic reasoning, factors should have other properties that make them effective for forecasting.

It is an advantage if factors are intuitive to investors. Many investors will only invest in a particular fund if they understand and agree with the basic ideas behind the trading strategies. Factors give portfolio managers a tool in communicating to investors what themes they are investing in.

The search for the economic meaningful factors should avoid strictly relying on pure historical analysis. Factors used in a model should not emerge from a sequential process of evaluating successful factors while removing less favorable ones.

Most importantly, a group of factors should be parsimonious in its description of the trading strategy. This requires careful evaluation of the interaction between the different factors. For example, highly correlated factors will cause the inferences made in a multivariate approach to be less reliable. Another possible problem when using multiple factors is the pos- sibility of overfitting in the modeling process.

Any data set contains outliers, that is, observations that deviate from the average properties of the data. Outliers are not always trivial to han- dle and sometimes we may want to exclude them and other times not. For example, they could be erroneously reported or legitimate abnormal values. Later in this chapter we discuss a few standard techniques to perform data cleaning. The success or failure of factors selected should not depend on a few outliers. In most cases, it is desirable to construct factors that are rea- sonably robust to outliers.

SOURCES FOR FACTORS

How do we find factors? The sources are widespread with no one source clear- ly dominating. Employing a variety of sources seems to provide the best op- portunity to uncover factors that will be valuable for developing a new model.

There are a number of ways to develop factors based on economic foun- dations. It may start with thoughtful observation or study of how market participants act. For example, we may ask ourselves how other market par- ticipants will evaluate the prospects of the earnings or business of a firm. We may also want to consider what stock characteristics investors will reward in the future. Another common approach is to look for inefficiencies in the way that investors process information. For instance, research may discover that consensus expectations of earnings estimates are biased.

274 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

A good source for factors is the various reports released by the manage- ment of companies. Many reports contain valuable information and may provide additional context on how management interprets the company results and financial characteristics. For example, quarterly earning reports (10-Qs) may highlight particular financial metrics relevant to the company and the competitive space they are operating within. Other company finan- cial statements and SEC filings, such as the 10-K or 8-K, also provide a source of information to develop factors. It is often useful to look at the financial measures that management emphasize in their comments.

Factors can be found through discussions with market participants such as portfolio managers and traders. Factors are uncovered by understanding the heuristics experienced investors have used successfully. These heuristics can be translated into factors and models.

Wall Street analyst reports—also called sell-side reports or equity research reports—may contain valuable information. The reader is often not interested in the final conclusions, but rather in the methodology or metrics the analysts use to forecast the future performance of a company. It may also be useful to study the large quantity of books written by portfolio managers and traders that describe the process they use in stock selection.

Academic literature in finance, accounting, and economics provides evidence of numerous factors and trading strategies that earn abnormal returns. Not all strategies will earn abnormal profits when implemented by practitioners, for example, because of institutional constraints and transac- tion costs. Bushee and Raedy13 find that trading strategy returns are sig- nificantly decreased due to issues such as price pressure, restrictions against short sales, incentives to maintain an adequately diversified portfolio, and restrictions to hold no more than 5% ownership in a firm.

In uncovering factors, we should put economic intuition first and data analysis second. This avoids performing pure data mining or simply overfit- ting our models to past history. Research and innovation is the key to find- ing new factors. Today, analyzing and testing new factors and improving upon existing ones, is itself a big industry.

BUILDING FACTORS FROM COMPANY CHARACTERISTICS

The following sections focus on the techniques for building factors from company characteristics. Often we desire our factors to relate the financial data provided by a company to metrics that investors use when making

13Brian J. Bushee and Jana Smith Raedy, “Factors Affecting the Implementability of Stock Market Trading Strategies,” working paper, University of Pennsylvania and University of North Carolina, 2006.

Factor-Based Trading Strategies I: Factor Construction and Analysis 275

decisions about the attractiveness of a stock such as valuation ratios, operat- ing efficiency ratios, profitability ratios, and solvency ratios. Factors should also relate to the market data such as analysts’ forecasts, prices and returns, and trading volume.

WORKING WITH DATA

In this section, we discuss how to work with data and data quality issues, including some well-probed techniques used to improve the quality of the data. Though the role of getting and analyzing data can be mundane and tedious, we need not forget that high-quality data are critical to the success of a trading strategy. It is important to realize model output is only as good as the data used to calibrate it. As the saying goes: “Garbage in, garbage out.”

Understanding the structure of financial data is important. We distin- guish three different categories of financial data: time series, cross-sectional, and panel data. Time series data consist of information and variables col- lected over multiple time periods. Cross-sectional data consist of data col- lected at one point in time for many different companies (the cross-section of companies of interest). A panel data set consists of cross-sectional data collected at different points in time. We note that a panel data set may not be homogeneous. For instance, the cross-section of companies may change from one point in time to another.

Data Integrity

Quality data maintain several attributes such as providing a consistent view of history, maintaining good data availability, containing no survivorship, and avoiding look-ahead bias. As all data sets have their limitations, it is impor- tant for the quantitative researcher to be able to recognize the limitations and adjust the data accordingly.14

Data used in research should provide a consistent view of history. Two common problems that distort the consistency of financial data are backfill- ing and restatements of data. Backfilling of data happens when a company

14Many years ago one of the coauthors met Marcus C. Bogue, founder of Charter Oak Investment Systems. His firm created a Compustat Add-On Database to address the needs of the more quantitatively oriented, longer-term backtesting researchers by storing all data from current Compustat data before it gets overwritten (updated). Mr. Bogue works with most of the quantitative investment management industry. In the conversion with him the question of what distinguishes the most successful quantita- tive managers came up. Mr Bogue suggested that their familiarity with the data is the differentiator. Familiarity entails understanding quality, definitions, measurement, and sample characteristics of the data sets used in the investment process.

276 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

is first entered into a database at the current period and its historical data are also added. This process of backfilling data creates a selection bias because we now find historical data on this recently added company when previously it was not available. Restatements of data are prevalent in dis- torting consistency of data. For example, if a company revises its earnings per share numbers after the initial earnings release, then many database companies will overwrite the number originally recorded in the database with the newly released figure.

A frequent and common concern with financial databases is data avail- ability. First, data items may only be available for a short period of time. For example, there were many years when stock options were granted to employees but the expense associated with the option grant was not required to be disclosed in financial statements. It was not until 2005 that account- ing standards required companies to recognize directly stock options as an expense on the income statement. Second, data items may be available for only a subset of the cross-section of firms. Some firms, depending on the business they operate in, have research and development expenses while others do not. For example, many pharmaceutical companies have research and development expenses while utilities companies do not. A third issue is that a data item may simply not be available because it was not recorded at certain points in time. Sometimes this happens for just a few observa- tions, other times it is the case for the whole time-series for a specific data item for a company. Fourth, different data items are sometimes combined. For example, sometimes depreciation and amortization expenses are not a separate line item on an income statement. Instead it is included in cost of goods sold. Fifth, certain data items are only available at certain periodici- ties. For instance, some companies provide more detailed financial reports quarterly while others report more details annually. Sixth, data items may be inconsistently reported across different companies, sectors, or industries. This may happen as the financial data provider translates financial measures from company reports to the specific database items (incomplete mapping), thereby ignoring or not correctly making the right adjustments.

For these issues some databases provide specific codes to identify the causes of missing data. It is important to have procedures in place that can distinguish among the different reasons for the missing data and be able to make adjustments and corrections.

Two other common problems with databases are survivorship and look-ahead bias. Survivorship bias occurs when companies are removed from the database when they no longer exist. For example, companies can be removed because of a merger or bankruptcy. This bias skews the results because only successful firms are included in the entire sample. Look-ahead bias occurs when data are used in a study that would not have been available

Factor-Based Trading Strategies I: Factor Construction and Analysis 277

during the actual period analyzed. For example, the use of year-end earnings data immediately at the end of the reporting period is incorrect because the data is not released by the firm until several days or weeks after the end of the reporting period.

Data alignment is another concern when working with multiple data- bases. Many databases have different identifiers used to identify a firm. Some databases have vendor specific identifiers, others have common iden- tifiers such as CUSIPs or ticker symbols. Unfortunately, CUSIPs and ticker symbols change over time and are often reused. This practice makes it dif- ficult to link an individual security across multiple databases across time.

Example: The EBITDA/EV Factor

This example illustrates how the nuances of data handling can influence the results of a particular study. We use data from the Compustat Point- In-Time database and calculate the EBITA/EV factor.15 This factor is de- fined as earnings before interest, taxes, depreciation, and amortization divided by enterprise value (EBITDA/EV). Our universe of stocks is the Russell 1000 from December 1989 to December 2008, excluding financial companies. We calculate EBITDA /EV by two equivalent but different ap- proaches. Each approach differs by the data items used in calculating the numerator (EBITDA):

1. EBITDA = Sales (Compustat data item 2) – Cost of goods sold (Compu- stat data item 30) – Selling and general administrative expenses (Com- pustat data item 1).

2. EBITDA = Operating income before depreciation (Compustat data item 21).

According to the Compustat manual, the following identity holds:

Operating income before depreciation = Sales – Cost of goods sold – Selling and general administrative expenses

However, while this mathematical identity is true, this is not what we discover in the data. After we calculate the two factors, we form quintile portfolios of each factor and compare the individual holding rankings between the portfolio. Exhibit 11.2 displays the percentage differences in

15The ability of EBITDA/EV to forecast future returns is discussed in, for example, Patricia M. Dechow, S. P. Kothari, and Ross L. Watts, “The Relation Between Earn- ings and Cash Flows,” Journal of Accounting and Economics 25, no. 2 (1998): 133–168.

278 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

rankings for individual companies between the two portfolios. We observe that the results are not identical. As a matter of fact, there are large differ- ences, particularly in the early period. In other words, the two mathemati- cally equivalent approaches do not deliver the same empirical results.

Potential Biases from Data

There are numerous potential biases that may arise from data quality issues. It is important to recognize the direct effects of these data issues are not ap- parent a priori. We emphasize three important effects:16

1. Effect on average stock characteristics. When calculating cross-sectional averages of various metrics such as book-to-price or market capital- ization, data issues can skew statistics and lead to incorrect inference about the population characteristics used in the study.

2. Effect on portfolio returns. The portfolio return implications of data issues are not always clear. For example, survivor bias results in firms

16Stefan Nagel, “Accounting Information Free of Selection Bias: A New UK Data- base 1953–1999,” working paper, Stanford Graduate School of Business, 2001.

EXHIBIT 11.2 Percentage of Companies in Russell 1000 with Different Ranking According to the EBITDA/EV Factor

19 89

19 90

19 91

19 92

19 93

19 94

19 95

19 96

19 97

19 98

19 99

20 00

20 01

20 02

20 03

20 04

20 05

20 06

20 07

20 08

Pe rc

en ta

ge o

f C

om pa

ni es

in R

us se

ll 10

00

35

30

25

20

15

10

5

0

Factor-Based Trading Strategies I: Factor Construction and Analysis 279

being removed from the sample. Typically firms are removed from the sample for one of two reasons—mergers and acquisitions or failure. In most cases firms are acquired at a premium from the prevailing stock price. Leaving these firms out of the sample would have a downward bias on returns. In cases where companies fail, the stock price falls dramatically and removing these firms from the sample will have an upward bias on returns.

3. Effects on estimated moments of returns. A study by Kothari, Sabino, and Zach17 found that nonsurviving firms tend to be either extremely bad or extremely good performers. Survivor bias implies truncation of such extreme observations. The authors of the study show that even a small degree of such nonrandom truncation can have a strong impact on the sample moments of stock returns.

Dealing with Common Data Issues

Most data sets are subject to some quality issues. To work effectively, we need to be familiar with data definitions and database design. We also need to use processes to reduce the potential impact of data problems as they could cause incorrect conclusions.

The first step is to become familiar with the data standardization pro- cess vendors use to collect and process data. For example, many vendors use different templates to store data. Specifically, the Compustat US database has one template for reporting income statement data, while the World- scope Global database has four different templates depending on whether a firm is classified as a bank, insurance company, industrial company, or other financial company. Other questions related to standardization a user should be familiar with include:

■ What are the sources of the data—publicly available financial state- ments, regulatory filings, newswire services, or other sources?

■ Is there a uniform reporting template? ■ What is the delay between publication of information and its availabil-

ity in the database? ■ Is the data adjusted for stock splits? ■ Is history available for extinct or inactive companies? ■ How is data handled for companies with multiple share classes? ■ What is the process used to aggregate the data?

17S. P. Kothari, Jowell S. Sabino, and Tzachi Zach, “Implications of Survival and Data Trimming for Tests of Market Efficiency,” Journal of Accounting and Econom- ics 39, no. 1 (2005): 129–161.

280 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Understanding of the accounting principles underlying the data is criti- cal. Here, two principles of importance are the valuation methodology and data disclosure or presentation. For the valuation, we should understand the type of cost basis used for the various accounting items. Specifically, are assets calculated using historical cost basis, fair value accounting, or another type? For accounting principles regarding disclosure and presenta- tion, we need to know the definition of accounting terms, the format of the accounts, and the depth of detail provided.

Researchers creating factors that use financial statements should review the history of the underlying accounting principles. For example, the cash flow statement reported by companies has changed over the years. Effective for fiscal years ending July 15, 1988, Statement of Financial Accounting Standards No. 85 (SFAS No. 85) requires companies to report the Statement of Cash Flows. Prior to the adoption of that accounting standard, compa- nies could report one of three statements: Working Capital Statement, Cash Statement by Source and Use of Funds, or Cash Statement by Activity. His- torical analysis of any factor that uses cash flow items will require adjust- ments to the definition of the factor to account for the different statements used by companies.

Preferably, automated processes should be used to reduce the potential impact of data problems. We start by checking the data for consistency and accuracy. We can perform time series analysis on individual factors looking at outliers and for missing data. We can use magnitude tests to compare current data items with the same items for prior periods, looking for data that are larger than a predetermined variance. When suspicious cases are identified, the cause of the error should be researched and any necessary changes made.

Methods to Adjust Factors At first, factors consist of raw data from a database combined in an eco- nomically meaningful way. After the initial setup, a factor may be adjusted using analytical or statistical techniques to be more useful for modeling. The following three adjustments are common.

Standardization

Standardization rescales a variable while preserving its order. Typically, we choose the standardized variable to have a mean of zero and a standard deviation of one by using the transformation

x x x

i i

x

new = −

σ

Factor-Based Trading Strategies I: Factor Construction and Analysis 281

where xi is the stock’s factor score, x is the universe average, and sx is the universe standard deviation. There are several reasons to scale a variable in this way. First, it allows one to determine a stock’s position relative to the universe average. Second, it allows better comparison across a set of factors since means and standard deviations are the same. Third, it can be useful in combining multiple variables.

Orthogonalization

Sometimes the performance of our factor might be related to another factor. Orthogonalizing a factor for other specified factor(s) removes this relation- ship. We can orthogonalize by using averages or running regressions.

To orthogonalize the factor using averages according to industries or sectors, we can proceed as follows. First, for each industry we calculate the industry scores

s

x

k

i i k i

n

i k i

n =

⋅ =

=

∑

∑

ind

ind

,

,

1

1

where xi is a factor and indi,k represent the weight of stock i in industry k. Next, we subtract the industry average of the industry scores, sk, from each stock. We compute

x x si i i k k

k new

Industries

ind= − ⋅ ∈ ∑ ,

where xi new is the new industry neutral factor.

We can use linear regression to orthogonalize a factor. We first deter- mine the coefficients in the equation

x a b fi i i= + ⋅ + ε

where fi is the factor to orthogonalize the factor xi by, b is the contribution of fi to xi, and ei is the component of the factor xi not related to fi. ei is or- thogonal to fi (that is, ei is independent of fi) and represents the neutralized factor

xi i new = ε

In the same fashion, we can orthogonalize our variable relative to a set of factors by using the multivariate linear regression

282 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

x a b fi j

j j i= + ⋅ +∑ ε

and then setting xi i new = ε .

Often portfolio managers use a risk model to forecast risk and an alpha model to forecast returns. The interaction between factors in a risk model and an alpha model often concerns portfolio managers. One possible approach to address this concern is to orthogonalize the factors or final scores from the alpha model against the factors used in the risk model. Later in the chapter, we discuss this issue in more detail.

Transformation

It is common practice to apply transformations to data used in statistical and econometric models. In particular, factors are often transformed such that the resulting series is symmetric or close to being normally distributed. Frequently used transformations include natural logarithms, exponentials, and square roots. For example, a factor such as market capitalization has a large skew because a sample of large-cap stocks typically includes mega- capitalization stocks. To reduce the influence of mega-capitalization compa- nies, we may instead use the natural logarithm of market capitalization in a linear regression model.

Outlier Detection and Management

Outliers are observations that seem to be inconsistent with the other values in a data set. Financial data contain outliers for a number of reasons in- cluding data errors, measurement errors, or unusual events. Interpretation of data containing outliers may therefore be misleading. For example, our estimates could be biased or distorted, resulting in incorrect conclusions.

Outliers can be detected by several methods. Graphs such as boxplots, scatter plots, or histograms can be useful to visually identify them. Alterna- tively, there are a number of numerical techniques available. One common method is to compute the interquartile-range and then identify outliers as those values that are some multiple of the range. The interquartile-range is a measure of dispersion and is calculated as the difference between the third and first quartiles of a sample. This measure represents the middle 50% of the data, removing the influence of outliers.

After outliers have been identified, we need to reduce their influence in our analysis. Trimming and winsorization are common procedures for this

Factor-Based Trading Strategies I: Factor Construction and Analysis 283

purpose. Trimming discards extreme values in the data set. This transforma- tion requires the researcher to determine the direction (symmetric or asym- metric) and the amount of trimming to occur.

Winsorization is the process of transforming extreme values in the data. First, we calculate percentiles of the data. Next we define outliers by refer- encing a certain percentile ranking. For example, any data observation that is greater than the 97.5 percentile or less than the 2.5 percentile could be considered an outlier. Finally, we set all values greater or less than the refer- ence percentile ranking to particular values. In our example, we may set all values greater than the 97.5 percentile to the 97.5 percentile value and all values less than 2.5 percentile set to the 2.5 percentile value. It is important to fully investigate the practical consequences of using either one of these procedures. In the companion chapter to follow, we apply what we learn from the following statistical summaries of the factors to build a model and implement our trading strategy.

ANALYSIS OF FACTOR DATA

After constructing factors for all securities in the investable universe, each factor is analyzed individually. Presenting the time-series and cross-sectional averages of the mean, standard deviations, and key percentiles of the dis- tribution provide useful information for understanding the behavior of the chosen factors.

Although we often rely on techniques that assume the underlying data generating process is normally distributed, or at least approximately, most financial data is not. The underlying data generating processes that embody aggregate investor behavior and characterize the financial markets are unknown and exhibit significant uncertainty. Investor behavior is uncertain because not all investors make rational decisions or have the same goals. Analyzing the properties of data may help us better understand how uncer- tainty affects our choice and calibration of a model.

Below we provide some examples of the cross-sectional characteristics of various factors. For ease of exposition we use histograms to evaluate the data rather than formal statistical tests. We let particular patterns or prop- erties of the histograms guide us in the choice of the appropriate technique to model the factor. We recommend that an intuitive exploration should be followed by a more formal statistical testing procedure. Our approach here is to analyze the entire sample, all positive values, all negative values, and zero values. Although omitted here, a thorough analysis should also include separate subsample analysis.

284 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Example 1: EBITDA/EV

The first factor we discuss is the earnings before interest taxes and amortiza- tion to enterprise value (EBITDA/EV) factor. Enterprise value is calculated as the market value of the capital structure. This factor measures the price (enter- prise value) investors pays to receive the cash flows (EBITDA) of a company. The economic intuition underlying this factor is that the valuation of a com- pany’s cash flow determines the attractiveness of companies to an investor.

Exhibit 11.3(A) presents a histogram of all cross-sectional values of the EBITDA/EV factor throughout the entire history of the study. The dis- tribution is close to normal, showing there is a fairly symmetric dispersion among the valuations companies receive. Exhibit 11.3(B) shows that the distribution of all the positive values of the factor is also almost normally distributed. On the other hand, Exhibit 11.3(C) shows that the distribution of the negative values is skewed to the left. However, because there are only a small number of negative values, it is likely that they will not greatly influ- ence our model.

Example 2: Revisions

We evaluate the cross-sectional distribution of the earnings revisions fac- tor.18 The revisions factor we use is derived from sell-side analyst earnings forecasts from the IBES database. The factor is calculated as the number of analysts who revise their earnings forecast upward minus the number of downward forecasts, divided by the total number of forecasts. The econom- ic intuition underlying this factor is that there should be a positive relation to changes in forecasts of earnings and subsequent returns.

In Exhibit 11.4(A) we see that the distribution of revisions is symmetric and leptokurtic around a mean of about zero. This distribution ties with the economic intuition behind the revisions. Since business prospects of compa- nies typically do not change from month-to-month, sell-side analysts will not revise their earnings forecast every month. Consequently, we expect and find the cross-sectional range to be peaked at zero. Exhibit 11.4(B) and (C), respec- tively, show there is a smaller number of both positive and negative earnings revisions and each one of these distributions are skewed.

Example 3: Share Repurchase

We evaluate the cross-sectional distribution of the shares repurchases factor. This factor is calculated as the difference of the current number of common

18For a representative study see, for example, Anthony Bercel, “Consensus Expec- tations and International Equity Returns,” Financial Analysts Journal 50, no. 4 (1994): 76–80.

Factor-Based Trading Strategies I: Factor Construction and Analysis 285

EXHIBIT 11.3 Histograms of the Cross-Sectional Values for the EBITDA/EV Factor A. All Factor Values

–0.1 0.0 0.1 0.2 0.3 0.4 0.5

0 5,

00 0

15 ,0

00 25

,0 00

B. Positive Factor Values

0.0 0.1 0.2 0.3 0.4

0 5,

00 0

15 ,0

00 25

,0 00

C. Negative Factor Values

–0.08 –0.06 –0.04 –0.02 0.0

0 20

0 40

0 60

0 80

0 1,

00 0

286 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 11.4 Histograms of the Cross-Sectional Values for the Revisions Factor A. All Factor Values

–1.5 –1.0 –0.5 0.0 0.5 1.0

0 20

,0 00

40 ,0

00 60

,0 00

B. Positive Factor Values

0.0 0.2 0.4 0.6 0.8 1.0

0 5,

00 0

10 ,0

00 15

,0 00

C. Negative Factor Values

–1.5 –1.0 –0.5 0.0

0 5,

00 0

10 ,0

00 15

,0 00

20 ,0

00

Factor-Based Trading Strategies I: Factor Construction and Analysis 287

shares outstanding and the number of shares outstanding 12 months ago, divided by the number of shares outstanding 12 months ago. The economic intuition underlying this factor is that share repurchase provides informa- tion to investors about future earnings and valuation of the company’s stock.19 We expect there to be a positive relationship between a reduction in shares outstanding and subsequent returns.

We see in Exhibit 11.5(A) that the distribution is leptokurtic. The positive values (see Exhibit 11.5(B)) are skewed to the right and the nega- tive values (see Exhibit 11.5(C)) are clustered in a small band. The eco- nomic intuition underlying share repurchases is the following. Firms with increasing share count indicate they require additional sources of cash. This need could be an early sign that the firm is experiencing higher oper- ating risks or financial distress. We would expect these firms to have lower future returns. Firms with decreasing share count have excess cash and are returning value back to shareholders. Decreasing share count could result because management believes the shares are undervalued. As expected, we find the cross-sectional range to be peaked at zero (see Exhibit 11.5(D)) since not all firms issue or repurchase shares on a regular basis.

KEY POINTS

■ A factor is a common characteristic among a group of assets. Factors should be founded on sound economic intuition, market insight, or an anomaly.

■ Factors fall into three categories—macroeconomic, cross-sectional, and statistical factors.

■ The main steps in the development of a factor-based trading strategy are (1) defining a trading idea or investment strategy, (2) developing factors, (3) acquiring and processing data, (4) analyzing the factors, (5) building the strategy, (6) evaluating the strategy, (7) backtesting the strategy, and (8) implementing the strategy.

■ Most trading strategies are exposed to risk. The main sources of risk are fundamental risk, noise trader risk, horizon risk, model risk, implemen- tation risk, and liquidity risk.

■ Factors are often derived from company characteristics and metrics, and market data. Examples of company characteristics and metrics include valuation ratios, operating efficiency ratios, profitability ratios, and sol- vency ratios. Example of useful market data include analysts forecasts, prices and returns, and trading volume.

19Gustavo Grullon and Roni Michaely, “The Information Content of Share Repur- chase Programs,” Journal of Finance 59, no. 2 (2004): 651–680.

288 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

EXHIBIT 11.5 Histograms of the Cross-Sectional Values for the Share Repurchase Factor A. Positive Factor Values

0.0 0.2 0.4 0.6

0 20

,0 00

60 ,0

00 10

0, 00

0

Panel B: Positive Factor Values

0.0 0.2 0.4 0.6

0 20

,0 00

60 ,0

00 10

0, 00

0

■ High-quality data are critical to the success of a trading strategy. Model output is only as good as the data used to calibrate it.

■ Some common data problems and biases are backfilling and restate- ments of data, missing data, inconsistently reported data, and survivor- ship and look-ahead biases.

■ The ability to detect and adjust outliers is crucial to a quantitative investment process.

■ Common methods used for adjusting data are standardization, orthog- onalization, transformation, trimming, and winsorization.

■ The statistical properties of factors need to be carefully analyzed. Basic statistical measures include the time-series and cross-sectional averages of the mean, standard deviations, and key percentiles.

Factor-Based Trading Strategies I: Factor Construction and Analysis 289

QUESTIONS

1. List and define the typical risks of an investment strategy.

2. What areas of finance use factor models?

3. Explain some of the major data issues encountered when working with financial data.

4. How are financial data organized?

5. a. What are outliers? b. Why do outliers occur in financial data?

EXHIBIT 11.5 (Continued) C. Negative Factor Values

–0.10 –0.08 –0.06 –0.04 –0.02 0.0

0 2,

00 0

6, 00

0 10

,0 00

D. Zero Factor Values

–1.0 –0.5 0.0 0.5 1.0

0 1,

00 0

2, 00

0 3,

00 0

4, 00

0 5,

00 0

291

CHAPTER 12 Cross-Sectional Factor-Based

Models and Trading Strategies Joseph A. Cerniglia

Visiting Researcher Courant Institute of Mathematical Sciences, New York University

Petter N. Kolm, Ph.D. Director of the Mathematics in Finance Masters Program

and Clinical Associate Professor Courant Institute of Mathematical Sciences, New York University

Frank J. Fabozzi, Ph.D., CFA, CPA Professor of Finance

EDHEC Business School

In the previous chapter, we demonstrated how factors are constructed from company characteristics and market data. Subsequently, we discussed the analysis of the statistical properties of the factors. In this chapter, we extend the analysis to include multiple factors with the purpose of developing a dynamic multifactor trading strategy that incorporates a number of com- mon institutional constraints such as turnover, transaction costs, sector, and tracking error. For this purpose, we use a combination of growth, value, quality, and momentum factors. Our universe of stocks is the Russell 1000 from December 1989 to December 2008, and we construct our factors by using the Compustat Point-In-Time and IBES databases. A complete list of the factors and data sets used in this chapter is provided in the appendix.

We begin by reviewing several approaches for the evaluation of return premiums and risk characteristics to factors, including portfolio sorts, fac- tor models, factor portfolios, and information coefficients. We then turn to techniques that are used to combine several factors into a single model—a

292 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

trading strategy. In particular, we discuss the data driven, factor model, heu- ristic, and optimization approaches. It is critical to perform out-of-sample backtests of a trading strategy to understand its performance and risk char- acteristics. We cover the split-sample and recursive out-of-sample tests.

Throughout this chapter, we provide a series of examples, including backtests of a multifactor trading strategy. As noted in the previous chap- ter, the purpose of these examples is not to provide yet another profitable trading strategy, but rather to illustrate the process an analyst may follow when performing research. We emphasize that the factors that we use are well known and have for years been exploited by industry practitioners. We think that the value added of these examples is in the concrete illustration of the research and development process of a factor-based trading model.

CROSS-SECTIONAL METHODS FOR EVALUATION OF FACTOR PREMIUMS

There are several approaches used for the evaluation of return premiums and risk characteristics to factors. In this section, we discuss the four most commonly used approaches: portfolio sorts, factor models, factor portfo- lios, and information coefficients. We examine the methodology of each approach and summarize its advantages and disadvantages.

In practice, to determine the right approach for a given situation there are several issues to consider. One determinant is the structure of the finan- cial data. A second determinant is the economic intuition underlying the factor. For example, sometimes we are looking for a monotonic relationship between returns and factors while at other times we care only about extreme values. A third determinant is whether the underlying assumptions of each approach are valid for the data generating process at hand.

Portfolio Sorts

In the asset pricing literature, the use of portfolio sorts can be traced back to the earliest tests of the capital asset pricing model (CAPM). The goal of this particular test is to determine whether a factor earns a systematic premium. The portfolios are constructed by grouping together securities with simi- lar characteristics (factors). For example, we can group stocks by market capitalization into 10 portfolios—from smallest to largest—such that each portfolio contains stocks with similar market capitalization. The next step is to calculate and evaluate the returns of these portfolios.

The return for each portfolio is calculated by equally weighting the indi- vidual stock returns. The portfolios provide a representation of how returns

Cross-Sectional Factor-Based Models and Trading Strategies 293

vary across the different values of a factor. By studying the return behavior of the factor portfolios, we may assess the return and risk profile of the fac- tor. In some cases, we may identify a monotonic relationship of the returns across the portfolios. In other cases, we may identify a large difference in returns between the extreme portfolios. Still in other cases, there may be no relationship between the portfolio returns. Overall, the return behavior of the portfolios will help us conclude whether there is a premium associated with a factor and describe its properties.

One application of the portfolio sort is the construction of a factor mimicking portfolio (FMP). An FMP is a long-short portfolio that goes long stocks with high values of a factor and short stocks with low values of a fac- tor, in equal dollar amounts. An FMP is a zero-cost factor trading strategy.

Portfolio sorts have become so widespread among practitioners and academics alike that they elicit few econometric queries, and often no econo- metric justification for the technique is offered. While a detailed discussion of these topics are beyond the scope of this book, we would like to point out that asset pricing tests used on sorted portfolios may exhibit a bias that favors rejecting the asset pricing model under consideration.1

The construction of portfolios sorted on a factor is straightforward:

■ Choose an appropriate sorting methodology. ■ Sort the assets according to the factor. ■ Group the sorted assets into N portfolios (usually N = 5, or N = 10). ■ Compute average returns (and other statistics) of the assets in each

portfolio over subsequent periods.

The standard statistical testing procedure for portfolios sorts is to use a Stu- dent’s t-test to evaluate the significance of the mean return differential between the portfolios of stocks with the highest and lowest values of the factor.

Choosing the Sorting Methodology

The sorting methodology should be consistent with the characteristics of the distribution of the factor and the economic motivation underlying its premium. We list six ways to sort factors:

Method 1 ■ Sort stocks with factor values from the highest to lowest.

Method 2 ■ Sort stocks with factor values from the lowest to highest.

1For a good overview of the most common issues, see Jonathan B. Berk, “Sorting out Sorts,” Journal of Finance 55, no. 1 (2000): 407–427 and references therein.

294 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Method 3 ■ First allocate stocks with zero factor values into the bottom portfolio. ■ Sort the remaining stocks with nonzero factor values into the remain-

ing portfolios.

For example, the dividend yield factor would be suitable for this sort- ing approach. This approach aligns the factor’s distributional characteristics of dividend and nondividend-paying stocks with the economic rationale. Typically, nondividend-paying stocks maintain characteristics that are dif- ferent from dividend paying stocks. So we group nondividend-paying stocks into one portfolio. The remaining stocks are then grouped into portfolios depending on the size of their nonzero dividend yields. We differentiate among stocks with dividend yield because of two reasons: (1) the size of the dividend yield is related to the maturity of the company, and (2) some inves- tors prefer to receive their investment return as dividends.

Method 4 ■ Allocate stocks with zero factor values into the middle portfolio. ■ Sort stocks with positive factor values into the remaining higher port-

folios (greater than the middle portfolio). ■ Sort stocks with negative factor values into the remaining lower port-

folios (less than the middle portfolio).

Method 5 ■ Sort stocks into partitions. ■ Rank assets within each partition. ■ Combine assets with the same ranking from the different partitions

into portfolios.

An example will clarify this procedure. Suppose we want to rank stocks according to earnings growth on a sector neutral basis. First, we separate stocks into groups corresponding to their sector. Within each sector, we rank the stocks according to their earnings growth. Lastly, we group all stocks with the same rankings of earning growth into the final portfolio. This process ensures that each portfolio will contain an equal number of stocks from every sector, thereby the resulting portfolios are sector neutral.

Method 6 ■ Separate all the stocks with negative factors values. Split the group

of stocks with negative values into two portfolios using the median value as the break point.

■ Allocate stocks with zero factor values into one portfolio.

Cross-Sectional Factor-Based Models and Trading Strategies 295

■ Sort the remaining stocks with nonzero factor values into portfolios based on their factor values.

For an example of method 6, recall the discussion of the share repur- chase factor from the prior companion chapter. We are interested in the extreme positive and negative values of this factor. As we see in Exhibit 12.5(A), the distribution of this factors is leptokurtic with the positive val- ues skewed to the right and the negative values clustered in a small range. By choosing method 6 to sort this variable, we can distinguish between those values we view as extreme. The negative values are clustered so we want to distinguish among the magnitudes of those values. We accomplish this because our sorting method separates the negative values by the median of the negative values. The largest negative values form the extreme negative portfolio. The positive values are skewed to the right, so we want to differ- entiate between the larger from smaller positive values. When implementing portfolio method 6, we would also separate the zero values from the posi- tive values.

The portfolio sort methodology has several advantages. The approach is easy to implement and can easily handle stocks that drop out or enter into the sample. The resulting portfolios diversify away idiosyncratic risk of individual assets and provide a way of assessing how average returns differ across different magnitudes of a factor.

The portfolio sort methodology has several disadvantages. The result- ing portfolios may be exposed to different risks beyond the factor the port- folio was sorted on. In those instances, it is difficult to know which risk characteristics have an impact on the portfolio returns. Because portfolio sorts are nonparametric, they do not give insight as to the functional form of the relation between the average portfolio returns and the factor.

Next we provide three examples to illustrate how the economic intu- ition of the factor and cross sectional statistics can help determine the sort- ing methodology.

Example 1: Portfolio Sorts Based on the EBITDA/EV Factor

In the previous chapter, we introduced the EBITDA/EV factor. Panel A of Exhibit 12.1 contains the cross-sectional distribution of the EBITDA/EV fac- tor. This distribution is approximately normally distributed around a mean of 0.1, with a slight right skew. We use method 1 to sort the variables into five portfolios (denoted by q1, …, q5) because this sorting method aligns the cross-sectional distribution of factor returns with our economic intuition that there is a linear relationship between the factor and subsequent return. In Exhibit 12.1(B), we see that there is a large difference between the equally

296 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

weighted monthly returns of portfolio 1 (q1) and portfolio 5 (q5). There- fore, a trading strategy (denoted by ls in the graph) that goes long portfolio 1 and short portfolio 5 appears to produce abnormal returns.

Example 2: Portfolios Sorts Based on the Revisions Factor

In Exhibit 12.2(A), we see that the distribution of earnings revisions is lep- tokurtic around a mean of about zero, with the remaining values symmetri- cally distributed around the peak. The pattern in this cross-sectional distri- bution provides insight on how we should sort this factor. We use method

EXHIBIT 12.1 Portfolio Sorts Based on the EBITDA/EV Factor A. All Factor Values

–0.1 0.0 0.1 0.2 0.3 0.4 0.5

0 5,

00 0

15 ,0

00 25

,0 00

B. Monthly Average Returns for the Sorted Portfolios

q1 q2 q3 q4 q5 ls 0.0

0.2

0.4

0.6

0.8

1.0

1.2

Cross-Sectional Factor-Based Models and Trading Strategies 297

3 to sort the variables into five portfolios. The firms with no change in revisions we allocate to the middle portfolio (portfolio 3). The stocks with positive revisions we sort into portfolios 1 and 2, according to the size of the revisions—while we sort stocks with negative revisions into portfolios 4 and 5, according to the size of the revisions. In Exhibit 12.2(B), we see there is the relationship between the portfolios and subsequent monthly returns. The positive relationship between revisions and subsequent returns agrees with the factor’s underlying economic intuition: We expect that firms with improving earnings should outperform. The trading strategy that goes long

EXHIBIT 12.2 The Revisions Factor A. All Factor Values

–1.5 –1.0 –0.5 0.0 0.5 1.0

0 20

,0 00

40 ,0

00 60

,0 00

B. Monthly Average Returns for the Sorted Portfolios

q1 q2 q3 q4 q5 ls 0.0

0.2

0.4

0.6

0.8

298 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

portfolio 1 and short portfolio 5 (denoted by ls in the graph) appears to produce abnormal returns.

Example 3: Portfolio Sorts Based on the Share Repurchase Factor

In Exhibit 12.3(A), we see the distribution of share repurchase is asym- metric and leptokurtic around a mean of zero. The pattern in this cross- sectional distribution provides insight on how we should sort this factor. We use method 6 to sort the variables into seven portfolios. We group stocks

EXHIBIT 12.3 The Share Repurchase Factor A. All Factor Values

0.0 0.2 0.4 0.6

0 20

,0 00

60 ,0

00 10

0, 00

0

B. Monthly Average Returns for the Sorted Portfolios

q–2 q–1 q1 q2 q3 q4 q5 ls 0.0

0.2

0.4

0.6

0.8

1.0

Cross-Sectional Factor-Based Models and Trading Strategies 299

with positive revisions into portfolios 1 through 5 (denoted by q1, …, q5 in the graph) according to the magnitude of the share repurchase factor. We allocate stocks with negative repurchases into portfolios q−2 and q−1 where the median of the negative values determines their membership. We split the negative numbers because we are interested in large changes in the shares outstanding. In Exhibit 12.3(B), unlike the other previous factors, we see that there is not a linear relationship between the portfolios. However, there is a large difference in return between the extreme portfolios (denoted by ls in the graph). This large difference agrees with the economic intuition of this factor. Changes in the number of shares outstanding is a potential signal for the future value and prospects of a firm. On the one hand, a large increase in shares outstanding may (1) signal to investors the need for additional cash because of financial distress, or (2) that the firm may be overvalued. On the other hand, a large decrease in the number of shares outstanding may indicate that management believes the shares are undervalued. Finally, small changes in shares outstanding, positive or negative, typically do not have an impact on stock price and therefore are not significant.

Information Ratios for Portfolio Sorts

The information ratio (IR) is a statistic for summarizing the risk-adjusted performance of an investment strategy. It is defined as the ratio of the average excess return to the standard deviation of return. For actively managed equity long portfolios, the IR measures the risk-adjusted value a portfolio manager is adding relative to a benchmark.2 IR can also be used to capture the risk-adjusted performance of long-short portfolios from a portfolio sorts. When comparing portfolios built using different factors, the IR is an effective measure for differentiating the performance between the strategies.

New Research on Portfolio Sorts

As we mentioned earlier in this section, the standard statistical testing pro- cedure for portfolios sorts is to use a Student’s t-test to evaluate the mean return differential between the two portfolios containing stocks with the

2See Richard C. Grinold and Ronald N. Kahn, Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk (New York: McGraw-Hill, 1999), the authors discuss the differences between the t-statis- tic and the information ratio. Both measures are closely related in their calculation. The t-statistic is the ratio of mean return of a strategy to its standard error. Grinold and Kahn state the related calculations should not obscure the distinction between the two ratios. The t-statistic measures the statistical significance of returns while the IR measures the risk-reward trade-off and the value added by an investment strategy.

300 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

highest and lowest values of the sorting factor. However, evaluating the re- turn between these two portfolios ignores important information about the overall pattern of returns among the remaining portfolios.

Recent research by Patton and Timmermann3 provides new analytical techniques to increase the robustness of inference from portfolios sorts. The technique tests for the presence of a monotonic relationship between the port- folios and their expected returns. To find out if there is a systematic relation- ship between a factor and portfolio returns, they use the monotonic relation (MR) test to reveal whether the null hypothesis of no systematic relationship can be rejected in favor of a monotonic relationship predicted by economic theory. By MR it is meant that the expected returns of a factor should rise or decline monotonically in one direction as one goes from one portfolio to another. Moreover, Patton and Timmermann develop separate tests to deter- mine the direction of deviations in support of or against the theory.

The authors emphasize several advantages in using this approach. The test is nonparametric and applicable to other cases of portfolios such as two-way and three-way sorts. This test is easy to implement via bootstrap methods. Furthermore, this test does not require specifying the functional form (e.g., linear) in relating the sorting variable to expected returns.

FACTOR MODELS

Classical financial theory states that the average return of a stock is the pay- off to investors for taking on risk. One way of expressing this risk-reward relationship is through a factor model. A factor model can be used to decom- pose the returns of a security into factor-specific and asset-specific returns,

r f fi t i i t i K K t i t, , , , , ,= + + + +α β β ε1 1 

where bi,1, bi,2, …, bi,K are the factor exposures of stock i, f1,t, f2,t, …, fK,t are the factor returns, ai is the average abnormal return of stock i, and ei,t is the residual.

This factor model specification is contemporaneous, that is, both left- and right-hand side variables (returns and factors) have the same time subscript, t. For trading strategies one generally applies a forecast- ing specification where the time subscript of the return and the factors are t + h (h ≥ 1) and t, respectively. In this case, the econometric specifi- cation becomes

3Andrew J. Patton and Allan Timmermann, “Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM and Portfolio Sorts,” working paper, University of California–San Diego, 2009.

Cross-Sectional Factor-Based Models and Trading Strategies 301

r f fi t h i i t i K K t i t h, , , , , ,+ += + + + +α β β ε1 1 

How do we interpret a trading strategy based on a factor model? The explanatory variables represent different factors that forecast security returns, each factor has an associated factor premium. Therefore, future security returns are proportional to the stock’s exposure to the factor premium,

E r f fi t h t K t i t( | ,..., ), , ,+ = + ′1 α ββif

and the variance of future stock return is given by

Var( | , ..., ) ( ), , ,r f f Ei t h t K t i t t i+ = ′ ′1 ββ ββf f

where ββi i i i K= ( ′β β β, , ,, , , )1 2  and ft t t K tf f f= ′( , , , ), , ,1 2  . In the next section we discuss some specific econometric issues regard-

ing cross-sectional regressions and factor models.

Econometric Considerations for Cross-Sectional Factor Models

In cross-sectional regressions, where the dependent variable4 is a stock’s re- turn and the independent variables are factors, inference problems may arise that are the result of violations of classical linear regression theory. The three most common problems are measurement problems, common varia- tions in residuals, and multicollinearity.

Measurement Problems

Some factors are not explicitly given, but need to be estimated. These factors are estimated with an error. This error can have an impact on the inference from a factor model. This problem is commonly referred to as the “errors in variables problem.” For example, a factor that is comprised of a stock’s beta is estimated with an error because beta is determined from a regression of stock excess returns on the excess returns of a market index. While beyond the scope of this book, several approaches have been suggested to deal with this problem.5

4See, for example, Eugene F. Fama and Kenneth R. French, “The Capital Asset Pricing Model: Theory and Evidence,” Journal of Economic Perspectives 18, no. 3 (2004): 25–46. 5One approach is to use the Bayesian or model averaging techniques. For more de- tails on the Bayesian approach, see, for example, Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and Frank J. Fabozzi, Baysian Methods in Finance (Hoboken, NJ: John Wiley & Sons, 2008).

302 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Common Variation in Residuals

The residuals from a regression often contain a source of common variation. Sources of common variation in the residuals are heteroskedasticity and serial correlation.6 We note that when the form of heteroskedasticity and serial correlation is known, we can apply generalized least squares (GLS). If the form is not known, it has to be estimated, for example as part of feasible generalized least squares (FGLS). We summarize some additional possibili- ties next.

Heteroskedasticity occurs when the variance of the residual differs across observations and affects the statistical inference in a linear regression. In particular, the estimated standard errors will be underestimated and the t-statistics will therefore be inflated. Ignoring heteroskedasticity may lead the researcher to find significant relationships where none actually exist. Several procedures have been developed to calculate standard errors that are robust to heteroskedasticity, also known as heteroskedasticity-consistent standard errors.

Serial correlation occurs when residuals terms in a linear regression are correlated, violating the assumptions of regression theory. If the serial cor- relation is positive, then the standard errors are underestimated and the t-sta- tistics will be inflated. Cochrane7 suggests that the errors in cross-sectional regressions using financial data are often off by a factor of 10. Procedures are available to correct for serial correlation when calculating standard errors.

When the residuals from a regression are both heteroskedastic and seri- ally correlated, procedures are available to correct them. One commonly used procedure is the one proposed by Newey and West referred to as the “Newey-West corrections,”8 and its extension by Andrews.9

Petersen10 provides guidance on choosing the appropriate method to use for correctly calculating standard errors in panel data regressions when the residuals are correlated. He shows the relative accuracy of the different methods depends on the structure of the data. In the presence of firm effects, where the residuals of a given firm may be correlated across years, ordinary

6For a discussion of dealing with these econometric problems, see Chapter 2 in Frank J. Fabozzi, Sergio Focardi, and Petter N. Kolm, Quantitative Equity Investing (Hoboken, NJ: John Wiley & Sons, 2010). 7John H. Cochrane, Asset Pricing (Princeton, NJ: Princeton University Press, 2005). 8Whitney K. Newey and Kenneth D. West, “A Simple, Positive Semidefinite Hetero- skedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica 56, no. 3 (1987): 703–708. 9Donald W. K. Andrews, “Heteroskedasticity and Autocorrelation Consistent Cova- riance Matrix Estimation,” Econometrica 59, no. 3 (1991): 817–858. 10Mitchell A. Petersen, “Estimating Standard Errors in Finance Panel Sets: Compar- ing Approached,” Review of Financial Studies 22, no. 1 (2009): 435–480.

Cross-Sectional Factor-Based Models and Trading Strategies 303

least squares (OLS), Newey-West (modified for panel data sets), or Fama- MacBeth,11 corrected for first-order autocorrelation, all produce biased standard errors. To correct for this, Petersen recommends using standard errors clustered by firms. If the firm effect is permanent, the fixed effects and random effects models produce unbiased standard errors. In the pres- ence of time effects, where the residuals of a given period may be correlated across difference firms (cross-sectional dependence), Fama-MacBeth pro- duces unbiased standard errors. Furthermore, standard errors clustered by time are unbiased when there are a sufficient number of clusters. To select the correct approach he recommends determining the form of dependence in the data and comparing the results from several methods.

Gow, Ormazabal, and Taylor12 evaluate empirical methods used in accounting research to correct for cross-sectional and time-series depen- dence. They review each of the methods, including several methods from the accounting literature that have not previously been formally evaluated, and discuss when each methods produces valid inferences.

Multicollinearity

Multicollinearity occurs when two or more independent variables are highly correlated. We may encounter several problems when this happens. First, it is difficult to determine which factors influence the dependent variable. Second, the individual p values can be misleading—a p value can be high even if the variable is important. Third, the confidence intervals for the re- gression coefficients will be wide. They may even include zero. This implies that, we cannot determine whether an increase in the independent variable is associated with an increase—or a decrease—in the dependent variable. There is no formal solution based on theory to correct for multicollinearity. The best way to correct for multicollinearity is by removing one or more of the correlated independent variables. It can also be reduced by increasing the sample size.

Fama-MacBeth Regression

To address the inference problem caused by the correlation of the residuals, Fama and MacBeth13 proposed the following methodology for estimating

11We cover Fama-MacBeth regression in this section. 12Ian D. Gow, Gaizka Ormazabal, and Daniel J. Taylor, “Correcting for Cross-Sec- tional and Time-Series Dependence in Accounting Research,” working paper, Kel- logg School of Business and Stanford Graduate School, 2009. 13Eugene F. Fama and James D. MacBeth, “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy 81, no. 3 (1973): 607–636.

304 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

cross-sectional regressions of returns on factors. For notational simplicity, we describe the procedure for one factor. The multifactor generalization is straightforward.

First, for each point in time t we perform a cross-sectional regression:

r f i Ni t i t t i t, , , , , ,= + =β ε , 1 2 

In the academic literature, the regressions are typically performed using monthly or quarterly data, but the procedure could be used at any frequency.

The mean and standard errors of the time series of slopes and residuals are evaluated to determine the significance of the cross-sectional regression. We estimate f and e

i as the average of their cross-sectional estimates, therefore,

ˆ ˆ , ˆ ˆ ,f T f

Ttt

T

i i t t

T

= = = = ∑ ∑1 1

1 1

ε ε

The variations in the estimates determine the standard error and cap- ture the effects of residual correlation without actually estimating the cor- relations.14 We use the standard deviations of the cross-sectional regression estimates to calculate the sampling errors for these estimates,

σ σ ε εεˆ ˆ ,ˆ ˆ , ˆ ˆf t t

T

i t iT f f

Ti 2

2

2

1

2 2

1 1= −( ) = −( = ∑ ))

= ∑ 2

1t

T

Cochrane15 provides a detailed analysis of this procedure and compares it to cross-sectional OLS and pooled time-series cross-sectional OLS. He shows that when the factors do not vary over time and the residuals are cross-sectionally correlated, but not correlated over time, then these proce- dures are all equivalent.

Information Coefficients

To determine the forecast ability of a model, practitioners commonly use a statistics called the information coefficient (IC). The IC is a linear statistic that measures the cross-sectional correlation between a factor and its subse- quent realized return:16

14Fama and French, “The Capital Asset Pricing Model: Theory and Evidence.” 15Cochrane, Asset Pricing. 16See, for example, Grinold and Kahn, Active Portfolio Management A Quantita- tive Approach for Providing Superior Returns and Controlling Risk; and Edward E. Qian, Ronald H. Hua, and Eric H. Sorensen, Quantitative Portfolio Management: Modern Techniques and Applications (New York: Chapman & Hall/CRC, 2007).

Cross-Sectional Factor-Based Models and Trading Strategies 305

ICt t k t t t k, ,( , )+ += corr f r

where ft is a vector of cross sectional factor values at time t and rt,t+k is a vec- tor of returns over the time period t to t + k.

Just like the standard correlation coefficient, the values of the IC range from −1 to +1. A positive IC indicates a positive relation between the factor and return. A negative IC indicates a negative relation between the factor and return. ICs are usually calculated over an interval, for example, daily or monthly. We can evaluate how a factor has performed by examining the time series behavior of the ICs. Looking at the mean IC tells how predictive the factor has been over time.

An alternate specification of this measure is to make ft the rank of a cross-sectional factor. This calculation is similar to the Spearman rank coef- ficient. By using the rank of the factor, we focus on the ordering of the factor instead of its value. Ranking the factor value reduces the unduly influence of outliers and reduces the influence of variables with unequal variances. For the same reasons, we may also choose to rank the returns instead of using their numerical value.

Sorensen, Qian, and Hua17 present a framework for factor analysis based on ICs. Their measure of IC is the correlation between the factor ranks, where the ranks are the normalized z-score of the factor,18 and subse- quent return. Intuitively, this IC calculation measures the return associated with a one standard deviation exposure to the factor. Their IC calculation is further refined by risk adjusting the value. To risk adjust, the authors remove systematic risks from the IC and accommodate the IC for specific risk. By removing these risks, Qian and Hua19 show that the resulting ICs provide a more accurate measure of the return forecasting ability of the factor.

The subsequent realized returns to a factor typically vary over different time horizons. For example, the return to a factor based on price reversal is realized over short horizons, while valuation metrics such as EBITDA/ EV are realized over longer periods. It therefore makes sense to calculate multiple ICs for a set of factor forecasts whereby each calculation varies the horizon over which the returns are measured.

17Eric H. Sorensen, Ronald Hua, and Edward Qian, “Contextual Fundamentals, Models, and Active Management,” Journal of Portfolio Management 32, no. 1 (2005): 23–36. 18A factor normalized z-score is given by the formula z-score ( std= −f f f) / ( ) where f is the factor, f is the mean and std(f) is the standard deviation of the factor. 19Ronald Hua and Edward Qian, “Active Risk and Information Ratio,” Journal of Investment Management 2, no. 3 (2004): 1–15.

306 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

The IC methodology has many of the same advantages as regression models. The procedure is easy to implement. The functional relationship between factor and subsequent returns is known (linear).

ICs can also be used to assess the risk of factors and trading strategies. The standard deviation of the time series (with respect to t) of ICs for a particular factor (std(ICt,t+k)) can be interpreted as the strategy risk of a factor. Exam- ining the time series behavior of std(ICt,t+k) over different time periods may give a better understanding of how often a particular factor may fail. Qian and Hua show that std(IC

t,t+k) can be used to more effectively understand the active risk of investment portfolios. Their research demonstrates that ex post tracking error often exceeds the ex ante tracking provided by risk models. The difference in tracking error occurs because tracking error is a function of both ex ante tracking error from a risk model and the variability of information coefficients, std(IC

t,t+k). They define the expected tracking error as

σ σTE t t kIC N= +std dismodel( ) ( ). Rt

where N is the number of stocks in the universe (breath), smodel is the risk model tracking error, and dis(Rt) is dispersion of returns

20 defined by

dis std( ) ( , , ..., ), , ,Rt = r r rt t N t1 2

Example: Information Coefficients

Exhibit 12.4 displays the time-varying behavior of ICs for each one of the factors EBITDA/EV, growth of fiscal year 1 and fiscal year 2 earnings esti- mates, revisions, and momentum. The graph shows the time series average of information coefficients:

ICk = mean( )ICt,t+k

The graph depicts the information horizons for each factor, showing how subsequent return is realized over time. The vertical axis shows the size of the average information coefficient ICk for k = 1, 2, …, 15.

Specifically, the EBITDA/EV factor starts at almost 0.03 and monotoni- cally increases as the investment horizon lengthens from one month to 15 months. At 15 months, the EBITDA/EV factor has an IC of 0.09, the high- est value among all the factors presented in the graph. This relationship

20We are conforming to the notation used in Qian and Hua, “Active Risk and Infor- mation Ratio.” To avoid confusion, Qian and Hua use dis() to describe the cross- sectional standard deviation and std() to describe the time series standard deviation.

Cross-Sectional Factor-Based Models and Trading Strategies 307

suggests that the EBITDA/EV factor earns higher returns as the holding period lengthens.

The other ICs of the factors in the graph are also interesting. The growth of fiscal year 1 and fiscal year 2 earnings estimates factor is defined as the growth in current fiscal year (fy1) earnings estimates to the next fis- cal year (fy2) earnings estimates provided by sell-side analysts.21 We call the growth of fiscal year 1 and fiscal year 2 earnings estimates factor the earnings growth factor throughout the remainder of the chapter. The IC is negative and decreases as the investment horizon lengthens. The momentum factor starts with a positive IC of 0.02 and increases to approximately 0.055 in the fifth month. After the fifth month, the IC decreases. The revisions fac- tor starts with a positive IC and increases slightly until approximately the eleventh month at which time the factor begins to decay.

Looking at the overall patterns in the graph, we see that the return realization pattern to different factors varies. One notable observation is that the returns to factors don’t necessarily decay but sometimes grow with the holding period. Understanding the multiperiod effects of each factor is important when we want to combine several factors. This information may influence how one builds a model. For example, we can explicitly incorpo- rate this information about information horizons into our model by using a function that describes the decay or growth of a factor as a parameter to be calibrated. Implicitly, we could incorporate this information by changing

21The earnings estimates come from the IBES database. See Appendix A for a more detailed description of the data.

EXHIBIT 12.4 Information Coefficients over Various Horizons for EBITDA/EV, Growth of Fiscal Year 1 and Fiscal Year 2 Earnings Estimates, Revisions, and Momentum Factors

–0.04 –0.03 –0.02 –0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

EBITDA/EV Earn FY1 & FY2 Revisions Momentum

308 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

the holding period for a security traded for our trading strategy. Specifically, Sneddon22 discusses an example that combines one signal that has short-range predictive power with another that has long-range power. Incorporating this information about the information horizon often improves the return poten- tial of a model. Kolm23 describes a general multiperiod model that combines information decay, market impact costs, and real world constraints.

Factor Portfolios

Factor portfolios are constructed to measure the information content of a factor. The objective is to mimic the return behavior of a factor and mini- mize the residual risk. Similar to portfolio sorts, we evaluate the behavior of these factor portfolios to determine whether a factor earns a systematic premium.

Typically, a factor portfolio has a unit exposure to a factor and zero exposure to other factors. Construction of factor portfolios requires holding both long and short positions. We can also build a factor portfolio that has exposure to multiple attributes, such as beta, sectors, or other characteristics. For example, we could build a portfolio that has a unit exposure to book- to-price and small size stocks. Portfolios with exposures to multiple factors provide the opportunity to analyze the interaction of different factors.

A Factor Model Approach

By using a multifactor model, we can build factor portfolios that control for different risks.24 We decompose return and risk at a point in time into a systematic and specific component using the regression:

r = Xb + u

where r is an N vector of excess returns of the stocks considered, X is an N by K matrix of factor loadings, b is a K vector of factor returns, and u is a N vector of firm specific returns (residual returns). Here, we assume that fac- tor returns are uncorrelated with the firm specific return. Further assuming

22Leigh Sneddon, “The Tortoise and the Hare: Portfolio Dynamics for Active Man- agers,” Journal of Investing 17, no. 4 (2008): 106–111. 23Petter N. Kolm, “Multi-Period Portfolio Optimization with Transaction Costs, Al- pha Decay, and Constraints,” working paper, Courant Institute of Mathematical Sciences, New York University, 2010. 24This derivation of factor portfolios is presented in Grinold and Kahn, Active Port- folio Management A Quantitative Approach for Providing Superior Returns and Controlling Risk.

Cross-Sectional Factor-Based Models and Trading Strategies 309

that firm specific returns of different companies are uncorrelated, the N by N covariance matrix of stock returns V is given by

V XFX= ′ + ∆∆

where F is the K by K factor return covariance matrix and ∆∆ is the N by N diagonal matrix of variances of the specific returns.

We can use the Fama-MacBeth procedure discussed earlier to estimate the factor returns over time. Each month, we perform a GLS regression to obtain

b X X X r= ′ ′− − −( )∆∆ ∆∆1 1 1

OLS would give us an unbiased estimate, but since the residuals are hetero- skedastic the GLS methodology is preferred and will deliver a more efficient estimate. The resulting holdings for each factor portfolio are given by the rows of ( )′ − − −X X X∆∆ ∆∆1 1 1.

An Optimization-Based Approach

A second approach to build factor portfolios uses mean-variance optimiza- tion. Using optimization techniques provide a flexible approach for imple- menting additional objectives and constraints.25

Using the notation from the previous subsection, we denote by X the set of factors. We would like to construct a portfolio that has maximum exposure to one target factor from X (the alpha factor), zero exposure to all other factors, and minimum portfolio risk. Let us denote the alpha fac- tor by X

a and all the remaining ones by X

s . Then the resulting optimization

problem takes the form

max

w w X w Vw

w X

′ − ′ 

  

′ =

a

1 2

0

λ

σs.t.

The analytical solution to this optimization problem is given by

h * - - -= − ′( ) ′ 

−1 1 1 1 1 λ σ σ σ σ α

V I X X V X X V X

25Dimitris Melas, Raghu Suryanarayanan, and Stefano Cavaglia, “Efficient Replica- tion of Factor Returns,” MSCI Barra Research Insight, June 2009.

310 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

We may want to add additional constraints to the problem. Constraints are added to make factor portfolios easier to implement and meet addi- tional objectives. Some common constraints include limitations on turnover, transaction costs, the number of assets, and liquidity preferences. These con- straints26 are typically implemented as linear inequality constraints. When no analytical solution is available to solve the optimization with linear inequality constraints, we have to resort to quadratic programming (QP).27

PERFORMANCE EVALUATION OF FACTORS

Analyzing the performance of different factors is an important part of the development of a factor-based trading strategy. A researcher may construct and analyze over a hundred different factors, so a process to evaluate and compare these factors is needed. Most often this process starts by trying to understand the time-series properties of each factor in isolation and then study how they interact with each other.

To give a basic idea of how this process may be performed, we use the five factors introduced earlier in this chapter: EBITDA/EV, revisions, share repurchase, momentum, and earnings growth. These are a subset of the fac- tors that we use in the factor trading strategy model discussed later in the chapter. We choose a limited number of factors for ease of exposition. In particular, we emphasize those factors that possess more interesting empiri- cal characteristics.

Exhibit 12.5(A) presents summary statistics of monthly returns of long- short portfolios constructed from these factors. We observe that the average monthly return ranges from −0.05% for the earnings growth to 0.90% for the momentum factor. The t-statistics for the mean return are significant at the 95% level for the EBITDA/EV, share repurchase, and momentum factors. The monthly volatility ranges from 3.77% for the revisions factor to 7.13% for the momentum factor. In other words, the return and risk characteristics among factors vary significantly. We note that the greatest monthly drawdown has been large to very large for all of the factors, imply- ing significant downside risk. Overall, the results suggest that there is a sys- tematic premium associated with the EBITDA/EV, share repurchase, and momentum factors.

26An exception is the constraint on the number of assets that results in integer con- straints. 27For a more detailed discussion on portfolio optimization problems and optimiza- tion software see, for example, Frank J. Fabozzi, Petter N. Kolm, Dessislava Pacha- manova, and Sergio M. Focardi, Robust Portfolio Optimization and Management (Hoboken, NJ: John Wiley & Sons, 2007).

311

EX HI

BI T

12 .5

R

es ul

ts f

ro m

P or

tf ol

io S

or ts

A . S

um m

ar y

St at

is ti

cs o

f M

on th

ly R

et ur

ns o

f L

on g-

sh or

t Po

rt fo

lio s

M ea

n St

de v

M ed

ia n

t- st

at M

ax M

in pc

tP os

pc tN

eg

R ev

is io

ns 0

.2 9

3. 77

0.

77

1 .1

7 10

.4 3

–1 9.

49 0.

55

0. 45

E B

IT D

A /E

V

0 .8

3 5.

80

0. 72

2

.1 6

31 .6

1 –3

0. 72

0. 55

0.

45

Sh ar

e re

pu rc

ha se

0 .7

2 3.

89

0. 43

2

.7 8

22 .0

1 –1

4. 06

0. 61

0.

39

M om

en tu

m 0

.9 0

7. 13

0.

97

1 .9

0 25

.4 3

–4 2.

71 0.

61

0. 39

E ar

ni ng

g ro

w th

–0 .0

5 4.

34

0. 25

–0

.1 8

14 .0

3 –2

3. 10

0. 53

0.

47

B . C

or re

la ti

on s

be tw

ee n

L on

g- Sh

or t

Po rt

fo lio

s

R ev

is io

ns E

B IT

D A

/E V

Sh

ar e

R ep

ur ch

as e

M om

en tu

m E

ar ni

ng s

G ro

w th

R ev

is io

ns 1

.0 0

–0 .2

8 0.

01

0 .7

9 0.

25

E B

IT D

A /E

V

–0 .2

8 1

.0 0

0. 78

–0

.1 2

0. 01

Sh ar

e re

pu rc

ha se

0 .0

1 0

.7 8

1. 00

0

.2 0

0. 12

M om

en tu

m 0

.7 9

–0 .1

2 0.

20

1 .0

0 0.

28

E ar

ni ng

s gr

ow th

0

.2 5

0 .0

1 0.

12

0 .2

8 1.

00

312 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Let pctPos and pctNeg denote the fraction of positive and negative returns over time, respectively. These measures offer another way of interpreting the strength and consistency of the returns to a factor. For example, EBITDA/EV and momentum have t-statistics of 2.16 and 1.90, respectively, indicating that the former is stronger. However, pctPos (pct- Neg) are 0.55 versus 0.61 (0.45 versus 0.39) showing that positive returns to momentum occur more frequently. This may provide reassurance of the usefulness of the momentum factor, despite the fact that its t-statistic is below the 95% level.

Exhibit 12.5(B) presents unconditional correlation coefficients of monthly returns for long-short portfolios. The comovement of factor returns varies among the factors. The lowest correlation is −0.28 between EBITDA/ EV and revisions. The highest correlation is 0.79 between momentum and revisions. In addition, we observe that the correlation between revisions and share repurchase, and between EBITDA/EV and earnings growth are close to zero. The broad range of correlations provides evidence that combining uncorrelated factors could produce a successful strategy.

Exhibit 12.6 presents the cumulative returns for the long-short portfo- lios. The returns of the long-short factor portfolios experience substantial

EXHIBIT 12.6 Cumulative Returns of Long-Short Portfolios

550

500

450

400

350

300

250

200

150

100

50

0

Revisions EBITDA/EV Share repurchase Momentum Earnings growth

D ec

-3 1-

19 89

Ju n-

30 -1

99 0

D ec

-3 1-

19 90

Ju n-

30 -1

99 1

D ec

-3 1-

19 91

Ju n-

30 -1

99 2

D ec

-3 1-

19 92

Ju n-

30 -1

99 3

D ec

-3 1-

19 93

Ju n-

30 -1

99 4

D ec

-3 1-

19 94

Ju n-

30 -1

99 5

D ec

-3 1-

19 95

Ju n-

30 -1

99 6

D ec

-3 1-

19 96

Ju n-

30 -1

99 7

D ec

-3 1-

19 97

Ju n-

30 -1

99 8

D ec

-3 1-

19 98

Ju n-

30 -1

99 9

D ec

-3 1-

19 99

Ju n-

30 -2

00 0

D ec

-3 1-

20 00

Ju n-

30 -2

00 1

D ec

-3 1-

20 01

Ju n-

30 -2

00 2

D ec

-3 1-

20 02

Ju n-

30 -2

00 3

D ec

-3 1-

20 03

Ju n-

30 -2

00 4

D ec

-3 1-

20 04

Ju n-

30 -2

00 5

D ec

-3 1-

20 05

Ju n-

30 -2

00 6

D ec

-3 1-

20 06

Ju n-

30 -2

00 7

D ec

-3 1-

20 07

Ju n-

30 -2

00 8

D ec

-3 1-

20 08

Cross-Sectional Factor-Based Models and Trading Strategies 313

volatility. We highlight the following patterns of cumulative returns for the different factors:

■ The cumulative return of the revisions factor is positive in the early periods (12/1989 to 6/1998). While it is volatile, its cumulative return is higher in the next period (7/1998 to 7/2000). It deteriorates sharply in the following period (8/2000 to 6/2003), and levels out in the later periods (7/2003 to 12/2008).

■ The performance of the EBITDA/EV factor is consistently positive in the early periods (12/1989 to 9/1998), deteriorates in the next period (10/1998 to 1/2000) and rebounds sharply (2/2000 to 7/2002), grows at slower but more historically consistent rate in the later periods (8/2002 to 4/2007), deteriorates in the next period (5/2007 to 9/2007), and returns to more historically consistent returns in last period (10/2007 to 12/2008).

■ The cumulative return of the share repurchase factor grows at a slower pace in the early years (12/1989 to 5/1999), falls slightly in the middle periods (6/1999 to 1/2000), rebounds sharply (2/2000 to 7/2002), falls then flattens out in the next period (8/2002 to 4/2008), and increases at a large rate late in the graph (5/2008 to 12/2008).

■ The momentum factor experiences the largest volatility. This factor performs consistently well in the early period (12/1989 to 12/1998), experiences sharp volatility in the middle period (1/1999 to 5/2003), flattens out (6/2003 to 6/2007), and grows at an accelerating rate from (7/2007 to 12/2008).

■ The performance of the earnings growth factor is flat or negative throughout the entire period.

The overall pattern of the cumulative returns among the factors clearly illustrate that factor returns and correlations are time varying.

In Exhibit 12.7(A), we present summary statistics of the monthly infor- mation coefficients of the factors. The average monthly information coef- ficients range from 0.03 for EBITDA/EV and momentum, to 0.01 for the share repurchase factor. The t-statistics for the mean ICs are significant at the 95% level for all factors except earnings growth. With the exception of share repurchase and earnings growth, the fraction of positive returns of the factors are significantly greater than that of the negative returns.

The share repurchase factor requires some comments. The information coefficient is negative, in contrast to the positive return in the long-short portfolio sorts, because negative share repurchases are correlated with sub- sequent return. The information coefficient is lower than we would expect because there is not a strong linear relation between the return and the

314

EX HI

BI T

12 .7

Su

m m

ar y

of M

on th

ly F

ac to

r In

fo rm

at io

n C

oe ffi

ci en

ts A

. B as

ic S

ta ti

st ic

s fo

r M

on th

ly I

nf or

m at

io n

C oe

ffi ci

en ts

M ea

n St

de v

M ed

ia n

t- st

at M

ax M

in pc

tP os

pc tN

eg

R ev

is io

ns 0

.0 2

0. 10

0

.0 2

2 .5

1 0.

31

–0 .2

9 0.

58

0. 42

E B

IT D

A /E

V

0 .0

3 0.

13

0 .0

2 3

.1 3

0. 48

–0

.4 1

0. 59

0.

41

Sh ar

e re

pu rc

ha se

–0 .0

1 0.

10

–0 .0

0 –2

.1 3

0. 20

–0

.4 5

0. 48

0.

52

M om

en tu

m 0

.0 3

0. 18

0

.0 5

2 .8

6 0.

50

–0 .5

7 0.

59

0. 41

E ar

ni ng

s gr

ow th

–0 .0

0 0.

13

0 .0

0 –0

.5 6

0. 26

–0

.2 8

0. 51

0.

49

B . C

or re

la ti

on s

fo r

M on

th ly

A ve

ra ge

I nf

or m

at io

n C

oe ffi

ci en

ts

R ev

is io

ns E

B IT

D A

/E V

Sh

ar e

R ep

ur ch

as e

M om

en tu

m E

ar ni

ng s

G ro

w th

R ev

is io

ns 1

.0 0

–0 .3

1 0

.1 3

0 .7

9 –0

.1 4

E B

IT D

A /E

V

–0 .3

1 1

.0 0

–0 .6

6 –0

.2 6

–0 .4

9

Sh ar

e re

pu rc

ha se

0 .1

3 –0

.6 6

1 .0

0 0

.0 2

0 .5

8

M om

en tu

m 0

.7 9

–0 .2

6 0

.0 2

1 .0

0 –0

.0 5

E ar

ni ng

s gr

ow th

–0 .1

4 –0

.4 9

0 .5

8 –0

.0 5

1 .0

0

Cross-Sectional Factor-Based Models and Trading Strategies 315

measures. As the results from the portfolio sorts indicate, the extreme values of this factor provide the highest returns.

Exhibit 12.7(B) displays unconditional correlation coefficients of the monthly information coefficients. The comovement of the ICs factor returns varies among the factors. The lowest correlation is −0.66 between EBITDA/ EV and share repurchases. But again this should be interpreted with caution because it is negative repurchases that we view as attractive. The highest correlation reported in the exhibit is 0.79 between momentum and revi- sions. Similar to the correlation of long-short factor portfolio returns, the diverse set of correlations provides evidence that combining uncorrelated factors may produce a successful strategy.

In Exhibit 12.8(A), we present summary statistics of the time series average of the monthly coefficients from the Fama-MacBeth (FM) regres- sions of the factors. The information provided by the FM coefficients differs from the information provided by portfolio sorts. The FM coefficients show the linear relationship between the factor and subsequent returns, while the results from the portfolio sorts provide information on the extreme val- ues of the factors and subsequent returns. The difference in the size of the mean returns between the FM coefficients and portfolio sorts exits partially because the intercept terms from the FM regressions are not reported in the exhibit.

The average monthly FM coefficient ranges from −0.18 for share repur- chase to 0.31 for the momentum factor. Again the share repurchase results should be interpreted with caution because it is negative repurchases that we view as attractive. The t-statistics are significant at the 95% level for the EBITDA/EV and share repurchase factors.

Also, we compare the results of portfolio sorts in Exhibit 12.7(A) with the FM coefficients in Exhibit 12.8(A). The rank ordering of the magnitude of factor returns is similar between the two panels. The t-statistics are slightly higher in the FM regressions than the portfolio sorts. The correlation coef- ficients for the portfolio sorts in Exhibit 12.7(B) are consistent with the FM coefficients in Exhibit 12.8(B) for all the factors except for shares repurchases. The results for share repurchases needs to be interpreted with caution because it is negative repurchases that we view as attractive. The portfolio sorts take that into account while FM regressions do not.

To better understand the time variation of the performance of these factors, we calculate rolling 24-month mean returns and correlations of the factors. The results are presented in Exhibit 12.9. We see that the returns and correlations to all factors are time varying. A few of the time series experience large volatility in the rolling 24-month returns. The EBITDA/ EV factor shows the largest variation followed by the momentum and share

316

EX HI

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12 .8

Su

m m

ar y

of M

on th

ly F

am a-

M ac

B et

h R

eg re

ss io

n C

oe ffi

ci en

ts A

. B as

ic S

ta ti

st ic

s fo

r Fa

m a-

M ac

B et

h R

eg re

ss io

n C

oe ffi

ci en

ts

M ea

n St

de v

M ed

ia n

t- st

at M

ax M

in pc

tP os

pc tN

eg

R ev

is io

ns 0

.0 9

1. 11

0

.2 2

1 .2

2 3.

36

– 5.

26 0.

59

0. 41

E B

IT D

A /E

V

0 .2

7 1.

61

0 .1

4 2

.5 0

8. 69

–

7. 81

0. 59

0.

41

Sh ar

e re

pu rc

ha se

–0 .1

8 0.

96

–0 .0

6 –2

.9 0

3. 21

–

5. 91

0. 44

0.

56

M om

en tu

m 0

.3 1

2. 42

0

.2 9

1 .9

4 9.

97

–1 2.

37 0.

60

0. 40

E ar

ni ng

s gr

ow th

–0 .0

8 0.

99

–0 .0

4 –1

.2 0

2. 83

–

4. 13

0. 48

0.

52

B . C

or re

la ti

on s

fo r

Fa m

a- M

ac B

et h

R eg

re ss

io n

C oe

ffi ci

en ts

R ev

is io

ns E

B IT

D A

/E V

Sh

ar e

R ep

ur ch

as e

M om

en tu

m E

ar ni

ng s

G ro

w th

R ev

is io

ns 1

.0 0

–0 .2

7 0

.0 5

0 .7

7 –0

.2 6

E B

IT D

A /E

V

–0 .2

7 1

.0 0

–0 .7

5 –0

.1 8

–0 .5

8

Sh ar

e re

pu rc

ha se

0 .0

5 –0

.7 5

1 .0

0 –0

.0 4

0 .6

4

M om

en tu

m 0

.7 7

–0 .1

8 –0

.0 4

1 .0

0 –0

.1 8

E ar

ni ng

s gr

ow th

–0 .2

6 –0

.5 8

0 .6

4 –0

.1 8

1 .0

0

Cross-Sectional Factor-Based Models and Trading Strategies 317

repurchase factors. All factors experience periods where the rolling average returns are both positive and negative.

Exhibit 12.10 presents the rolling correlation between pairs of the fac- tors. There is substantial variability in many of the pairs. In most cases the correlation moves in a wave-like pattern. This pattern highlights the time- varying property of the correlations among the factors. This property will be important to incorporate in a factor trading model. The most consistent correlation is between momentum and revisions factors and this correlation is, in general, fairly high.

MODEL CONSTRUCTION METHODOLOGIES FOR A FACTOR-BASED TRADING STRATEGY

In the previous section, we analyzed the performance of each factor. The next step in building our trading strategy is to determine how to combine the factors into one model. The key aspect of building this model is to (1) determine what factors to use out of the universe of factors that we have, and (2) how to weight them.

EXHIBIT 12.9 Rolling 24-Month Mean Returns for the Factors N

ov -3

0- 19

91 A

ug -3

1- 19

92

M ay

-3 1-

19 93

Fe b-

28 -1

99 4

N ov

-3 0-

19 94

A ug

-3 1-

19 95

M ay

-3 1-

19 96

Fe b-

28 -1

99 7

N ov

-3 0-

19 97

A ug

-3 1-

19 98

M ay

-3 1-

19 99

Fe b-

29 -2

00 0

N ov

-3 0-

20 00

A ug

-3 1-

20 01

M ay

-3 1-

20 02

Fe b-

28 -2

00 3

N ov

-3 0-

20 03

A ug

-3 1-

20 04

M ay

-3 1-

20 05

Fe b-

28 -2

00 6

N ov

-3 0-

20 06

A ug

-3 1-

20 07

M ay

-3 1-

20 08

8.0

6.0

4.0

2.0

0.0

–2.0

–4.0

–6.0

EBITDA to EV Share Repurchase Revisions Momentum Growth Fy1 & Fy2 Earn Est.

318 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

We describe four methodologies to combine and weight factors to build a model for a trading strategy. These methodologies are used to translate the empirical work on factors into a working model. Most of the methodologies are flexible in their specification and there is some overlap between them. Though the list is not exhaustive, we highlight those processes frequently used by quantitative portfolio managers and researchers today. The four methodologies are the data driven, the factor model, the heuristic, and the optimization approaches.

It is important to be careful how each methodology is implemented. In particular, it is critical to balance the iterative process of finding a robust model with good forecasting ability versus finding a model that is a result of data mining.

The Data Driven Approach

A data driven approach uses statistical methods to select and weight factors in a forecasting model. This approach uses returns as the independent variables and factors as the dependent variables. There are a variety of estimation pro- cedures, such as neural nets, classification trees, and principal components, that can be used to estimate these models. Usually a statistic is established to

EXHIBIT 12.10 Rolling 24-Month Correlations of Monthly Returns for the Factors N

ov -3

0- 19

91

A ug

-3 1-

19 92

M ay

-3 1-

19 93

Fe b-

28 -1

99 4

N ov

-3 0-

19 94

A ug

-3 1-

19 95

M ay

-3 1-

19 96

Fe b-

28 -1

99 7

N ov

-3 0-

19 97

A ug

-3 1-

19 98

M ay

-3 1-

19 99

Fe b-

29 -2

00 0

N ov

-3 0-

20 00

A ug

-3 1-

20 01

M ay

-3 1-

20 02

Fe b-

28 -2

00 3

N ov

-3 0-

20 03

A ug

-3 1-

20 04

M ay

-3 1-

20 05

Fe b-

28 -2

00 6

N ov

-3 0-

20 06

A ug

-3 1-

20 07

M ay

-3 1-

20 08

1.0

0.8

0.6

0.4

0.2

0.0

–0.2

–0.4

–0.6

–0.8

–1.0

corr(ebitdaev, share repur) corr(ebitdaev, earn growth)

corr(ebitdaev, revisions) corr(share repur, mom)

corr(ebitdaev, mom) corr(revisions, mom)

Cross-Sectional Factor-Based Models and Trading Strategies 319

determine the criteria for a successful model. The algorithm of the statistical method evaluates the data and compares the results against the criteria.

Many data driven approaches have no structural assumptions on poten- tial relationships the statistical method finds. Therefore, it is sometimes dif- ficult to understand or even explain the relationship among the dependent variables used in the model.

Deistler and Hamann28 provide an example of a data driven approach to model development. The model they develop is used for forecasting the returns to financial stocks. To start, they split their data sample into two parts—an in-sample part for building the model, and out-of-sample part to validate the model. They use three different types of factor models for fore- casting stocks returns: quasistatic principal components, quasistatic factor models with idiosyncratic noise, and reduced rank regression. For model selection Deistler and Hamann use an iterative approach where they find the optimal mix of factors based on the Akaike’s information criterion and the Bayesian information criterion. A large number of different models are compared using the out-of-sample data. They find that the reduced rank model provides the best performance. This model produced the highest out- of-sample R2s, hit rates,29 and Diebold Mariano test statistic30 among the different models evaluated.

The Factor Model Approach

In this section, we briefly address the use of factor models for forecasting. The goal of the factor model is to develop a parsimonious model that fore- cast returns accurately. One approach is for the researcher to predetermine the variables to be used in the factor model based on economic intuition. The model is estimated and then the estimated coefficients are used to pro- duce the forecasts.

A second approach is to use statistical tools for model selection. In this approach we construct several models—often by varying the factors and the

28Manfred Deistler and Eva Hamann, “Identification of Factor Models for Forecast- ing Returns,” Journal of Financial Econometrics 3, no. 2 (2005): 256–281. 29The hit rate is calculated as

h T T

y yt i

t t i

t T

T

= − −= +

∑1 2 1

1 11

2

sign( ˆ )|

where yt i is one-step ahead realized value and ˆ |yt t

i −1 is the one-step ahead predicted

value. 30For calculation of this measure, see Francis X. Diebold and Roberto S. Mariano, “Comparing Predictive Accuracy,” Journal of Business and Economic Statistics 13, no. 3 (2005): 253–263.

320 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

number of factors used—and have them compete against each other, just like in a horse race. We then choose the best performing model.

Factor model performance can be evaluated in three ways. We can eval- uate the fit, forecast ability, and economic significance of the model. The measure to evaluate the fit of a model is based on statistical measures includ- ing the model’s R2 and adjusted R2, and F- and t-statistics of the model coefficients.

There are several methods to evaluate how well a model will forecast. West31 discusses the theory and conventions of several measures of relative model quality. These methods use the resulting time series of predictions and prediction errors from a model. In the case where we want to com- pare models, West suggests ratios or differences of mean; mean-square or mean-absolute prediction errors; correlation between one model’s predic- tion and another model’s realization (also know as forecast encompassing); or comparison of utility or profit-based measures of predictive ability. In other cases where we want to assess a single model, he suggests measuring the correlation between prediction and realization, the serial correlation in one step ahead prediction errors, the ability to predict direction of change, and the model prediction bias.

We can evaluate economic significance by using the model to predict values and using the predicted values to build portfolios. The profitability of the portfolios is evaluated by examining statistics such as mean returns, information ratios, dollar profits, and drawdown.

The Heuristic Approach

The heuristic approach is another technique used to build trading models. Heuristics are based on common sense, intuition, and market insight and are not formal statistical or mathematical techniques designed to meet a given set of requirements. Heuristic-based models result from the judgment of the researcher. The researcher decides the factors to use, creates rules in order to evaluate the factors, and chooses how to combine the factors and implement the model.

Piotroski32 applies a heuristic approach in developing an investment strategy for high value stocks (high book-to-market firms). He selects nine

31Kenneth D. West, “Forecast Evaluation,” in Handbook of Economic Forecasting, vol. 1, edited by Graham Elliot, Clive W. J. Granger, and Allan G. Timmermann (Amsterdam: Elsevier, 2006). 32Joseph D. Piotroski, “Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers,” Journal of Accounting Research 38, no. 3 supplement (2000): 1–41.

Cross-Sectional Factor-Based Models and Trading Strategies 321

fundamental factors33 to measure three areas of the firm’s financial condi- tion: profitability, financial leverage and liquidity, and operating efficiency. Depending on the factor’s implication for future prices and profitability, each factor is classified as either “good” or “bad.” An indicator variable for the factor is equal to one (zero) if the factor’s realization is good (bad). The sum of the nine binary factors the F_SCORE. This aggregate score measures the overall quality, or strength, of the firm’s financial position. According to the historical results provided by Piotroski, this trading strategy is very profitable. Specifically, a trading strategy that buys expected winners and shorts expected losers would have generated a 23% annual return between 1976 and 1996.

There are different approaches to evaluate a heuristic approach. Sta- tistical analysis can be used to estimate the probability of incorrect out- comes. Another approach is to evaluate economic significance. For example, Piotroski determines economic significance by forming portfolios based on the firm’s aggregate score (F_SCORE) and then evaluates the size of the subsequent portfolio returns.

There is no theory that can provide guidance when making modeling choices in the heuristic approach. Consequently, the researcher has to be careful not to fall into the data-mining trap.

The Optimization Approach

In this approach, we use optimization to select and weight factors in a fore- casting model. An optimization approach allows us flexibility in calibrating the model and simultaneously optimize an objective function specifying a desirable investment criteria.

There is substantial overlap between optimization use in forecast mod- eling and portfolio construction. There is frequently an advantage in work- ing with the factors directly, as opposed to all individual stocks. The fac- tors provide a lower dimensional representation of the complete universe of the stocks considered. Besides the dimensionality reduction, which reduces computational time, the resulting optimization problem is typically more robust to changes in the inputs.

Sorensen, Hua, Qian, and Schoen34 present a process that uses an opti- mization framework to combine a diverse set of factors (alpha sources) into

33The nine factors are return on assets, change in return on assets, cash flow from operations scaled by total assets, cash compared to net income scaled by total assets, change in long-term debt/assets, change in current ratio, change in shares outstand- ing, change in gross margin, and change in asset turnover. 34Eric H. Sorensen, Ronald Hua, Edward Qian, and Robert Schoen, “Multiple Al- pha Sources and Active Management,” Journal of Portfolio Management 30, no. 2 (2004): 39–45.

322 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

a multifactor model. Their procedure assigns optimal weights across the factors to achieve the highest information ratio. They show that the optimal weights are a function of average ICs and IC covariances. Specifically,

w (IC)∝ ×−cov 1 IC

where w is the vector of factor weights, IC is the vector of the average of the risk-adjusted ICs, and cov(IC)–1 is the inverse of the covariance matrix of the ICs.

In a subsequent paper, Sorensen, Hua, and Qian35 apply this optimi- zation technique to capture the idiosyncratic return behavior of different security contexts. The contexts are determined as a function of stock risk characteristics (value, growth, or earnings variability). They build a mul- tifactor model using the historical risk-adjusted IC of the factors, deter- mining the weights of the multifactor model by maximizing the IR of the combined factors. Their research demonstrates that the weights to factors of an alpha model (trading strategy) differ depending on the security contexts (risk dimensions). The approach improves the ex post information ratio compared to a model that uses a one-size-fits-all approach.

Importance of Model Construction and Factor Choice

Empirical research shows that the factors and the weighting scheme of the factors are important in determining the efficacy of a trading strategy model. Using data from the stock selection models of 21 major quantitative funds, the quantitative research group at Sanford Bernstein analyzed the degree of overlap in rankings and factors.36 They found that the models maintained similar exposures to many of the same factors. Most models showed high exposure to cash flow–based valuations (e.g., EV/EBITDA) and price mo- mentum, and less exposure to capital use, revisions, and normalized valu- ation factors. Although they found commonality in factor exposures, the stock rankings and performance of the models were substantially different. This surprising finding indicates that model construction differs among the various stock selection models and provides evidence that the efficacy of common signals has not been completely arbitraged away.

35Eric H. Sorensen, Ronald Hua, and Edward Qian, “Contextual Fundamentals, Models, and Active Management,” Journal of Portfolio Management 32, no. 1 (2005): 23–36. 36Vadim Zlotnikov, Ann Marie Larson, Wally Cheung, Serdar Kalaycioglu, Ronna D. Lao, and Zachary A. Apoian, “Quantitative Research—January 2007: Survey of Quantitative Models—Vastly Different Rankings and Performance, Despite Similar- ity in Factor Exposures,” Bernstein Research, January 16, 2007.

Cross-Sectional Factor-Based Models and Trading Strategies 323

A second study by the same group showed commonality across models among cash flow and price momentum factors, while stock rankings and realized performance were vastly different.37 They hypothesize that the dif- ference between good and poor performing models may be related to a few unique factors identified by portfolio managers, better methodologies for model construction (e.g., static, dynamic, or contextual models), or good old-fashioned luck.

Example: A Factor-Based Trading Strategy

In building this model, we hope to accomplish the following objectives: identify stocks that will outperform and underperform in the future, main- tain good diversification with regard to alpha sources, and be robust to changing market conditions such as time varying returns, volatilities, and correlations.

We have identified 10 factors that have an ability to forecast stock returns.38 Of the four model construction methodologies discussed previ- ously, we use the optimization framework to build the model as it offers the greatest flexibility.

We determine the allocation to specific factors by solving the following optimization problem:

min

. w

w w′ ≥

≥

≥ ∈

∈

∑ ∑

ΣΣ ,

Value

Growth

w 0

0 35

0

w

w

v v

g g

..20

3 7 1

10

≤ ≤ = ∑δi i

with the budget constraint

′ = = ′w e e1 1 1, ( ,..., )

37Vadim Zlotnikov, Ann Marie Larson, Serdar Kalaycioglu, Ronna D. Lao, and Zachary A. Apoian, “Quantitative Research: Survey of Quantitative Models—Con- tinued Emphasis on EV/EBIT, Momentum, Increased Focus on Capital Use; Some Evidence on Non-linear Factor Implementation; Low Return Consistency,” Bern- stein Research, November 21, 2007. 38We use a combination of growth, value, quality, and momentum factors. The ap- pendix to this chapter contains definitions of all of them.

324 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

where ΣΣ is the covariance matrix of factor returns, Value and Growth are the sets of value and growth factors, and di is equal to one if wi > 0 or zero otherwise.

We constrain the minimum exposure to values factors to be greater than or equal to 35% of the weight in the model based on the belief that there is a systematic long-term premium to value.

Using the returns of our factors, we perform this optimization monthly to determine which factors to hold and in what proportions. Exhibit 12.11 displays how the factor weights change over time.

In the next step, we use the factor weights to determine the attractive- ness of the stocks in our universe. We score each stock in the universe by multiplying the standardized values of the factors by the weights provided by the optimization of our factors. Stocks with high scores are deemed attractive and stocks with low scores are deemed unattractive.

To evaluate how the model performs, we sort the scores of stocks into five equally weighted portfolios and evaluate the returns of these portfo- lios. Exhibit 12.12(A) provides summary statistics of the returns for each portfolio. Note that there is a monotonic increasing relationship among the portfolios with portfolio 1 (q1) earning the highest return and portfolio 5 (q5) earning the lowest return. Over the entire period, the long-short port- folio (LS) that is long portfolio 1 and short portfolio 5 averages about 1% per month with a monthly Sharpe ratio of 0.33. Its return is statistically significant at the 97.5% level.

Exhibit 12.12(B) shows the monthly average stock turnover of portfolio 1 (q1) and portfolio 5 (q5). Understanding how turnover varies from month to month for a trading strategy is important. If turnover is too high then it might be prohibitive to implement because of execution costs. While beyond the scope of this chapter, we could explicitly incorporate transaction costs in this trading strategy using a market impact model.39 Due to the dynamic nature of our trading strategy—where active factors may change from month to month—our turnover of 20% is a bit higher than what would be expected using a static approach.

We evaluate the monthly information coefficient between the model scores and subsequent return. This analysis provides information on how well the model forecasts return. The monthly mean information coefficient of the model score is 0.03 and is statistically significant at the 99% level. The monthly standard deviation is 0.08. We note that both the information coef- ficients and returns were stronger and more consistent in the earlier periods.

39See Joseph A. Cerniglia and Petter N. Kolm, “Factor-Based Trading Strategies and Market Impact Costs,” working paper, Courant Institute of Mathematical Sciences, New York University, 2010.

325

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Sept-30-1998

Feb-28-1999

Jul-31-1999

Dec-31-1999

May-31-2000

Oct-31-2000

Mar-31-2001

Aug-31-2001

Jan-31-2002

Jun-30-2002

Nov-30-2002

Apr-30-2003

Sept-30-2003

Feb-28-2004

Jul-31-2004

Dec-31-2004

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326 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Exhibit 12.13 displays the cumulative return to portfolio 1 through portfolio 5. Throughout the entire period there is a monotonic relationship between the portfolios. To evaluate the overall performance of the model, we analyze the performance of the long-short portfolio returns. We observe that the model performs well in December 1994 to May 2007 and April 2008 to June 2008. This is due to the fact that our model correctly picked the factors that performed well in those periods. We note that the model performs poorly in the period July 2007–April 2008, losing an average of 1.09% a month. The model appears to suffer from the same problems many quantitative equity funds and hedge funds faced during this period.40 The worst performance in a single month was –6.87, occurring in January 2001,

40Matthew S. Rothman, “Turbulent Times in Quant Land,” Lehman Brothers Equity Research, August 9, 2007; and Kent Daniel, “The Liquidity Crunch in Quant Equities Analysis and Implications,” Goldman Sachs Asset Management, December 13, 2007 presentation from The Second New York Fed-Princeton Liquidity Conference.

EXHIBIT 12.12 Summary of Model Results A. Summary Statistics of the Model Returns

q1 q2 q3 q4 q5 LS

Mean 1.06 0.98 0.83 0.65 0.12 0.94

Stdev 5.64 5.18 4.98 5.31 5.88 2.82

Median 1.61 1.61 1.58 1.55 1.11 0.71

Max 15.79 11.18 10.92 13.26 13.01 12.84

Min –23.59 –23.32 –19.45 –21.25 –24.51 –6.87

Num 169 169 169 169 169 169

t-statistic 2.44 2.45 2.17 1.59 0.27 4.33

IR 0.19 0.19 0.17 0.12 0.02 0.33

B. Summary Statistics of Turnover for Portfolio 1 (q1) and Portfolio 5 (q5)

q1 q5

Mean 0.20 0.17

Stdev 0.07 0.06

Median 0.19 0.16

Max 0.53 0.39

Min 0.07 0.05

Num 169 169

t-statistic 36.74 39.17

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q1 q2 q3 q4 q5

328 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

and the maximum drawdown of the model was −13.7%, occurring during the period from May 2006 (peak) to June 2008 (trough).41

To more completely understand the return and risk characteristic of the strategy, we would have to perform a more detailed analysis, including risk and performance attribution, and model sensitivity analysis over the full period as well as over subperiods. As the turnover is on the higher side, we may also want to introduce turnover constraints or use a market impact model.

Periods of poor performance of a strategy should be disconcerting to any analyst. The poor performance of the model during the period June 2007–March 2008 indicates that many of the factors we use were not work- ing. We need to go back to each individual factor and analyze them in iso- lation over this time frame. In addition, this highlights the importance of research to improve existing factors and develop new ones using unique data sources.

BACKTESTING

In the research phase of the trading strategy, model scores are converted into portfolios and then examined to assess how these portfolios perform over time. This process is referred to as backtesting a strategy. The backtest should mirror as closely as possible the actual investing environment incor- porating both the investment’s objectives and the trading environment.

When it comes to mimicking the trading environment in backtests, spe- cial attention needs to be given to transaction costs and liquidity consid- erations. The inclusion of transaction costs is important because they may have a major impact on the total return. Realistic market impact and trading costs estimates affect what securities are chosen during portfolio construc- tion. Liquidity is another attribute that needs to be evaluated. The invest- able universe of stocks should be limited to stocks where there is enough liquidity to be able to get in and out of positions.

Portfolio managers may use a number of constraints during portfolio construction. Frequently these constraints are derived from the portfolio policy of the firm, risk management policy, or investor objectives. Common constraints include upper and lower bounds for each stock, industry, or risk factor—as well as holding size limits, trading size limits, turnover, and the number of assets long or short.

41We ran additional analysis on the model by extending the holding period of the model from 1 to 3 months. The results were much stronger as returns increased to 1.6% per month for a two-month holding period and 1.9% per month for a three- month holding period. The risk as measured by drawdown was higher at –17.4% for a two-month holding period and –29.5% for the three-month holding period.

Cross-Sectional Factor-Based Models and Trading Strategies 329

To ensure the portfolio construction process is robust we use sensitivity analysis to evaluate our results. In sensitivity analysis we vary the different input parameters and study their impact on the output parameters. If small changes in inputs give rise to large changes in outputs, our process may not be robust enough. For example, we may eliminate the five best and worst performing stocks from the model, rerun the optimization, and evaluate the performance. The results should be similar as the success of a trading strat- egy should not depend on a handful of stocks.

We may want to determine the effect of small changes in one or more parameters used in the optimization. The performance of the optimal port- folio should in general not differ significantly after we have made these small changes.

Another useful test is to evaluate a model by varying the investment objective. For example, we may evaluate a model by building a low-tracking- error portfolio, a high-tracking-error portfolio, and a market-neutral port- folio. If the returns from each of these portfolios are decent, the underlying trading strategy is more likely to be robust.

Understanding In-Sample and Out-of-Sample Methodologies

There are two basic backtesting methodologies: in-sample and out-of-sample. It is important is to understand the nuances of each.

We refer to a backtesting methodology as an in-sample methodology when the researcher uses the same data sample to specify, calibrate, and evaluate a model.

An out-of-sample methodology is a backtesting methodology where the researcher uses a subset of the sample to specify and calibrate a model, and then evaluates the forecasting ability of the model on a different subset of data. There are two approaches for implementing an out-of-sample method- ology. One approach is the split-sample method. This method splits the data into two subsets of data where one subset is used to build the model while the remaining subset is used to evaluate the model.

A second method is the recursive out-of-sample test. This approach uses a sequence of recursive or rolling windows of past history to forecast a future value and then evaluates that value against the realized value. For example, in a rolling regression–based model we will use data up to time t to calculate the coefficients in the regression model. The regression model forecasts the t + h dependent values, where h > 0. The prediction error is the difference between the realized value at t + h and the predicted value from the regression model. At t + 1 we recalculate the regression model and evalu- ate the predicted value of t + 1 + h against realized value. We continue this process throughout the sample.

330 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

The conventional thinking among econometricians is that in-sample tests tend to reject the null hypotheses of no predictability more often than out-of-sample tests. This view is supported by many researchers because they reason that in-sample tests are unreliable, often finding spurious pre- dictability. Two reasons given to support this view is the presence of unmod- eled structural changes in the data and the use of techniques that result in data mining and model overfitting.

Inoune and Kilian42 question this conventional thinking. They use asymptotic theory to evaluate the “trade-offs between in-sample tests and out-of-sample tests of predictability in terms of their size and power.” They argue strong in-sample results and weak out-of-sample results are not nec- essarily evidence that in-sample tests are not reliable. Out-of-sample tests using sample-splitting result in a loss of information and lower power for small samples. As a result, an out-of-sample test may fail to detect predict- ability while the in-sample test will correctly identify predictability. They also show that out-of-sample tests are not more robust to parameter insta- bility that results from unmodeled structural changes.

A Comment on the Interaction between Factor-Based Strategies and Risk Models

Frequently, different factor models are used to calculate the risk inputs and the expected return forecasts in a portfolio optimization. A common con- cern is the interaction between factors in the models for risk and expected returns. Lee and Stefek43 evaluate the consequences of using different factor models, and conclude that (1) using different models for risk and alpha can lead to unintended portfolio exposures that may worsen performance; (2) aligning risk factors with alpha factors may improve information ratios; and (3) modifying the risk model by including some of the alpha factors may mitigate the problem.

BACKTESTING OUR FACTOR TRADING STRATEGY

Using the model scores from the trading strategy example, we build two optimized portfolios and evaluate their performance. Unlike the five equally weighted portfolios built only from model scores, the models we now discuss

42Atsushi Inoune and Lutz Kilian, “In-Sample or Out-of-Sample Tests of Predictabil- ity: Which One Should We Use?” working paper, North Carolina State University and University of Michigan, 2002. 43Jyh-Huei Lee and Dan Stefek, “Do Risk Factors Eat Alphas?” Journal of Portfolio Management 34, no. 4 (2008): 12–24.

Cross-Sectional Factor-Based Models and Trading Strategies 331

were built to mirror as close as possible tradable portfolios a portfolio man- ager would build in real time. Our investable universe is the Russell 1000. We assign alphas for all stock in the Russell 1000 with our dynamic factor model. The portfolios are long only and benchmarked to the S&P 500. The difference between the portfolios is in their benchmark tracking error. For the low-tracking error portfolio the risk aversion in the optimizer is set to a high value, sectors are constrained to plus or minus 10% of the sector weightings in the benchmark, and portfolio beta is constrained to 1.00. For the high-tracking error portfolio, the risk aversion is set to a low value, the sectors are constrained to plus or minus 25% of the sector weightings in the benchmark, and portfolio beta is constrained to 1.00. Rebalancing is per- formed once a month. Monthly turnover is limited to 10% of the portfolio value for the low-tracking error portfolio and 15% of the portfolio value for the high-tracking error portfolio.

Exhibit 12.14 presents the results of our backtest. The performance numbers are gross of fees and transaction costs. Performance over the entire period is good and consistent throughout. The portfolios outperform the benchmark over the various time periods. The resulting annualized Sharpe ratios over the full period are 0.66 for the low-tracking error portfolio, 0.72 for the high-tracking error portfolio, and 0.45 for the S&P 500.44

KEY POINTS

■ The four most commonly used approaches for the evaluation of return premiums and risk characteristics to factors are portfolio sorts, factor models, factor portfolios, and information coefficients.

■ The portfolio sorts approach ranks stocks by a particular factor into a number of portfolios. The sorting methodology should be consistent with the characteristics of the distribution of the factor and the eco- nomic motivation underlying its premium.

■ The information ratio (IR) is a statistic for summarizing the risk- adjusted performance of an investment strategy and is defined as the ratio of average excess return to the standard deviation of return.

■ We distinguish between contemporaneous and forecasting factor mod- els, dependent on whether both left- and right-hand side variables (returns and factors) have the same time subscript, or the time subscript of the left-hand side variable is greater.

■ The three most common violations of classical regression theory that occur in cross-sectional factor models are (1) the errors in variables

44Here we calculate the Sharpe ratio as portfolio excess return (over the risk-free rate) divided by the standard deviation of the portfolio excess return.

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Cross-Sectional Factor-Based Models and Trading Strategies 333

problem, (2) common variation in residuals such as heteroskedastic- ity and serial correlation, and (3) multicollinearity. There are statistical techniques that address the first two. The third issue is best dealt with by removing collinear variables from the regression, or by increasing the sample size.

■ The Fama-MacBeth regression addresses the inference problem caused by the correlation of the residuals in cross-sectional regressions.

■ The information coefficient (IC) is used to evaluate the return forecast ability of a factor. It measures the cross-sectional correlation between a factor and its subsequent realized return.

■ Factor portfolios are used to measure the information content of a factor. The objective is to mimic the return behavior of a factor and minimize the residual risk. We can build factor portfolios using a factor model or an optimization. An optimization is more flexible as it is able to incorporate constraints.

■ Analyzing the performance of different factors is an important part of the development of a factor-based trading strategy. This process begins with understanding the time-series properties of each factor in isolation and then studying how they interact with each other.

■ Techniques used to combine and weight factors to build a trading strat- egy model include the data driven, the factor model, the heuristic, and the optimization approaches.

■ An out-of-sample methodology is a backtesting methodology where the researcher uses a subset of the sample to specify a model and then evalu- ates the forecasting ability of the model on a different subset of data. There are two approaches for implementing an out-of-sample method- ology: the split-sample approach and the recursive out-of-sample test.

■ Caution should be exercised if different factor models are used to cal- culate the risk inputs and the expected return forecasts in a portfolio optimization.

APPENDIX: THE COMPUSTAT POINT-IN-TIME, IBES CONSENSUS DATABASES AND FACTOR DEFINITIONS

The factors used in this chapter and Chapter 11 were constructed on a monthly basis with data from the Compustat Point-In-Time and IBES Con- sensus databases. Our sample includes all stocks contained in the Russell 1000 index over the period December 31, 1989, to December 31, 2008.

The Compustat Point-In-Time database45 contains quarterly financial data from the income, balance sheet, and cash flow statements for active 45Capital IQ, Compustat, http://www.compustat.com.

334 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

and inactive companies. This database provides a consistent view of histori- cal financial data, both reported data and subsequent restatements, the way it appeared at the end of any month. Using this data allows the researcher to avoid common data issues such as survivorship and look-ahead bias. The data is available from March 1987.

The Institutional Brokers Estimate System (IBES) database46 provides actual earnings from companies and estimates of various financial measures from sell-side analysts. The estimated financial measures include estimates of earnings, revenue and sales, operating profit, analyst recommendations, and other measures. The data is offered on a summary (consensus) level or detailed (analyst-by-analyst) basis. The U.S. data covers reported earnings estimates and results since January 1976.

The factors used in this chapter and the prior one are defined as follows.47

Value Factors

Operating income before depreciation to enterprise value = EBITDA/EV

where

EBITDA = Sales LTM (Compustat Item 2) – Cost of goods Sales LTM (Compustat Item 30) – SG&A Exp (Compustat Item 1)

and

EV = [Long-term debt (Compustat Item 51) + Common shares outstanding (Computstat Item 61) × Price (PRCCM) – Cash (Compustat Item 36)]

Book to price = Stockholders’ equity total (Computstat Item 60) ÷ [Common shares outstanding (Computstat Item 59) × Price (PRCCM)]

Sales to price = Sales LTM (Computstat Item 2) ÷ [Common shares outstanding (Computstat Item 61) × Price (PRCCM)]

46Thomson Reuters, http://www.thomsonreuters.com. 47LTM refers to the last four reported quarters.

Cross-Sectional Factor-Based Models and Trading Strategies 335

Quality Factors

Share repurchase = [Common shares outstanding (Computstat Item 61) – Common shares outstanding (Computstat Item 61) from 12 months ago] ÷ Common shares outstanding (Computstat Item 61) from 12 months ago

Asset turnover = Sales LTM (Computstat Item 2)/[(Assets (Computstat Item 44) – Assets (Computstat Item 44) from 12 months ago)/ 2]

Return on invested capital = Income/Invested capital

where

Income = Income before extra items LTM (Computstat Item 8) + Interest expense LTM (Computstat Item 22) + Minority interest expense LTM (Computstat Item 3)

and

Invested capital = Common equity (Computstat Item 59) + Long-term debt (Computstat Item 51) + Minority interest (Computstat Item 53) + Preferred stock (Computstat Item 55)

Debt to equity = Total debt/Stockholder’s equity

where

Total debt = [Debt in current liabilities (Computstat Item 45) + Long-term debt – Total (Computstat Item 51)]

and

Stockholder’s equity = Stockholder’s equity (Computstat Item 60)

Chg. debt to equity = (Total debt – Total debt from 12 months ago) ÷ [(Stockholder’s equity + Stockholder’s equity from 12 months ago)/2]

336 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Growth

Revisions = [Number of up revisions (IBES item NUMUP) – Number of down revisions (IBES item NUMDOWN)] ÷ Number of estimates revisions (IBES item NUMEST)

Growth of fiscal Year 1 and fiscal Year 2 earnings estimates = Consensus mean of FY2 (IBES item MEAN FY2)

÷ Consensus mean of FY1 (IBES item MEAN FY1) – 1

Momentum

Momentum = Total return of last 11 months excluding the most returns from the most recent month

Summary Statistics

Exhibit 12.A1 contains monthly summary statistics of the factors defined previously. Factor values greater than the 97.5 percentile or less than the 2.5 percentile are considered outliers. We set factor values greater than the 97.5 percentile value to the 97.5 percentile value, and factor values less than the 2.5 percentile value to the 2.5 percentile value, respectively.

EXHIBIT 12.A1 Summary Statistics

Mean Standard Deviation Median

25 Percentile

75 Percentile

EBITDA/EV 0.11 0.06 0.11 0.07 0.15

Book to price 0.46 0.30 0.40 0.24 0.62

Sales to price 0.98 0.91 0.69 0.36 1.25

Share repurchase 0.03 0.09 0.00 –0.01 0.03

Asset turnover 1.83 1.89 1.46 0.64 2.56

Return on invested capital 0.13 0.11 0.11 0.07 0.17

Debt to equity 0.97 1.08 0.62 0.22 1.26

Change in debt to equity 0.10 0.31 0.01 –0.04 0.17

Revisions –0.02 0.33 0.00 –0.17 0.11

Growth of fiscal year 1 and fiscal year 2 earnings estimates

0.37 3.46 0.15 0.09 0.24

Momentum 13.86 36.03 11.00 –7.96 31.25

Cross-Sectional Factor-Based Models and Trading Strategies 337

QUESTIONS

1. a. Why is the portfolio sorts methodology used? b. What is an application of the portfolio sort methodology?

2. How is the interpretation of a factor model using stock returns influ- enced by the specification of time lag of the (or no time lag) dependent variable?

3. Explain some of the common inference problems that arise in cross- sectional regressions where the dependent variable is a stock’s return.

4. a. What are factor portfolios? b. What methodologies can be used to build these portfolios?

5. What is the difference between in-sample and out-of-sample testing?

339

CHAPTER 13 Multifactor Equity Risk Models

and Their Applications* Anthony Lazanas, Ph.D.

Managing Director Barclays Capital

António Baldaque da Silva, Ph.D. Director

Barclays Capital

Arne D. Staal, Ph.D. Director

Barclays Capital

Cenk Ural, Ph.D. Vice President

Barclays Capital

R isk management is an integral part of the portfolio management process. Risk models are central to this practice, allowing managers to quan- tify and analyze the risk embedded in their portfolios. Risk models provide managers insight into the major sources of risk in a portfolio, helping them to control their exposures and understand the contributions of different portfolio components to total risk. They help portfolio managers in their decision-making process by providing answers to important questions such as: How does my small-cap exposure affect portfolio risk? Does my under- weight in diversified financials hedge my overweight in banks? Risk models are also widely used in various other areas such as in portfolio construction, performance attribution, and scenario analysis.

*The authors would like to thank Andy Sparks, Anuj Kumar, and Chris Sturhahn of Barclays Capital for their help and comments.

340 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

In this chapter, we discuss the structure of multifactor equity risk mod- els, types of factors used in these models, and describe certain estimation techniques. We also illustrate the use of equity risk factor models in various applications, namely the analysis of portfolio risk, portfolio construction, scenario analysis, and performance attribution.

Throughout this chapter, we will be using the Barclays Capital Global Risk Model1 for illustration purposes. For completeness, we also refer to other approaches one can take to construct such a model.

MOTIVATION

In this section, we discuss the motivation behind the multifactor equity risk models. Let’s assume that a portfolio manager wants to estimate and analyze the volatility of a large portfolio of stocks. A straightforward idea would be to compute the volatility of the historical returns of the portfolio and use this measure to forecast future volatility. However this framework does not provide any insight into the relationships between different securities in the portfolio or the major sources of risk. For instance it does not assist a portfolio manager interested in diversifying her portfolio or constructing a portfolio that has better risk adjusted performance.

Instead of estimating the portfolio volatility using historical portfolio returns, one could utilize a different strategy. The portfolio return is a func- tion of stock returns and the market weights of these stocks in the portfolio. Using this, the forecasted volatility of the portfolio (sP) can be computed as a function of the weights (w) and the covariance matrix (Ss) of stock returns in the portfolio:

σP T

sw w 2 = ⋅ ∑ ⋅

This covariance matrix can be decomposed into individual stock vola- tilities and the correlations between stock returns. Volatilities measure the riskiness of individual stock returns and correlations represent the relation- ships between the returns of different stocks. Looking into these correlations 1The Barclays Capital Global Risk Model is available through POINT®, Barclays Capital portfolio management tool. It is a multicurrency cross-asset model that cov- ers many different asset classes across the fixed income and equity markets, includ- ing derivatives in these markets. At the heart of the model is a covariance matrix of risk factors. The model has more than 500 factors, many specific to a particular asset class. The asset class models are periodically reviewed. Structure is imposed to increase the robustness of the estimation of such large covariance matrix. The model is estimated from historical data. It is calibrated using extensive security-level historical data and is updated on a monthly basis.

Multifactor Equity Risk Models and Their Applications 341

and volatilities, the portfolio manager can gain insight into her portfolio, namely the riskiness of different parts of the portfolio or how the portfolio can be diversified. As we outlined above, to estimate the portfolio volatility we need to estimate the correlation between each pair of stocks. Unfortu- nately, this means that the number of parameters to be estimated grows quadratically with the number of stocks in the portfolio.2 For most practi- cal portfolios, the relatively large number of stocks makes it difficult to estimate the relationship between stock returns in a robust way. Moreover, this framework uses the history of individual stock returns to forecast future stock volatility. However stocks characteristics are dynamic and hence using returns from different time periods may not produce good forecasts.3 Finally, the analysis does not provide much insight regarding the broad fac- tors influencing the portfolio. These drawbacks constitute the motivation for the multifactor risk models, detailed in this chapter.

One of the major goals of multifactor risk models is to describe the return of a portfolio using a smaller set of variables, called factors. These factors should be designed to capture broad (systematic) market fluctua- tions, but should also be able to capture specific nuances of individual portfolios. For instance, a broad U.S. market factor would capture the gen- eral movement in the equity market, but not the varying behavior across industries. If our portfolio is heavily biased toward particular industries, the broad U.S. market factor may not allow for a good representation of our portfolio’s return.

In the context of factor models, the total return of a stock is decomposed into a systematic and an idiosyncratic component. Systematic return is the component of total return due to movements in common risk factors, such as industry or size. On the other hand, idiosyncratic return can be described as the residual component that cannot be explained by the systematic factors. Under these models, the idiosyncratic return is uncorrelated across issuers. Therefore, correlations across securities are driven by their exposures to the systematic risk factors and the correlation between those factors.

The following equation demonstrates the systematic and the idiosyn- cratic components of total stock return:

r L Fs s s= ⋅ + ε

The systematic return for security s is the product of the loadings of that security (L

s , also called sensitivities) to the systematic risk factors and the

2As an example, if the portfolio has 10 stocks, we need to estimate 45 parameters, with 100 stocks we would need to estimate 4,950 parameters. 3This is especially the case over crisis periods where stock characteristics can change dramatically over very short periods of time.

342 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

returns of these factors (F). The idiosyncratic return is given by es. Under these models, the portfolio volatility can be estimated as

σp p T

F p TL L w w2 = ⋅ ∑ ⋅ + ⋅ ⋅Ω

Models represented by equations of this form are called linear factor models. Here Lp represents the loadings of the portfolio to the risk factors (deter- mined as the weighted average of individual stock loadings) and S

F is the

covariance matrix of factor returns. w is the vector of security weights in the portfolio and W is the covariance matrix of idiosyncratic stock returns. Due to the uncorrelated nature of these returns, this covariance matrix is diagonal, with all elements outside its diagonal being zero. As a result, the idiosyncratic risk of the portfolio is diversified away as the number of se- curities in the portfolio increases. This is the diversification benefit attained when combining uncorrelated exposures.

For most practical portfolios, the number of factors is significantly smaller than the number of stocks in the portfolio. Therefore, the number of parameters in S

F is much smaller than in S

S , leading to a generally more

robust estimation. Moreover, the factors can be designed in a way that they are relatively more stable than individual stock returns, leading to models with potentially better predictability.

Another important advantage of using linear factor models is the detailed insight they provide into the structure and properties of portfo- lios. These models characterize stock returns in terms of systematic fac- tors that (can) have intuitive economic interpretations. Linear factor models can provide important insights regarding the major systematic and idiosyn- cratic sources of risk and return. This analysis can help managers to better understand their portfolios and can guide them through the different tasks they perform, such as rebalancing, hedging or the tilting of their portfolios. The Barclays Capital Global Risk Model—the model used for illustration throughout this chapter—is an example of such a linear factor model.

EQUITY RISK FACTOR MODELS

The design of a linear factor model usually starts with the identification of the major sources of risk embedded in the portfolios of interest. For an equity portfolio manager who invests in various markets across the globe, the major sources of risk are typically country, industry membership, and other funda- mental or technical exposures such as size, value, and momentum. The rela- tive significance of these components varies across different regions. For in- stance, for regional equity risk models in developed markets, industry factors

Multifactor Equity Risk Models and Their Applications 343

tend to be more important than country factors, although in periods of fi- nancial distress country factors become more significant. On the other hand, for emerging markets models the country factor is still considered to be the most important source of risk. For regional models, the relative significance of industry factors depends on the level of financial integration across differ- ent local markets in that region. The importance of these factors is also time- varying, depending on the particular time period of the analysis. For instance, country risk used to be a large component of total risk for European equity portfolios. However, country factors have been losing their significance in this context due to financial integration in the region as a result of the European Union and a common currency, the euro. This is particularly true for larger European countries. Similarly, the relative importance of industry factors is higher over the course of certain industry-led crises, such as the dot-com bub- ble burst (2000–2002) and the 2007–2009 banking and credit crisis. As we will see, the relative importance of different risk factors varies also with the particular design and the estimation process chosen to calibrate the model.

A typical global or regional equity risk model has the following structure:

r F F F Fi i i i ij j= ⋅ + ⋅ + ⋅ + ⋅β β β MKT MKT IND IND CNT CNT



FFT

j

n

i =

∑ + 1

ε

where

r i = the rate of return for stock i

FMKT = the market factor FIND = the industry factor corresponding to stock i FCNT = the country factor corresponding to stock i b

i = the exposure (beta) of the stock to the corresponding factor

FFT = the set of fundamental and technical factors  ij = the loading of stock i to factor Fj

FT

e i = the residual return for stock i

There are different ways in which these factors can be incorporated into an equity risk model. The choice of a particular model affects the interpreta- tion of the factors. For instance, consider a model that has only market and industry factors. Industry factors in such a model would represent industry- specific moves net of the market return. On the other hand, if we remove the market factor from the equation, the industry factors now incorporate the overall market effect. Their interpretation would change, with their returns now being close to market value-weighted industry indexes. Country-spe- cific risk models are a special case of the previous representation where the country factor disappears and the market factor is represented by the

344 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

returns of the countrywide market. Macroeconomic factors are also used in some equity risk models, as discussed later.

The choice of estimation process also influences the interpretation of the factors. As an example, consider a model that has only industry and country factors. These factors can be estimated jointly in one step. In this case, both factors represent their own effect net of the other one. On the other hand, these factors can be estimated in a multistep process—e.g., industry factors estimated in the first step and then the country factors estimated in the sec- ond step, using residual returns from the first step. In this case, the industry factors have an interpretation close to the market value-weighted industry index returns, while the country factors would now represent a residual country average effect, net of industry returns. We discuss this issue in more detail in the following section.

Model Estimation

In terms of the estimation methodology, there are three major types of multi- factor equity risk models: cross-sectional, time series, and statistical. All three of these methodologies are widely used to construct linear factor mod- els in the equity space.4 In cross-sectional models, loadings are known and factors are estimated. Examples of loadings used in these models are indus- try membership variables and fundamental security characteristics (e.g., the book-to-price ratio). Individual stock returns are regressed against these se- curity-level loadings in every period, delivering estimation of factor returns for that period. The interpretation of these estimated factors is usually intui- tive, although dependent on the estimation procedure and on the quality of the loadings. In time-series models, factors are known and loadings are esti- mated. Examples of factors in these models are financial or macroeconomic variables, such as market returns or industrial production. Time series of individual equity returns are regressed against the factor returns, delivering empirical sensitivities (loadings or betas) of each stock to the risk factors. In these models, factors are constructed and not estimated, therefore, their interpretation is straightforward. In statistical models (e.g., principal com- ponent analysis), both factors and loadings are estimated jointly in an itera- tive fashion. The resulting factors are statistical in nature, not designed to be intuitive. That being said, a small set of the statistical factors can be (and usually are) correlated with broad economic factors, such as the market. Exhibit 13.1 summarizes some of the characteristics of these models.

An important advantage of cross-sectional models is that the number of parameters to be estimated is generally significantly smaller as compared to the other two types of models. On the other hand, cross-sectional models 4Fixed income managers typically use cross-sectional type of models.

Multifactor Equity Risk Models and Their Applications 345

require a much larger set of input data (company-specific loadings). Cross- sectional models tend to be relatively more responsive as loadings can adjust faster to changing market conditions. There are also hybrid models, which combine cross-sectional and time-series estimation in an iterative fashion; these models allow the combination of observed and estimated factors. Sta- tistical models on the other hand require only a history of security returns as input to the process. They tend to work better when economic sources of risk are hard to identify and are primarily used in high-frequency applications.

As we mentioned in the previous section, the estimation process is a major determinant in the interpretation of factors. Estimating all factors jointly in one-step regression allows for a natural decomposition of total variance in stock returns. However it also complicates the interpretation of factors as each factor now represents its own effect net of all other factors. Moreover, multicollinearity problems arise naturally in this set-up, poten- tially delivering lack of robustness to the estimation procedure and leading to unintuitive factor realizations. This problem can be serious when using factors that are highly correlated.

An alternative in this case is to use a multistep estimation process where different sets of factors are estimated sequentially, in separate regressions. In the first step, stock returns are used in a regression to estimate a certain set of factors and then residual returns from this step are used to estimate the second step factors and so on. The choice of the order of factors in such estimation influences the nature of the factors and their realizations. This choice should be guided by the significance and the desired interpretation

EXHIBIT 13.1 Cross-Sectional, Time-Series, and Statistical Factor Models

Model Cross-Sectional Time-Series Statistical

Input set Security-specific loadings and returns

Factor and security returns

Security returns

Factors and loadings

Factors are estimat- ed using the known loadings (e.g., indus- try beta or momen- tum score)

Factors are known (e.g., market or industrial production) and loadings are esti- mated (e.g., industry or momentum betas)

Both factors and loadings are estimated

Interpretation Clean interpretation of loadings; general- ly intuitive interpre- tation of factors

Straightforward inter- pretation of factors

Factors may have no intuitive inter- pretation

Number of parameters

(No. of factors) × (No. of time periods)

(No. of securities) × (No. of factors)

(No. of securities) × (No. of factors)

346 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

of the resulting factors. The first-step factors have the most straightforward interpretation as they are estimated in isolation from all other factors using raw stock returns. For instance in a country-specific equity risk model where there are only industry and fundamental or technical factors, the return series of industry factors would be close to the industry index returns if they are estimated in isolation in the first step. This would not be the case if all industry, fundamental, and technical factors are estimated in the same step.

An important input to the model estimation is the security weights used in the regressions. There is a variety of techniques employed in practice but generally more weight is assigned to less volatile stocks (usually represented by larger companies). This enhances the robustness of the factor estimates as stocks from these companies tend to have relatively more stable return distributions.

Types of Factors

In this section, we analyze in more detail the different types of factors typi- cally used in equity risk models. These can be classified under five major categories: market factors, classification variables, firm characteristics, mac- roeconomic variables, and statistical factors.

Market Factors

A market factor can be used as an observed factor in a time-series setting (e.g., in the capital asset pricing model, the market factor is the only system- atic factor driving returns). As an example, for a U.S. equity factor model, S&P 500 can be used as a market factor and the loading to this factor— market beta—can be estimated by regressing individual stock returns to the S&P 500. On the other hand, in a cross-sectional setting, the market factor can be estimated by regressing stock returns to the market beta for each time period (this beta can be empirical—estimated via statistical techniques—or set as a dummy loading, usually 1). When incorporated into a cross-section- al regression with other factors, it generally works as an intercept, capturing the broad average return for that period. This changes the interpretation of all other factors to returns relative to that average (e.g. industry factor returns would now represent industry-specific moves net of market).

Classification Variables

Industry and country are the most widely used classification variables in eq- uity risk models. They can be used as observed factors in time-series models

Multifactor Equity Risk Models and Their Applications 347

via country/industry indexes (e.g. return series of GICS indexes5 can be used as observed industry factors). In a cross-sectional setting, these factors are estimated by regressing stock returns to industry/country betas (either esti- mated or represented as a 0/1 dummy loading). These factors constitute a significant part of total risk for a majority of equity portfolios, especially for portfolios tilted toward specific industries or countries.

Firm Characteristics

Factors that represent firm characteristics can be classified as either funda- mental or technical factors. These factors are extensively used in equity risk models; exposures to these factors represent tilts towards major investment themes such as size, value, and momentum. Fundamental factors generally employ a mix of accounting and market variables (e.g., accounting ratios) and technical factors commonly use return and volume data (e.g., price mo- mentum or average daily volume traded).

In a time-series setting, these factors can be constructed as representa- tive long-short portfolios (e.g., Fama-French factors). As an example, the value factor can be constructed by taking a long position in stocks that have a large book to price ratio and a short position in the stocks that have a small book to price ratio. On the other hand, in a cross-sectional setup, these factors can be estimated by regressing the stock returns to observed firm characteristics. For instance, a book to price factor can be estimated by regressing stock returns to the book to price ratios of the companies. In practice, fundamental and technical factors are generally estimated jointly in a multivariate setting.

A popular technique in the cross-sectional setting is the standardization of the characteristic used as loading such that it has a mean of zero and a standard deviation of one. This implies that the loading to the corresponding factor is expressed in relative terms, making the exposures more comparable across the different fundamental/technical factors. Also, similar characteris- tics can be combined to form a risk index and then this index can be used to estimate the relevant factor (e.g., different value ratios such as earnings to price and book to price can be combined to construct a value index, which would be the exposure to the value factor). The construction of an index from similar characteristics can help reduce the problem of multicol- linearity referred to above. Unfortunately, it can also dilute the signal each characteristic has, potentially reducing its explanatory power. This trade-off should be taken into account while constructing the model. The construc- tion of fundamental factors and their loadings requires careful handling 5GICS is the Global Industry Classification Standard by Standard & Poor’s, a widely used classification scheme by equity portfolio managers.

348 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

of accounting data. These factors tend to become more significant for port- folios that are hedged with respect to the market or industry exposures.

Macroeconomic Variables

Macroeconomic factors, representing the state of the economy, are gener- ally used as observed factors in time-series models. Widely used examples include interest rates, commodity indexes, and market volatility (e.g., the VIX index). These factors tend to be better suited for models with a long ho- rizon. For short to medium horizons, they tend to be relatively insignificant when included in a model that incorporates other standard factors such as industry. The opposite is not true, suggesting that macro factors are rela- tively less important for these horizons. This does not mean that the mac- roeconomic variables are not relevant in explaining stock returns; it means that a large majority of macroeconomic effects can be captured through the industry factors. Moreover, it is difficult to directly estimate stock sensitivi- ties to slow-moving macroeconomic variables. These considerations lead to the relatively infrequent use of macro variables in short to medium horizon risk models.6

Statistical Factors

Statistical factors are very different in nature than all the aforementioned factors as they do not have direct economic interpretation. They are estimat- ed using statistical techniques such as principal component analysis where both factors and loadings are estimated jointly in an iterative fashion. Their interpretation can be difficult, yet in certain cases they can be re-mapped to well-known factors. For instance, in a principal component analysis model for the U.S. equity market, the first principal component would represent the U.S. market factor. These models tend to have a relatively high in-sample explanatory power with a small set of factors and the marginal contribu- tion of each factor tends to diminish significantly after the first few factors. Statistical factors can also be used to capture the residual risk in a model

6An application of macro variables in the context of risk factor models is as follows. First, we get the sensitivities of the portfolio to the model’s risk factors. Then we project the risk factors into the macro variables. We then combine the results from these two steps to get the indirect loadings of the portfolio to the macro factors. Therefore, instead of calculating the portfolio sensitivities to macro factors by ag- gregating individual stock macro sensitivities—that are always hard to estimate—we work with the portfolio’s macro loadings, estimated indirectly from the portfolio’s risk factor loadings as described above. This indirect approach may lead to statisti- cally more robust relationships between portfolio returns and macro variables.

Multifactor Equity Risk Models and Their Applications 349

with economic factors. These factors tend to work better when there are unidentified sources of risk such as in the case of high frequency models.

Other Considerations in Factor Models

Various quantitative and qualitative measures can be employed to evalu- ate the relative performance of different model designs. Generically, better risk models are able to forecast more accurately the risk of different types of portfolios, across different economic environments. Moreover, a better model allows for an intuitive analysis of the portfolio risk along the direc- tions used to construct and manage the portfolio. The relative importance of these considerations should frame how we evaluate different models.

A particular model is defined by its estimation framework and the selec- tion of its factors and loadings. Typically, these choices are evaluated jointly, as the contributions of specific components are difficult to measure in prac- tice. Moreover, decisions on one of these components (partially) determine the choice of the others. For instance, if a model uses fundamental firm characteristics as loadings, it also uses estimated factors—more generally, decisions on the nature of the factors determine the nature of the loadings and vice-versa.

Quantitative measures of factor selection include the explanatory power or significance of the factor, predictability of the distribution of the factor and correlations between factors. On a more qualitative perspective, port- folio managers usually look for models with factors and loadings that have clean and intuitive interpretation, factors that correspond to the way they think about the asset class, and models that reflect their investment charac- teristics (e.g., short vs. long horizon, local vs. global investors).

Idiosyncratic Risk

Once all systematic factors and loadings are estimated, the residual return can be computed as the component of total stock return that cannot be ex- plained by the systematic factors. Idiosyncratic return—also called residual, nonsystematic or name-specific return—can be a significant component of total return for individual stocks, but tends to become smaller for portfolios of stocks as the number of stocks increases and concentration decreases (the aforementioned diversification effect). The major input to the computation of idiosyncratic risk is the set of historical idiosyncratic returns of the stock. Because the nature of the company may change fast, a good idiosyncratic risk model should use only recent and relevant idiosyncratic returns. Moreover, recent research suggests that there are other conditional variables that may help improving the accuracy of idiosyncratic risk estimates. For instance,

350 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

there is substantial evidence that the market value of a company is highly correlated with its idiosyncratic risk, where larger companies exhibit small- er idiosyncratic risk. The use of such variables as an extra adjustment factor can improve the accuracy of idiosyncratic risk estimates.

As mentioned before, idiosyncratic returns of different issuers are assumed to be uncorrelated. However different securities from the same issuer can show a certain level of comovement, as they are all exposed to specific events affecting their common issuer.

Interestingly, this comovement is not perfect or static. Certain news can potentially affect the different securities issued by the same company (e.g., equity, bonds, or equity options) in different ways. Moreover, this relation- ship changes with the particular circumstances of the firm. For instance, returns from securities with claims to the assets of the firm should be more highly correlated if the firm is in distress. A good risk model should be able to capture these phenomena.

APPLICATIONS OF EQUITY RISK MODELS

Multifactor equity risk models are employed in various applications such as the quantitative analysis of portfolio risk, hedging unwanted exposures, portfolio construction, scenario analysis, and performance attribution. In this section we discuss and illustrate some of these applications.

Portfolio managers can be divided broadly into indexers (those that measure their returns relative to a benchmark index) and absolute return managers (typically hedge fund managers). In between stand the enhanced indexers, those that are allowed to deviate from the benchmark index in order to express views, presumably leading to superior returns. All are typi- cally subject to a risk budget that prescribes how much risk they are allowed to take to achieve their objectives: minimize transaction costs and match the index return for the pure indexers, maximize the net return for the enhanced indexers, or maximize absolute return for absolute return managers. In all of these cases, the manager has to merge all her views and constraints into a final portfolio.

The investment process of a typical portfolio manager involves several steps. Given the investment universe and objective, the steps usually con- sist of portfolio construction, risk prediction, and performance evaluation. These steps are iterated throughout the investment cycle over each rebal- ancing period. The examples in this section are constructed following these steps. In particular, we start with a discussion on the portfolio construction process for three equity portfolio managers with different goals: The first aims to track a benchmark, the second to build a momentum portfolio,

Multifactor Equity Risk Models and Their Applications 351

and the third to implement sector views in a portfolio. We conduct these exercises through a risk-based portfolio optimization approach at a monthly rebalancing frequency. For the index-tracking portfolio example, we then conduct a careful evaluation of its risk exposures and contributions to ensure that the portfolio manager’s views and intuition coincide with the actual portfolio exposures. Once comfortable with the positions and the associated risk, the portfolio is implemented. At the end of the monthly investment cycle, the performance of the portfolio and return contributions of its different components can be evaluated using performance attribution.

Scenario analysis can be employed in both the portfolio construction and the risk evaluation phases of the portfolio process. This exercise allows the manager to gain additional intuition regarding the exposures of her portfolio and how it may behave under particular economic circumstances. It usually takes the form of stress testing the portfolio under historical or hypothetical scenarios. It can also reveal the sensitivity of the portfolio to particular movements in economic and financial variables not explicitly considered during the portfolio construction process. The last application in this chapter illustrates this kind of analysis.

Throughout our discussion, we use a suite of global cash equity risk models available through POINT®, the Barclays Capital portfolio analytics and modeling platform.7

Portfolio Construction

Broadly speaking there are two main approaches to portfolio construction: a formal quantitative optimization-based approach and a qualitative ap- proach that is based primarily on manager intuition and skill. There are many variations within and between these two approaches. In this section, we focus on risk-based optimization using a linear factor model. We do not discuss other more qualitative or nonrisk-based approaches (e.g., a strati- fied sampling). A common objective in a risk-based optimization exercise is the minimization of volatility of the portfolio, either in isolation or when evaluated against a benchmark. In the context of multifactor risk models, total volatility is composed of a systematic and an idiosyncratic compo- nent, as described above. Typically, both of these components are used in the objective function of the optimization problems. We demonstrate three

7The equity risk model suite in POINT consists of six separate models across the globe: the United States, United Kingdom, Continental Europe, Japan, Asia (exclud- ing Japan), and global emerging markets equity risk models (for details see Antonio B. Silva, Arne D. Staal, and Cenk Ural, “The U.S. Equity Risk Model,” Barclays Capital Publication, July 2009). It incorporates many unique features related to fac- tor choice, industry and fundamental exposures, and risk prediction.

352 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

different portfolio construction exercises and discuss how equity factor models are employed in this endeavor. The examples were constructed us- ing the POINT® Optimizer.8

Tracking an Index

In our first example, we study the case of a portfolio manager whose goal is to create a portfolio that tracks a benchmark equity index as closely as possible, using a limited number of stocks. This is a very common problem in the investment industry since most assets under management are bench- marked to broad market indexes. Creating a benchmark-tracking portfolio provides a good starting point for implementing strategic views relative to that benchmark. For example, a portfolio manager might have a mandate to outperform a benchmark under particular risk constraints. One way to implement this mandate is to dynamically tilt the tracking portfolio towards certain investment styles based on views on the future performance of those styles at a particular point in the business cycle.

Consider a portfolio manager who is benchmarked to the S&P 500 index and aims to build a tracking portfolio composed of long-only posi- tions from the set of S&P 500 stocks. Because of transaction cost and posi- tion management limitations, the portfolio manager is restricted to a maxi- mum number of 50 stocks in the tracking portfolio. Her objective is to minimize the tracking error volatility (TEV) between her portfolio and the benchmark. Tracking error volatility can be described as the volatility of the return differential between the portfolio and the benchmark (i.e. measures a typical movement in this net position). A portfolio’s TEV is commonly referred to as the risk or the (net) volatility of the portfolio.

As mentioned before, the total TEV is decomposed into a systematic TEV and an idiosyncratic TEV. Moreover, because these two components are assumed to be independent,

Total Systematic + Idiosyncratic2TEV TEV= TTEV 2

The minimization of systematic TEV is achieved by setting the portfolio’s factor exposures (net of benchmark) as close to zero as possible, while re- specting other potential constraints of the problem (e.g., maximum number of 50 securities in the portfolio). The minimization of idiosyncratic volatility is achieved through the diversification of the portfolio holdings.

Exhibit 13.2 illustrates the total risk for portfolio versus benchmark that comes out of the optimization problem. We see that total TEV of the 8See Anuj Kumar, “The POINT Optimizer,” Barclays Capital Publication, June 2010. All optimization problems were run as of July 30, 2010.

Multifactor Equity Risk Models and Their Applications 353

net position is 39.6 bps/month with 16.9 bps/month of systematic TEV and 35.8 bps/month of idiosyncratic TEV. If the portfolio manager wants to reduce her exposure to name-specific risk, she can increase the upper bound on the number of securities picked by the optimizer to construct the optimal portfolio (increasing the diversification effect). Another option would be to increase the relative weight of idiosyncratic TEV compared to the systematic TEV in the objective function. The portfolio resulting from this exercise would have smaller idiosyncratic risk but, unfortunately, would also have higher systematic risk. This trade-off can be managed based on the portfolio manager’s preferences.

Exhibit 13.3 depicts the distribution of the position amount for indi- vidual stocks in the portfolio. We can see that the portfolio is well diversified across the 50 constituent stocks with no significant concentrations in any of the individual positions. The largest stock position is 4.1%, about three times larger than the smallest holding. Later in this chapter, we analyze the risk of this particular portfolio in more detail.

EXHIBIT 13.2 Total Risk of Index-Tracking Portfolio vs. the Benchmark (bps/month)

Attribute Realized Value

Total TEV 39.6

Idiosyncratic TEV 35.8

Systematic TEV 16.9

EXHIBIT 13.3 Position Amount of Individual Stocks in the Optimal Tracking Portfolio

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354 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Constructing a Factor-Mimicking Portfolio

Factor-mimicking portfolios allow portfolio managers to capitalize on their views on various investment themes. For instance, the portfolio manager may forecast that small-cap stocks will outperform large-cap stocks or that value stocks will outperform growth stocks in the near future. By construct- ing long-short factor-mimicking portfolios, managers can place positions in line with their views on these investment themes without taking explicit directional views on the broader market.

Considering another example, suppose our portfolio manager forecasts that recent winner (high momentum) stocks will outperform recent losers (low momentum). To implement her views, she constructs two portfolios, one with winner stocks and one with loser stocks (100 stocks from the S&P 500 universe in each portfolio). She then takes a long position in the winners portfolio and a short position in the losers portfolio. While a sen- sible approach, a long-short portfolio constructed in this way would cer- tainly have exposures to risk factors other than momentum. For instance, the momentum view might implicitly lead to unintended sector bets. If the portfolio manager wants to understand and potentially limit or avoid these exposures, she needs to perform further analysis. The use of a risk model will help her substantially.

Exhibit 13.4 illustrates one of POINT®’s risk model outputs—the 10 largest risk factor exposures by their contribution to TEV (last column in the exhibit) for this initial long-short portfolio. While momentum has the

EXHIBIT 13.4 Largest Risk Factor Exposures for the Momentum Winners/Losers Portfolio (bps/month)

Factor Name Sensitivity/ Exposure

Net Exposure

Factor Volatility

Contribution to TEV

EQUITIES DEVELOPED MARKETS

U.S. Equity Energy Empirical beta –0.094 651 25.3

U.S. Equity Materials Empirical beta –0.045 808 15.9

U.S. Equity CYC Media Empirical beta 0.027 759 –9.9

U.S. Equity FIN Banks Empirical beta 0.088 900 13.0

U.S. Equity FIN Diversified Financials Empirical beta –0.108 839 39.6

U.S. Equity FIN Real Estate Empirical beta 0.100 956 –19.0

U.S. Equity TEC Software Empirical beta –0.057 577 17.2

U.S. Equity TEC Semiconductors Empirical beta –0.029 809 9.9

U.S. Equity Corporate Default Probability CDP –0.440 76 23.2

U.S. Equity Momentum (9m) Momentum 1.491 73 74.9

Multifactor Equity Risk Models and Their Applications 355

largest contribution to volatility, other risk factors also play a significant role. As a result, major moves in risk factors other than momentum can have a significant—and potentially unintended—impact on the portfolio’s return.

Given this information, suppose our portfolio manager decides to avoid these exposures to the extent possible. She can do that by setting all expo- sures to factors other than momentum to zero (these type of constraints may not always be feasible and one may need to relax them to achieve a solution). Moreover, because she wants the portfolio to represent a pure systematic momentum effect, she seeks to minimize idiosyncratic risk. There are many ways to implement these goals, but increasingly portfolio manag- ers are turning to risk models (using an optimization engine) to construct their portfolios in a robust and convenient way. She decides to setup an optimization problem where the objective function is the minimization of idiosyncratic risk. The tradable universe is the set of S&P 500 stocks and the portfolio is constructed to be dollar-neutral. This problem also incorporates the aforementioned factor exposure constraints.

The resulting portfolio has exactly the risk factor exposures that were specified in the problem constraints. It exhibits a relatively low idiosyncratic TEV as a result of being well diversified with no significant concentrations in individual positions. Exhibit 13.5 depicts the largest 10 positions on the long and short sides of the momentum factor-mimicking portfolio; we see that there are no significant individual stock concentrations.

EXHIBIT 13.5 Largest 10 Positions on Long and Short Sides for the Momentum Portfolio

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356 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

Implementing Sector Views

For our final portfolio construction example, let’s assume we are entering a recessionary environment. An equity portfolio manager forecasts that the consumer staples sector will outperform the consumer discretionary sector in the near future, so she wants to create a portfolio to capitalize on this view. One simple idea would be to take a long position in the consumer staples sector (NCY: noncyclical) and a short position in the consumer dis- cretionary sector (CYC: cyclical) by using, for example, sector ETFs. Similar to the previous example, this could result in exposures to risk factors other than the industry factors. Exhibit 13.6 illustrates the exposure of this long- short portfolio to the risk factors in the POINT® U.S. equity risk model. As we can see in the table, the portfolio has significant net exposures to certain

EXHIBIT 13.6 Factor Exposures and Contributions for Consumer Staples vs. Consumer Discretionary Portfolio (bps/month)

Factor Name Sensitivity/ Exposure

Net Exposure

Factor Volatility

Contribution to TEV

CURRENCY

USD (U.S. dollar) Market weight (%) 0.00 0 0.0

EQUITIES DEVELOPED MARKETS

U.S. Equity CYC Automobiles Empirical beta –0.069 1,086 60.3

U.S. Equity CYC Consumer Durables Empirical beta –0.093 822 59.1

U.S. Equity CYC Consumer Services Empirical beta –0.140 690 71.1

U.S. Equity CYC Media Empirical beta –0.292 759 172.8

U.S. Equity CYC Retailing Empirical beta –0.317 745 185.1

U.S. Equity NCY Retailing Empirical beta 0.226 404 –44.9

U.S. Equity NCY Food Empirical beta 0.546 418 –96.4

U.S. Equity NCY Household Empirical beta 0.236 415 –55.3

U.S. Equity Total Yield Total yield 0.269 36 –3.7

U.S. Equity Corporate Default Probability CDP –0.201 76 9.0

U.S. Equity Share Turnover Rate Share turnover –0.668 59 –10.3

U.S. Equity Momentum (9m) Momentum –0.144 73 –5.6

U.S. Equity Discretionary Accruals Accruals –0.020 31 –0.2

U.S. Equity Market Value Size 0.193 111 1.7

U.S. Equity Realized Volatility Realized volatility –0.619 97 5.5

U.S. Equity Earnings to Price Earnings–Price 0.024 44 0.0

U.S. Equity Book to Price Book–Price –0.253 40 5.8

U.S. Equity Earnings Forecast Earnings forecast 0.038 67 –0.4

Multifactor Equity Risk Models and Their Applications 357

fundamental and technical factors, especially realized volatility and share turnover.

Suppose the portfolio manager decides to limit exposures to fundamen- tal and technical factors. We can again use the optimizer to construct a long- short portfolio, with an exposure (beta) of 1 to the consumer staples sector and a beta of –1 to the consumer discretionary sector. To limit the exposure to fundamental and technical risk factors, we further impose the exposure to each of these factors to be between –0.2 and 0.2.9 We also restrict the portfolio to be dollar neutral, and allow for only long positions in the con- sumer staples stocks and for only short positions in consumer discretionary stocks. Finally, we restrict the investment universe to the members of the S&P 500 index10.

The resulting portfolio consists of 69 securities (approximately half of discretionary and staples stocks in S&P 500) with 31 long positions in the consumer staples stocks and 38 short positions in consumer discretionary stocks. Exhibit 13.7 depicts the factor exposures for this portfolio. As we can see in the table, the sum of the exposures to the industry factors is 1 for the consumer staples stocks and –1 for the consumer discretionary stocks. Exposures to fundamental and technical factors are generally significantly smaller when compared to the previous table, limiting the adverse effects of potential moves in these factors. Interestingly, no stocks from the automo- biles industry are selected in the optimal portfolio, potentially due to exces- sive idiosyncratic risk of firms in that particular industry. The contribution to volatility from the discretionary sector is higher than that from the staples sector, due to higher volatility of industry factors in the discretionary sector.

The bounds used for the fundamental and technical factor exposures in the portfolio construction process were set to force a reduction in the expo- sure to these factors. However, there is a trade-off between having smaller exposures and having smaller idiosyncratic risk in the final portfolio. The resolution of this trade-off depends on the preferences of the portfolio manager. When the bounds are more restrictive, we are also decreasing the feasible set of solutions available to the problem and therefore potentially achieving a higher idiosyncratic risk (remember that the objective is the minimization of idiosyncratic risk). In our example, the idiosyncratic TEV of the portfolio increases from 119 bps/month (for staples—discretionary portfolio before the optimization) to 158 bps/month on the optimized portfolio.

9The setting of these exposures and its trade-offs are discussed later in this chapter. 10As POINT® U.S. equity risk model incorporates industry level factors, a unit expo- sure to a sector is implemented by restricting exposures to different industries within that sector to sum up to 1. Also, note that as before, the objective in the optimiza- tion problem is the minimization of idiosyncratic TEV to ensure that the resulting portfolio represents systematic—not idiosyncratic—effects.

358 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

This change is the price paid for the ability to limit certain systematic risk factor exposures.

Analyzing Portfolio Risk Using Multifactor Models

Now that we have seen examples of using multifactor equity models for portfolio construction and briefly discussed their risk outcomes, we take a more in-depth look at portfolio risk. Risk analysis based on multifac- tor models can take many forms; from a relatively high-level aggregate ap- proach, to an in-depth analysis of the risk properties of individual stocks and groups of stocks. Multifactor equity risk models provide the tools to perform the analysis of portfolio risk in many different dimensions, includ- ing exposures to risk factors, security factor contributions to total risk,

EXHIBIT 13.7 Factor Exposures and Contributions for the Optimal Sector View Portfolio (bps/month)

Factor Name Sensitivity/ Exposure

Net Exposure

Factor Volatility

Contribution to TEV

CURRENCY

USD (U.S. dollar) Market weight (%) 0.00 0.00 0.00

EQUITIES DEVELOPED MARKETS

U.S. Equity CYC Consumer Durables Empirical beta –0.118 822 80.6

U.S. Equity CYC Consumer Services Empirical beta –0.222 690 124.9

U.S. Equity CYC Media Empirical beta –0.242 759 151.0

U.S. Equity CYC Retailing Empirical beta –0.417 745 264.2

U.S. Equity NCY Retailing Empirical beta 0.287 404 –67.9

U.S. Equity NCY Food Empirical beta 0.497 418 –112.6

U.S. Equity NCY Household Empirical beta 0.216 415 –56.2

U.S. Equity Total Yield Total yield –0.059 36 0.8

U.S. Equity Corporate Default Probability CDP –0.042 76 1.7

U.S. Equity Share Turnover Rate Share turnover –0.196 59 –3.9

U.S. Equity Momentum (9m) Momentum –0.138 73 –4.7

U.S. Equity Discretionary Accruals Accruals –0.014 31 –0.1

U.S. Equity Market Value Size –0.011 111 –0.1

U.S. Equity Realized Volatility Realized volatility –0.199 97 –0.1

U.S. Equity Earnings to Price Earnings–Price 0.027 44 0.0

U.S. Equity Book to Price Book–Price –0.070 40 1.4

U.S. Equity Earnings Forecast Earnings forecast 0.085 67 –1.1

Multifactor Equity Risk Models and Their Applications 359

analysis at the ticker level, and scenario analysis. In this section, we provide an overview of such detailed analysis using the S&P 500 index tracker ex- ample we created in the previous section.

Recall from Exhibit 13.2 that the TEV of the optimized S&P 500 track- ing portfolio was 39.6 bps/month, composed mostly of idiosyncratic risk (35.8 bps/month) and a relatively small amount of systematic risk (16.9 bps/month). To analyze further the source of these numbers, we first com- pare the holdings of the portfolio with those of the benchmark and then study the impact of the mismatch to the risk of the net position (Portfolio – Benchmark). The first column in Exhibit 13.8 shows the net market weights (NMW) of the portfolio at the sector level (GICS level 1). Our portfolio appears to be well balanced with respect to the benchmark both from a market value and from a risk contribution perspective. The largest market value discrepancies are an overweight in information technology and an underweight in consumer discretionary and health care companies. How- ever, the sector with the largest contribution to overall risk (contribution to TEV, or CTEV) is financials (7.5 bps/month). This may seem unexpected, given the small NMW of this sector (only 0.1%). This result is explained by the fact that contributions to risk (CTEV) are dependent on the net market weight, the risk of the underlying positions and also the correlation between the different exposures. Looking into the decomposition of the CTEV, the exhibit also shows that most of the total contribution to risk from financials is idiosyncratic (7.0 bps/month). This result is due to the small number of

EXHIBIT 13.8 Net Market Weights and Risk Contributions by Sector (bps/month)

Net Market Weight (%)

Contribution to TEV (CTEV)

Systematic Idiosyncratic Total

Total 0.0 7.2 32.7 39.8

Energy 1.4 1.3 4.4 5.7

Materials –2.1 1.0 1.3 2.3

Industrials 2.1 0.3 3.8 4.1

Consumer discretionary –3.6 1.7 4.7 6.3

Consumer staples –0.5 0.5 2.2 2.6

Health care –3.3 1.3 2.2 3.4

Financials 0.1 0.6 7.0 7.5

Information tech 5.2 0.6 5.5 6.1

Telecom services 2.4 0.2 0.8 1.0

Utilities –1.7 –0.1 0.9 0.8

360 EQUITY VALUATION AND PORTFOLIO MANAGEMENT

securities our portfolio has in this sector and the underlying high volatility of these stocks. In short, the diversification benefits across financial stocks are small in our portfolio: we could potentially significantly reduce total risk by constructing our financials exposure using more names. Note that this analysis is only possible with a risk model.

Exhibit 13.9 highlights additional risk measures by sector. What we see in the first column is the isolated TEV, that is, the risk associated with the stocks in that particular sector only. On an isolated basis, the information technology sector has the highest risk in the portfolio. This top position in terms of isolated risk does not translate into the highest contribution to overall portfolio risk, as we saw in Exhibit 13.8. The discrepancy between isolated risk numbers and contributions to risk is explained by the correla- tion between the exposures and allows us to understand the potential hedg- ing effects present across our portfolio. The liquidation effect reported in the table represents the change in TEV when we completely hedge that particu- lar position, that is, enforce zero net exposure to any stock in that particu- lar sector. Interestingly, eliminating our exposure to information technology stocks would actually increase our overall portfolio risk by 6.2 bps/month. This happens because the overweight in this sector is effectively hedging out risk contributions from other sectors. If we eliminate this exposure, the portfolio balance is compromised. The TEV elasticity reported gives an additional perspective regarding how the TEV in the portfolio changes when we change the exposure to that sector. Specifically, it tells us the

EXHIBIT 13.9 Additional Risk Measures by Sector

Isolated TEV

(bps/month)

Liquidation Effect on TEV (bps/month)

TEV Elasticity (x100) (bps)

Systematic Beta (bps)

Total 39.64 –39.64 100.00 1.00

Energy 13.94 –3.38 14.25 0.89

Materials 16.94 1.29 5.74 1.25

Industrials 20.99 1.41 10.27 1.20

Consumer discretionary 29.34 4.25 15.89 1.11

Consumer Staples 10.70 –1.20 6.59 0.70

Health Care 17.37 0.37 8.56 0.65

Financials 20.77 –2.19 18.93 1.34

Information Tech 31.90 6.20 15.30 0.99

Telecom Services 11.58 0.67 2.53 0.76

Utilities 10.30 0.56 1.93 0.79

Multifactor Equity Risk Models and Their Applications 361

percentage change in TEV for each 1% change in our exposure to that par- ticular sector. For example, if we double our exposure to the energy sector, our TEV would increase by 14.25% (from 39.6 bps/month to 45.2 bps/ month). Finally, the report estimates the portfolio to have a beta of 1.00 to the benchmark, which is, of course, in line with our index tracking objec- tive. The beta statistic measures the comovement between the systematic risk drivers of the portfolio and the benchmark and should be interpreted only as that. In particular, a low portfolio beta (relative to the benchmark) does not imply low portfolio risk. It signals relatively low systematic co- movement between the two universes or a relatively high idiosyncratic risk for the portfolio. For example, if the sources of systematic risk from the portfolio and the benchmark are distinct, the portfolio beta is close to zero. The report also provides the systematic beta associated with each sector. For instance, we see that a movement of 1% in the benchmark leads to a 1.34% return in the financials component of our portfolio. As expected, consumer staples and health care are two low beta industries, as they tend to be more stable through the business cycle.11

Although important, the information we examined so far is still quite aggregated. For instance, we know from Exhibit 13.8 that a large compo- nent of idiosyncratic risk comes from financials. But what names are con- tributing most? What are the most volatile sectors? How are systematic exposures distributed within each sector? Risk models should be able to provide answers to all these questions, allowing for a detailed view of the portfolio’s risk exposures and contributions. As an example, Exhibit 13.10 displays all systematic risk factors the portfolio or the benchmark loads onto. It also provides the portfolio, benchmark, and net exposures for each risk factor, the volatility of each of these factors, and their contributions to total TEV. The table shows that the net exposures to the risk factors are generally low, meaning that the tracking portfolio has small active expo- sures. This finding is in line with the evidence from Exhibit 13.2, where we see that the systematic risk is small (16.9 bps/month). If we look into the contributions of individual factors to total TEV, the exhibit shows that the top contributors are the size, share turnover, and realized volatility factors. The optimal index tracking portfolio tends to be composed of very large-cap names within the specified universe, and that explains the net positive load- ing to the market value (size) factor. This portfolio tilt is due to the gener- ally low idiosyncratic risk large companies have. This is seen favorably by the optimization engine, as it tries to minimize idiosyncratic risk. This same tilt would explain our net exposure to both the share turnover and realized volatility factors, as larger companies tend to have lower realized volatility 11Note that we can sum the sector betas into the portfolio beta, using portfolio sector weights (not net weights) as weights in the summation.

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