FNCE 625 – Investment Analysis and Management

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Investments: Analysis and Management

Fourteenth Edition

Gerald R. Jensen and Charles P. Jones

Chapter 9

Capital Market Theory and Asset Pricing Models

Capital Asset Pricing Model 1

Positive rather than normative

It is objective and fact-based, not subjective or opinion-based

Focus on the equilibrium relationship between the risk and expected return on risky assets

Builds on Markowitz portfolio theory

Each investor is assumed to diversify his or her portfolio according to the Markowitz model

Capital Asset Pricing Model 2

Assumes all investors:

Use the same information to generate an efficient frontier

Have the same one-period time horizon

Can borrow or lend money at the risk-free return

No transaction costs, no income taxes, no inflation

No single investor can affect the price of a stock

Capital markets are in equilibrium

Risk-Free Asset, Borrowing, Lending

Risk free asset

No correlation with risky assets

Usually proxied by a Treasury security

Adding a risk-free asset extends and changes the efficient frontier

Risk-free investing is “lending” because investor lends money to issuer

With borrowing, investor no longer restricted to personal wealth

Risk-Free Lending/Borrowing

Risk-free asset combined with port. T (T is part of efficient set AB)

RF to T: lending portfolios

T to L: borrowing portfolios

Portfolios on line R F to L dominate all portfolios below (e.g., Z and X)

The New Efficient Set

Risk-free investing and borrowing creates a new set of risk-expected return possibilities

Addition of risk-free asset results in:

A change in the efficient set from an arc to a straight line tangent to the original frontier

Chosen (optimal) portfolio depends on investor’s risk-return preferences

Capital Market Line 1

Line from RF to L is capital market line (CML)

x = risk premium = E(RM) − RF

y-intercept = RF

Capital Market Line 2

Slope of C M L is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market

Relationship between risk and expected return for portfolio P (Equation for C M L):

Market Portfolio

Most important implications of C M L

The portfolio of all risky assets is the optimal risky portfolio (called the market portfolio)

The expected price of risk is always positive

The optimal portfolio is at the highest point of tangency between R F and efficient frontier

All investors hold the same optimal portfolio of risky assets

Characteristics of Market Portfolio

All risky assets must be in portfolio, so it is completely diversified

Includes only systematic risk

Unobservable but approximated with portfolio of all common stocks

In turn, approximated with S and P 500

All securities included in proportion to their market value

The Separation Theorem

Investors use their preferences (indifference curves) to determine optimal portfolio

Separation Theorem

The investment decision about which risky portfolio to hold is separate from the financing decision

Investment decision does not involve investor

Financing decision depends on investor’s preferences

Remaining Questions Not Addressed by CML

How do you determine the expected return for individual securities or undiversified portfolios?

How do investors determine the risk a security will add to their portfolio?

* Solution is achieved by assuming investors hold well-diversified portfolios

Security Market Line

C M L only applies to markets in equilibrium and efficient portfolios

The security market line (S M L) depicts tradeoff between risk and expected return for individual securities and portfolios

Under C A P M, all investors hold the market portfolio

Relevant risk of any security is, therefore, its covariance with the market portfolio

Beta – What does it tell us?

Standardized measure of systematic risk

Relative measure of risk: risk of an individual stock relative to the market portfolio of all assets

Relates an asset’s covariance with the market portfolio to the variance of the market portfolio

Beta (β) – What is it?

Risk an asset will add to a well-diversified portfolio

Measures an asset's nondiversifiable risk

Slope of the line formed when an asset’s returns are regressed against the market return

Measure of the sensitivity of an asset’s returns to changes in the market return

The relevant risk measure for well-diversified investors

Beta Characteristics

Beta > 1; security moves with the market, only more; security is riskier than average

0 < Beta < 1; security moves with the market, only less

Beta < 0; security moves counter to the market

Market beta equals 1

Portfolio beta is a weighted average of individual stock betas

Betas of Selected Companies

Company	Beta
Amazon	1.35
McDonald’s	0.72
Kellogg Company	0.64
Bristol- Myers Squibb	0.80
Walmart	0.87
FirstEnergy	0.50
Conoco Philips	0.74
Delta Air Lines	1.29
Goldman Sachs	1.35
Barrick Gold	0.32
FedEx	1.31

C A P M’s Expected Return-Beta Relationship

Required return on asset (ki) is composed of:

Risk-free rate (RF )

Risk premium

The greater the systematic risk, the greater the required return

Beta and the SML/CAPM

Beta = 1.0; equal risk to market (average)

Securities A and B are more risky than the market

Beta > 1.0

Security C is less risky than the market

Beta < 1.0

Estimating the S M L

Treasury bond rate used to estimate R F

Expected market return unobservable

Often estimated using past market returns and taking a mean value

Estimating security betas is difficult

Beta is only company-specific factor in C A P M

Beta estimation requires asset-specific forecast

SML and Under(Over)-Valued Assets

Securities ABC and XYZ are undervalued

Security L M N is overvalued

C A P M/S M L Implications

Higher risk assets require higher returns

Investors are only compensated for bearing non-diversifiable risk

Asset prices are not impacted by diversifiable risk

Undiversified investors have an inferior risk-expected return trade-off

Investors determine the risk they bear; market determines their compensation

Estimating Beta

Market model

Relates a stock’s return to the return on the market, assumes a linear relationship

Produces an estimate of return for any stock

Characteristic line

Line fit to a security’s return relative to the market index

Amazon’s Characteristic Line

Slope = rise ÷ run = Beta

Is AMZN’s beta > 1?

How Accurate Are Beta Estimates? 1

Betas change with a company’s situation

Estimating a future beta

May differ from the historical beta

RM represents the total of all marketable assets in the economy

Approximated with a stock market index

Approximates return on all common stocks

How Accurate Are Beta Estimates? 2

Methods for estimating beta vary by time period, market index, return interval, etc.

Therefore, estimates of beta vary

Regression estimates of true

from the

characteristic line are subject to error

Portfolio betas are more reliable than individual security betas

Tests of C A P M

Assumptions are mostly unrealistic

Empirical evidence has not led to consensus

Points widely agreed upon

S M L (C A P M) appears to be linear

Intercept is generally higher than R F

Slope of S M L is generally less than theory predicts

It is likely that only systematic risk is rewarded

Arbitrage Pricing Theory

Based on Law of One Price

Two assets with identical future cash flow streams cannot sell at different prices

Equilibrium prices adjust to eliminate all arbitrage opportunities

Unlike C A P M, A P T does not assume

Single-period investment horizon, absence of taxes, riskless borrowing or lending, mean-variance decisions

Factors

A P T assumes returns generated by a factor model that allows for more than 1 factor

Factor Characteristics

Each risk must have a pervasive influence on stock returns

Risk factors must influence expected return and have non-zero prices

Risk factors must be unpredictable to the market

A P T Model

Most important - the deviations of the factors from their expected values

Expected return is directly related to sensitivity

C A P M assumes only risk is sensitivity to market

Expected return-risk relationship for the A P T can be described as:

Problems with A P T

Risk factors are not specified ex ante

To implement A P T model, need factors that account for differences in security returns

C A P M identifies market portfolio as single factor

Studies suggest certain factors are reflected in security returns

Both C A P M and A P T rely on unobservable expectations

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FNCE 625 – Investment Analysis and Management

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