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ERIC WANG
Chapter71.pptx
7. Capital asset pricing and arbitrage pricing theory
Instructor: Seongcheol Paeng
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Table
7.1 The Capital Asset Pricing Model
7.2 The CAPM and Index Models
7.3 The CAPM and The Real World
7.4 Multifactor Models and The CAPM
7.5 Arbitrage Pricing Theory
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7.1 The Capital Asset Pricing Model
The Model: Assumptions and Implications
Historically, the CAPM was developed prior to the index model introduced in the previous chapter (Equation 6.11).
The capital asset pricing model (CAPM) was developed by Treynor, Sharpe, Lintner, and Mossin in the early 1960s, and further refined later.
The model predicts the relationship between the risk and equilibrium expected returns on risky assets.
The conditions that lead to the CAPM ensure competitive security markets, where investors will choose identical efficient portfolios using the mean-variance criterion:
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7.1 The Capital Asset Pricing Model
The Model: Assumptions and Implications
1. Markets for securities are perfectly competitive and equally profitable to all investors.
1.A. No investor is sufficiently wealthy that his or her actions alone can affect market prices.
1.B. All information relevant to security analysis is publicly available at no cost.
1.C. All securities are publicly owned and traded, and investors may trade all of them. Thus, all risky assets are in the investment universe.
1.D. There are no taxes on investment returns. Thus, all investors realize identical returns from securities.
1.E. Investors confront no transaction costs that inhibit their trading.
1.F. Lending and borrowing at a common risk-free rate are unlimited.
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7.1 The Capital Asset Pricing Model
The Model: Assumptions and Implications
2. Investors are alike in every way except for initial wealth and risk aversion; hence, they all choose investment portfolios in the same manner.
2.A. Investors plan for the same (single-period) horizon.
2.B. Investors are rational, mean-variance optimizers.
2.C. Investors are efficient users of analytical methods, and by assumption 1.B they have access to all relevant information. Hence, they use the same inputs and consider identical portfolio opportunity sets. This assumption is often called homogeneous expectations.
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7.1 The Capital Asset Pricing Model
The Model: Assumptions and Implications
Given these assumptions, we summarize the equilibrium that will prevail in this hypothetical world of securities and investors. We elaborate on these implications in the following sections.
1. All investors will choose to hold the market portfolio (M), which includes all assets of the security universe. For simplicity, we shall refer to all assets as stocks. The proportion of each stock in the market portfolio equals the market value of the stock (price per share times the number of shares outstanding) divided by the total market value of all stocks.
2. The market portfolio will be on the efficient frontier. Moreover, it will be the optimal risky portfolio, the tangency point of the capital allocation line (CAL) to the efficient frontier. As a result, the capital market line (CML), the line from the risk-free rate through the market portfolio, M, is also the best attainable capital allocation line. All investors hold M as their optimal risky portfolio, differing only in the amount invested in it versus in the risk-free asset.
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7.1 The Capital Asset Pricing Model
The Model: Assumptions and Implications
3. The risk premium on the market portfolio will be proportional to the variance of the market portfolio and investors’ typical degree of risk aversion. Mathematically, (7.1) where is the standard deviation of the return on the market portfolio and represents the degree of risk aversion of the average investor.
4. The risk premium on individual assets will be proportional to the risk premium on the market portfolio (M) and to the beta coefficient of the security on the market portfolio. Beta measures the extent to which returns respond to the market portfolio. Formally, beta is the regression (slope) coefficient of the security return on the market return, representing sensitivity to fluctuations in the overall security market.
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7.1 The Capital Asset Pricing Model
Why Do All Investors Hold the Market Portfolio?
When we sum over, or aggregate, the portfolios of all individual investors, lending and borrowing will cancel out (because each lender has a corresponding borrower), and the value of the aggregate risky portfolio will equal the entire wealth of the economy. This is the market portfolio, M.
Now suppose that the optimal portfolio of our investors does not include the stock of some company, such as Delta Airlines. When all investors avoid Delta stock, the demand is zero, and Delta’s price takes a free fall. As Delta stock gets progressively cheaper, it becomes ever more attractive and other stocks look relatively less attractive. Ultimately, Delta reaches a price where it is attractive enough to include in the optimal stock portfolio.
Such a price adjustment process guarantees that all stocks will be included in the optimal portfolio. It shows that all assets have to be included in the market portfolio. The only issue is the price at which investors will be willing to include a stock in their optimal risky portfolio.
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7.1 The Capital Asset Pricing Model
The Passive Strategy Is Efficient
The CAPM implies that a passive strategy, using the CML (Capital Market Line) as the optimal CAL (Capital Allocation Line), is a powerful alternative to an active strategy.
In fact, an active investor who chooses any other portfolio will end on a CAL that is inferior to the CML used by passive investors.
We sometimes call this result a mutual fund theorem because it implies that only one mutual fund of risky assets—the market index fund—is sufficient to satisfy the investment demands of all investors.
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7.1 The Capital Asset Pricing Model
The Risk Premium of the Market Portfolio
If the risk premium is too high, there will be excess demand for securities, and prices will rise; if it is too low, investors will not hold enough stock to absorb the supply, and prices will fall.
The equilibrium risk premium of the market portfolio is therefore proportional both to the risk of the market, as measured by the variance of its returns, and to the degree of risk aversion of the average investor, denoted by in Equation 7.1.
Expected Returns on Individual Securities
expected return (mean return)–beta relationship: Implication of the CAPM that security risk premiums (expected excess returns) will be proportional to beta.
)- (7.2)
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7.1 The Capital Asset Pricing Model
The Security Market Line
Security Market Line (SML): Graphical representation of the expected return-beta relationship of the CAPM.
The CML graphs the risk premiums of efficient complete portfolios (made up of the market portfolio and the risk-free asset) as a function of portfolio standard deviation.
This is appropriate because standard deviation is a valid measure of risk for portfolios that are candidates for an investor’s complete portfolio.
The SML, in contrast, graphs individual-asset risk premiums as a function of asset risk (which we measure by beta).
The relevant measure of risk for an individual asset (which is held as part of a well-diversified portfolio) is not the asset standard deviation but rather the asset beta. The SML is valid both for individual assets and portfolios.
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Figure 7.2 The security market line and a positive-alpha stock
7.1 The Capital Asset Pricing Model
The Security Market Line
Because the SML is the graphical representation of the mean–beta relationship, “fairly priced” assets plot exactly on the SML. The expected returns of such assets are commensurate with their risk.
Whenever the CAPM holds, all securities must lie on the SML. Underpriced stocks plot above the SML: Given beta, their expected returns are greater than is indicated by the CAPM.
Overpriced stocks plot below the SML. The difference between fair and actual expected rates of return on a stock is the alpha, denoted α. The expected return on a mispriced security is given by
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Figure 7.2 The security market line and a positive-alpha stock
7.1 The Capital Asset Pricing Model
Application of the CAPM
One place the CAPM may be used is in the investment management industry. The SML provides a benchmark to assess the fair expected return on any risky asset. Then an analyst calculates the return she actually expects.
If a stock is perceived to be a good buy, or underpriced, it will provide a positive alpha, that is, an expected return in excess of the fair return stipulated by the SML.
The CAPM is also useful in capital budgeting decisions. When a firm is considering a new project, the SML provides the required return demanded of the project.
Yet another use of the CAPM is in utility rate-making cases. Here the issue is the rate of return a regulated utility should be allowed to earn on its investment in plant and equipment.
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7.2 The CAPM and Index Models
The CAPM has two limitations:
It relies on the theoretical market portfolio, which includes all assets (such as real estate, foreign stocks, etc.), and it applies to expected as opposed to actual returns. An index model replaces the theoretical all-inclusive portfolio with a market index such as the S&P 500. The composition and rate of return of the index are unambiguous and widely published, and therefore provide a clear benchmark for performance evaluation.
We can start with the central prediction of the CAPM: The market portfolio is mean-variance efficient. An index model can be used to test this hypothesis by verifying that an index designed to represent the full market is mean-variance efficient. To test mean-variance efficiency of an index, we must show that its Sharpe ratio is not surpassed by any other portfolio.
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7.2 The CAPM and Index Models
The Index Model, Realized Returns, and the Mean-Beta Equation
()+ (7.3)
(7.4)
)- (7.2)
Comparing Equation 7.4 to Equation 7.2 reveals that the CAPM predicts = 0.
Thus, we have converted the CAPM prediction about unobserved expectations of security returns relative to an unobserved market portfolio into a prediction about the intercept in a regression of observed variables: realized excess returns of a security relative to those of an observed index.
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7.2 The CAPM and Index Models
The Index Model, Realized Returns, and the Mean-Beta Equation
In actuality, some instances of persistent, positive significant alpha values have been identified. Among these are
(1) small versus large stocks;
(2) stocks of companies that have recently announced unexpectedly good earnings;
(3) stocks with high ratios of book value to market value; and
(4) stocks with “momentum” that have experienced recent advances in price.
In general, however, future alphas are practically impossible to predict from past values.
The result is that index models are widely used to operationalize capital asset pricing theory.
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7.2 The CAPM and Index Models
Estimating the Index Model
Let us rewrite Equation 7.3 for Google, denoting Google’s excess return as and denoting months using the subscript t.
Residual = Actual excess return − Predicted excess return for Google
We conduct the analysis in three steps:
1. Collect and process relevant data;
2. feed the data into a statistical program (here we use Excel) to estimate the regression Equation 7.3;
3. and use the results to answer these questions about Google’s stock.
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7.2 The CAPM and Index Models
For the same period we compiled monthly rates of return on one-month T-bills.
With these three series of returns we generate monthly excess return on Google’s stock and the market index.
Some statistics for these returns are shown in Table 7.1.
Notice that the monthly variation in the T-bill return reported in Table 7.1 does not reflect risk, as investors knew the return on bills at the beginning of each month.
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7.2 The CAPM and Index Models
Figure 7.3, Panel A shows the monthly return on the securities during the sample period. The significantly higher volatility of Google is evident, and the graph suggests that its beta is greater than 1: When the market moves, Google tends to move in the same direction, but by greater amounts.
Figure 7.3, Panel B shows the evolution of cumulative returns. It illustrates the positive index returns in the early years of the sample, the steep decline during the recession, and the significant partial recovery of losses at the end of the sample period.
Whereas Google outperforms T-bills, T-bills outperform the market index over the period, highlighting the worse-than-expected realizations in the capital market.
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7.2 The CAPM and Index Models
We regressed Google’s excess returns against those of the index using the Regression command from the Data Analysis menu of Excel.
The scatter diagram in Figure 7.4 shows the data points for each month as well as the regression line that best fits the data.
As noted in the previous chapter, this is called the security characteristic line (SCL), because it describes the relevant characteristics of the stock.
Figure 7.4 allows us to view the residuals, the deviation of Google’s return each month from the prediction of the regression equation.
By construction, these residuals average to zero, but in any particular month, the residual may be positive or negative.
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Figure 7.4 Scatter diagram and security characteristic line for Google against the S&P 500, Jan 2006-Dec 2010
7.2 The CAPM and Index Models
Table 7.2 is the regression output from Excel.
The adjusted R-square tells us that 34.97% of the variance of Google’s excess returns is explained by the variation in the excess returns of the index,
and hence the remainder, or 65.03%, of the variance is firm specific, or unexplained by market movements.
The standard deviation of the residuals is referred to in the output (below the adjusted R-square) as the “standard error” of the regression (8.46%). In roughly two-thirds of the months, the firm-specific component of Google’s excess return was between ±8.46%.
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7.2 The CAPM and Index Models
Finally, the lower panel of the table shows the estimates of the regression intercept and slope (alpha = .88% and beta = 1.20).
The positive alpha means that, measured by realized returns, Google stock was above the security market line (SML) for this period.
But the next column shows considerable imprecision in this estimate as measured by its standard error, 1.09, considerably larger than the estimate itself.
The t-statistic (the ratio of the estimate of alpha to its standard error) is only .801, indicating low statistical significance.
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7.2 The CAPM and Index Models
The second line in the panel gives the estimate of Google’s beta, which is 1.20.
The standard error of this estimate is .215, resulting in a t-statistic of 5.58, and a practically zero p-value for the hypothesis that the true beta is in fact zero.
In other words, the probability of observing an estimate this large if the true beta were zero is negligible.
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7.2 The CAPM and Index Models
Another important question is whether Google’s beta is significantly different from the average stock beta of 1. This hypothesis can be tested by computing the t-statistic:
This value is considerably below the conventional threshold for statistical significance; we cannot say with confidence that Google’s beta differs from 1. The 95% confidence interval for beta ranges from .69 to 1.72.
What We Learn From This Regression
Despite these qualifications, we can safely say that Google is a cyclical stock.
Its returns vary equally with or more than the overall market, as its beta is higher than the average value of 1, albeit not significantly so.
Thus, we would expect Google’s excess return to respond, on average, more than one-for-one with the market index.
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7.2 The CAPM and Index Models
What We Learn From This Regression
Suppose the current T-bill rate is 2.75%, and our forecast for the market excess return is 5.5%. Then the required rate of return for an investment with the same risk as Google’s equity would be
Predicting Betas
A single-index model may not be fully consistent with the CAPM and may not be a sufficiently accurate predictor of risk premiums. Still the concept of systematic versus diversifiable risk is useful. Systematic risk is approximated well by the regression equation beta and nonsystematic risk by the residual variance of the regression.
As an empirical rule, it appears that betas exhibit a statistical property called mean reversion. This suggests that high-β (that is, β > 1) securities tend to exhibit a lower β in the future, while low-β (that is, β < 1) securities exhibit a higher β in future periods. Researchers who desire predictions of future betas often adjust beta estimates from historical data to account for regression toward 1. For this reason, it is necessary to verify whether the estimates are already “adjusted betas.”
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7.2 The CAPM and Index Models
Predicting Betas
Example 7.7 Suppose that past data yield a beta estimate of .65. A common weighting scheme is ⅔ on the sample estimate and ⅓ on the value 1. Thus, the adjusted forecast of beta will be
Adjusted beta = ⅔ × .65 + ⅓ × 1 = .77
The final forecast of beta is in fact closer to 1 than the sample estimate.
One might hope that more precise estimates of beta could be obtained by using a long time series of returns. Unfortunately, this is not a solution because betas change over time and old data can provide a misleading guide to current betas.
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7.3 The CAPM and The Real World
The CAPM was first published by Sharpe in 1964 and took the world of finance by storm. Early tests by Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) were partially supportive of the CAPM: Average returns were higher for higher-beta portfolios, but the reward for beta risk was less than predicted by the simple version of the CAPM.
While this sort of evidence against the CAPM remained largely within the ivory towers of academia, Roll’s (1977) paper “A Critique of Capital Asset Pricing Tests” shook the practitioner world as well. Roll argued that the true market portfolio can never be observed.
The usual stock market indexes used as proxies for the market portfolio ignore the large majority of investor wealth, for example, real estate, fixed income securities, foreign investments, and not least, the value of human capital. Without a good measure of the return on a broad measure of investor assets, the theory is necessarily untestable.
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7.3 The CAPM and The Real World
Although Roll is absolutely correct on theoretical grounds, more recent research suggests that the error introduced by using a broad market index as proxy for the true, unobserved market portfolio is perhaps not even the greatest problem of the CAPM.
For example, Fama and French (1992) published a study that dealt the CAPM an even harsher blow. They found that in contradiction to the CAPM, certain characteristics of the firm, namely, size and the ratio of market to book value, were far more useful in predicting future returns than beta.
Fama and French and several others have published many follow-up studies on this topic. It seems clear from these studies (to which we will return in more detail later in the chapter) that beta does not tell the whole story of risk.
Liquidity, a different kind of risk factor, was ignored for a long time. Although first analyzed by Amihud and Mendelson as early as 1986, it is yet to be accurately measured and incorporated in portfolio management.
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7.3 The CAPM and The Real World
Despite all these issues, beta is not dead. Research shows that when we use a more inclusive proxy for the market portfolio than the S&P 500 (specifically, an index that includes human capital) and allow for the fact that beta changes over time, the performance of beta in explaining security returns is enhanced (Jagannathan and Wang, 1996).
We know that the CAPM is not a perfect model and that it will continue to be refined. Still, the logic of the model is compelling and captures the two key points made by all of its more sophisticated variants:
first, the crucial distinction between diversifiable risk and systematic risk that cannot be avoided by diversification, and
second, the fact that investors will demand a premium for bearing non-diversifiable risk.
Diversifiable Risk, also known as unsystematic risk, is defined as the danger of an event that would affect an industry and not the market. This type of risk can only be mitigated through diversifying investments and maintaining a portfolio diversification.
The CAPM therefore provides a useful framework for thinking rigorously about the relationship between security risk and return.
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7.4 Multifactor Models and The CAPM
It stands to reason that a more explicit representation of systematic risk, allowing stocks to exhibit different sensitivities to its various facets, would constitute a useful refinement of the single-factor model.
We can expect that models that allow for several systematic factors— multifactor models—can provide better descriptions of security returns.
Therefore, we can expand the single-index model, Equation 7.3, describing the excess rate of return on stock i in some time period t as follows where is the sensitivity of the stock’s excess return to that of the T-bond portfolio and is the excess return of the T-bond portfolio in month t.
+ + (7.5)
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7.4 Multifactor Models and The CAPM
Such a multifactor CAPM was first presented by Merton (1973). In the two-factor economy of Equation 7.5, the expected rate of return on a security would be the sum of three terms:
1. The risk-free rate of return.
2. The sensitivity to the market index (i.e., the market beta, ) times the risk premium of the index, .
3. The sensitivity to interest rate risk (i.e., the T-bond beta, ) times the risk premium of the T-bond portfolio, .
This assertion is expressed mathematically as a two-factor security market line for security i: (7.6)
The multifactor model clearly gives us a richer way to think about risk exposures and compensation for those exposures than the single-index model or the CAPM.
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7.4 Multifactor Models and The CAPM
The Fama-French Three-Factor Model
Fama and French proposed a three-factor model that has become a standard tool for empirical studies of asset returns.
They add to the market-index portfolios formed on the basis of firm size and book-to-market ratio to explain average returns.
These additional factors are motivated by the observations that average returns on stocks of small firms and firms with high ratios of book value of equity to market value of equity have been higher than predicted by the CAPM.
This observation suggests that size and book-to-market (B/M) ratio may be proxies for exposures to sources of systematic risk not captured by beta and thus result in return premiums.
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7.4 Multifactor Models and The CAPM
Collecting and Processing Data
To create portfolios that track the size and B/M factors, one can sort industrial firms by size (market capitalization or market “cap”) and by B/M ratio.
The size premium is constructed as the difference in returns between small and large firms and is denoted by SMB (“small minus big”).
Similarly, the B/M premium is calculated as the difference in returns between firms with a high versus low B/M ratio and is denoted HML (“high minus low”).
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Fama-French Model Data Link
https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
7.4 Multifactor Models and The CAPM
Collecting and Processing Data
To apply the FF three-factor portfolio to Google, we need to estimate Google’s beta on each factor. To do so, we generalize regression Equation 7.3 of the single-index model and fit a multivariate regression:
(7.7)
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7.4 Multifactor Models and The CAPM
Estimation Results
Both the single-index model (alternatively employing the S&P 500 Index and the broad market index) and the FF three-factor model are summarized in Table 7.4.
The broad market index includes more than 4,000 stocks, while the S&P 500 includes only 500 of the largest U.S. stocks, in which list Google ranked fourteenth in January 2012.
In this sample, the broad market index tracks Google’s returns better than the S&P 500, and the three-factor model is a better specification than the one-factor model.
This is reflected in three aspects of a successful specification: a higher adjusted R-square, a lower residual SD, and a smaller value of alpha.
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7.4 Multifactor Models and The CAPM
What We Learn From This Regression
While the FF three-factor model offers a richer and more accurate description of asset returns, applying this model requires two more forecasts of future returns, namely, for the SMB and HML portfolios.
We have so far in this section been using a T-bill rate of 2.75% and a market risk premium of 5.5%. If we add to these values a forecast of 2.5% for the SMB premium and 4% for HML, the required rate for an investment with the same risk as Google’s equity would be
=2.75 + (1.51 × 5.5) + (−.20 × 2.5) + (−1.33 × 4) = 5.24%
which is considerably lower than the rate (9.35%) derived from cyclical considerations alone (i.e., single-beta models).
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7.4 Multifactor Models and The CAPM
Multifactor Models and the Validity of the CAPM
The single-index CAPM fails empirical tests because its empirical representation, the single-index model, inadequately explains returns on too many securities. In short, too many statistically significant values of alpha (which should be zero) show up in single-index regressions. Despite this failure, it is still widely used in the industry.
Multifactor models such as the FF model may also be tested by the prevalence of significant alpha values. The three-factor model shows a material improvement over the single-index model in that regard. But the use of multi-index models comes at a price: They require forecasts of the additional factor returns.
If forecasts of those additional factors are themselves subject to forecast error, these models will be less accurate than the theoretically inferior single-index model.
Nevertheless, multifactor models have a definite appeal because it is clear that real-world risk is multifaceted.
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7.5 Arbitrage Pricing Theory
Stephen Ross developed the arbitrage pricing theory (APT) in 1976. Like the CAPM, the APT predicts a security market line linking expected returns to risk, but the path it takes to the SML is quite different. Ross’s APT relies on three key propositions:
(1) Security returns can be described by a factor model;
(2) there are sufficient securities to diversify away idiosyncratic risk; and
(3) well-functioning security markets do not allow for the persistence of arbitrage opportunities.
Arbitrage is the purchase and sale of an asset in order to profit from a difference in the asset's price between markets.
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7.5 Arbitrage Pricing Theory
Well-Diversified Portfolios (Bodie, Zvi. Investments (p. 313~). McGraw-Hill Higher Education.)
We begin by considering the risk of a portfolio of stocks in a single-factor market. We first show that if a portfolio is well diversified, its firm-specific or nonfactor risk becomes negligible, so that only factor (F, equivalently, systematic) risk remains. The excess return, , on an n-stock portfolio with weights , ∑ = 1, is
= E( ) + F + (10.3)
where = ∑ ; E() = ∑ E()
are the weighted averages of the and risk premiums of the n securities. The portfolio nonsystematic component (which is uncorrelated with F) is = ∑ , which similarly is a weighted average of the of the n securities.
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7.5 Arbitrage Pricing Theory
Well-Diversified Portfolios (Bodie, Zvi. Investments (p. 313~). McGraw-Hill Higher Education.)
This property is true of portfolios other than the equally weighted one. Portfolio nonsystematic risk will approach zero for any portfolio for which each becomes consistently smaller as n gets large (more precisely, for which each approaches zero as n increases). This property motivates us to define a well-diversified portfolio as one with each weight, , small enough that for practical purposes the nonsystematic variance, , is negligible.
= E( ) + F (10.4)
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7.5 Arbitrage Pricing Theory
Well-Diversified Portfolios (Bodie, Zvi. Investments (p. 313~). McGraw-Hill Higher Education.)
The solid line in Figure 10.1, Panel A, plots the excess return of a well-diversified portfolio A with E() = 10% and = 1 for various realizations of the systematic factor.
The expected return of portfolio A is 10%; this is where the solid line crosses the vertical axis. At this point, the systematic factor is zero, implying no macro surprises.
If the macro factor is positive, the portfolio’s return exceeds its expected value; if it is negative, the portfolio’s return falls short of its mean. The excess return on the portfolio is therefore
=E() + F = 10% + 1.0 × F
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7.5 Arbitrage Pricing Theory
Well-Diversified Portfolios (Bodie, Zvi. Investments (p. 313~). McGraw-Hill Higher Education.)
Compare Panel A in Figure 10.1 with Panel B, which is a similar graph for a single stock (S) with = 1.
The undiversified stock is subject to nonsystematic risk, which is seen in a scatter of points around the line.
The well-diversified portfolio’s return, in contrast, is determined completely by the systematic factor.
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7.5 Arbitrage Pricing Theory
The APT and the CAPM (Bodie, Zvi. Investments (p. 319~). McGraw-Hill Higher Education.)
A violation of the APT’s pricing relationships will cause extremely strong pressure to restore them even if only a limited number of investors become aware of the disequilibrium. Moreover, the APT provides an expected return–beta relationship using a well-diversified portfolio that can be constructed from a large number of securities.
In spite of these apparent advantages, the APT does not fully dominate the CAPM. The CAPM provides an unequivocal statement on the expected return–beta relationship for all securities, whereas the APT implies that this relationship holds for all but perhaps a small number of securities.
Moreover, while the APT is built on the foundation of well-diversified portfolios, we’ve seen, for example in Table 10.1, that even large portfolios may have non-negligible residual risk.
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7.5 Arbitrage Pricing Theory
The APT and the CAPM (Bodie, Zvi. Investments (p. 319~). McGraw-Hill Higher Education.)
Despite these shortcomings, the APT is valuable.
First, recall that the CAPM requires that almost all investors be mean-variance optimizers. The APT frees us of this assumption. It is sufficient that a small number of sophisticated arbitrageurs scour the market for arbitrage opportunities.
Moreover, when we replace the unobserved market portfolio of the CAPM with an observed, broad index portfolio that may not be efficient, we no longer can be sure that the CAPM predicts risk premiums of all assets with no bias. Therefore, neither model is free of limitations.
In the end, however, it is noteworthy and comforting that despite the very different paths they take to get there, both models arrive at the same security market line.
Most important, they both highlight the distinction between firm-specific and systematic risk, which is at the heart of all modern models of risk and return.
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Assignments
Problem Sets (Paraphrase with your own words.)
Explain Implications of the CAPM.
Explain the Security Market Line (SML).
Explain what we learn from Table 7.2.
Explain the Two-Factor model by Merton.
Explain the Fama-French Three-Factor Model.
Explain what we learn from Table 7.4.
Compare the APT with the CAPM.
Deadline: 7/17
Submit it via email to [email protected]
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