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Chapter Nine

The Capital Asset Pricing Model

No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

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CAPM is a set of predictions concerning equilibrium expected returns on risky assets

Based on two sets of assumptions

Individual behavior

Market structure

Markowitz established modern portfolio management in 1952

Sharpe, Lintner and Mossin published CAPM in 1964

Capital Asset Pricing Model (CAPM)

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Assumptions

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All investors will hold the same portfolio for risky assets — market portfolio

Market portfolio contains all securities

Proportion of each stock in this portfolio equals the market value of the stock (price per share times number of shares outstanding) divided by the sum of the market value of all stocks

The Market Portfolio

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Capital Allocation Line

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Capital Market Line

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The market risk premium is proportional to its risk and the degree of risk aversion:

Where

representative investor’s risk aversion

variance of the market portfolio

The Risk Premium of the Market Portfolio

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CAPM is build on the insight that the appropriate risk premium on an asset will be determined by its contribution to the risk of investors’ overall portfolios

All investors use the same input list (i.e., they all end up using the market as their optimal risky portfolio)

Expected Returns on Individual Securities

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Covariance of GE return with the market portfolio:

The reward-to-risk ratio for GE would be:

Individual Securities: Example

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Reward-to-risk ratio for investment in market portfolio (i.e., market price of risk):

Equilibrium dictates all investments should offer the same reward-to-risk ratio

GE Example (1 of 2)

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Fair risk premium for GE stock:

Restating, we obtain:

GE Example (2 of 2)

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Expected return-beta relationship tells us the total expected rate of return is the sum of the risk-free rate plus a risk premium

Risk premium is the product of a “benchmark risk premium” and the relative risk of the particular asset as measured by its beta

Expected Return-Beta Relationship

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The Security Market Line

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The SML and a Positive-Alpha Stock

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Index model states the realized excess return on any stock is the sum of the following:

Realized excess return due to marketwide factors

A nonmarket premium

Firm-specific outcomes

The index model beta coefficient is the same as the beta of the CAPM expected return-beta relationship

The CAPM and the Single-Index Market

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Fundamental distinction between systematic and diversifiable risk remains in each variant of the basic model

CAPM is build on “uncomfortably restrictive” assumptions

See assumption from Table 9.1

Assumptions and Extensions of the CAPM

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Identical Input Lists

In the absence of private information, investors should assume alpha values are zero

Zero-Beta Model

Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks

Labor Income and Other Nontraded Assets

Many assets are not tradeable (e.g., private businesses, human capital, earning power of individuals, etc.)

Extensions of the CAPM (1 of 3)

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Multiperiod Model and Hedge Portfolios

Investors should be more concerned with the stream of consumption that wealth can buy for them

Consumption-Based CAPM (CCAPM)

Rubinstein, Lucas, and Breeden

Investors allocate wealth between consumption today and investment for the future

Extensions of the CAPM (2 of 3)

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Liquidity

Financial costs inhibit trades

Liquidity of an asset is the ease and speed with which it can be sold at fair market value

Illiquidity can be measured in part by the discount from fair market value a seller must accept if the asset is to be sold quickly

Extensions of the CAPM (3 of 3)

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The Relationship Between Illiquidity and Average Returns

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In a financial crisis, liquidity can unexpectedly dry up

When liquidity in one stock decreases, it commonly tends to decrease in other stocks at the same time

Investors demand compensation for liquidity risk, demonstrated by firms with greater liquidity risk having higher average returns

“Liquidity betas”

Liquidity Risk

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Testing the CAPM is surprisingly difficult

Cannot observe all tradable assets

Impossible to pin down market portfolio

Both alpha and beta, as well as residual variance, are likely time varying

Most tests of the CAPM are directed at the mean-beta relationship as applied to assets with respect to an observed, but perhaps inefficient, stock index portfolio

The CAPM and Academic World

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Portfolio theory and the CAPM have become accepted tools in the practitioner community

Many professionals are comfortable with the use of beta to measure systematic risk

Most investors don’t beat the index portfolio

The CAPM and Investment Industry

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