7-1 McGraw-Hill/Irwin Copyright © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.

CHAPTER 7

Capital Asset Pricing Model

7-2

Capital Asset Pricing Model (CAPM)

• CAPM is a theory of the relationship between risk and return

• CAPM underlies all modern finance

7-3

CAPM Assumptions

• Information is costless and available to all investors

• Investors are risk averse• Investors make optimal investment decisions• Homogeneous expectations

7-4

CAPM Resulting Equilibrium Conditions

• Investors will diversify• All investors hold the same portfolio of risky

assets – the market portfolio• Market portfolio contains all available in the

market

7-5

Total Risk & Systematic Risk• Total Risk = Systematic + Firm-specific Risk Risk

Because firm-specific risk can be eliminated by diversifying, the only risk that is relevant to diversified investors is systematic risk (measured by beta)

7-6

Security Market Line• According to CAPM, the required return on

a security (or portfolio) is shown by the Security Market Line (SML).

• The SML relationship can be shown algebraically or graphically.rX = rf + X (ERM – rf)

Where rX = required return on X

ERM – rf = Market risk premium

7-7

rr

E(rE(rMM))

rrff

SMLSML

MMßßßß = 1.0= 1.0

Security Market Line

7-8

Sample Calculations for SML

ERm = 14% rf = 6%

x = 1.20

rx = 6 + 1.20(8) = 15.6%

7-9

Market Equilibrium

• The expected (or predicted) return for a security equals its required return only if the security is fairly priced; in other words, if a market equilibrium exists.

7-10

Disequilibrium Example

• Suppose Security X with a of 1.2 has a predicted return of 17%

• According to SML, its required return is 15.6%• X is underpriced in the market: it offers too

high of a rate of return for its level of risk

7-11

Figure 7.2 The Security Market Line and Positive Alpha Stock

7-12

Disequilibrium Example• For Stock X, with a predicted return of 17%

and a required return of 15.6%:X = predicted return – required return

= 17% - 15.6% =1.4%

• Stocks with positive alphas are undervalued. Their predicted returns plot above the SML.

7-13

Estimating Betas

• Stock betas are estimated using historical data on a stock index and individual securities

• Returns for individual stocks are regressed against the returns for the stock index

• Slope is the beta for the individual stock

7-14

Figure 7.4 Characteristic Line for GM

7-15

Predicting Betas

• The beta from the regression equation is an estimate based on past history

• Betas exhibit a statistical property:– Regression toward the mean

7-16

CAPM

• Limitations of CAPM:– Market Portfolio is not directly observable (Roll’s

critique)– Research shows that other factors affect returns

7-17

Fama French Three-Factor Model

• Returns are related to three factors:– Size– Book value relative to market value – Beta

Three factor model describes returns better than beta alone