McGraw-Hill/Irwin Copyright © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Capital Asset Pricing and Arbitrage Pricing Theory CHAPTER 7

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 ______________________ Investors make ____________________ investment decisions Homogeneous expectations

7-4 CAPM Resulting Equilibrium Conditions Investors will ________________ All investors hold the same portfolio of risky assets – the market portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

7-5 Total Risk & Systematic Risk Total Risk = Systematic + Firm-specific Risk Risk 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. r X = r f +  X (ER M – r f ) Where r X = required return on X ER M – r f = Market risk premium ER M – r f = Market risk premium

7-7 r E(r M ) rfrfrfrf SML M ß ß = 1.0 Security Market Line

7-8 Sample Calculations for SML ER m =.11 r f =.03  x = 1.25 r x = (.08) = ______________

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 1.25 has a predicted return of 15% According to SML, its required return is 13% 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 15% and a required return of 13%:  X = predicted return – required return = 15% - 13% = __________ = 15% - 13% = __________ 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 T-bills, a stock index and individual securities Risk premiums for individual stocks are regressed against the risk premiums 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 _______________

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