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 ____________________________ CAPM underlies all modern finance Sharpe, Lintner and Mossin are credited with its development (especially Sharpe)

7-3 CAPM Assumptions Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes nor transaction costs

7-4 CAPM Assumptions (cont.) Information is costless and available to all investors Investors are risk averse Investors make optimal investment decisions Homogeneous expectations

7-5 Resulting Equilibrium Conditions Investors will _____________________ All investors hold the same portfolio of risky assets – the ___________ portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

7-6 Total Risk & Systematic Risk Total Risk = Systematic + Firm-specific Risk Risk Risk Risk Because firm-specific risk can be eliminated by diversifying, the only type of risk that is relevant to diversified investors is systematic risk (measured by beta)

7-7 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

7-8 Figure 7.1 The Efficient Frontier and the Capital Market Line

7-9 Sample Calculations for SML E(r m ) - r f =.08r f =.03  x = 1.25 r x = (.08) =.13 or 13%  y =.6 r y = (.08) =.078 or 7.8%

7-10 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.

7-11 Disequilibrium Example Suppose a 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

7-12 Figure 7.2 The Security Market Line and Positive Alpha Stock

7-13 Disequilibrium Example For Stock X, with a predicted return of 15% and a required return of 13%:  X = predicted return – required return = 15% - 13% = 2% = 15% - 13% = 2% Stocks with positive alphas are _______________________. Their predicted returns plot ________ the SML.

7-14 Estimating Betas Stock betas are estimated using historical data on T-bills, S&P 500 and individual securities Regress risk premiums for individual stocks against the risk premiums for the S&P 500 Slope is the __________________ for the individual stock

7-15 Figure 7.4 Characteristic Line for GM

7-16 Predicting Betas The beta from the regression equation is an estimate based on past history Betas exhibit a statistical property: –____________________________________

7-17 CAPM and the Real World The CAPM was first published by Sharpe in the Journal of Finance in 1964 Many tests of the theory have since followed including Roll’s critique in 1977 and the Fama and French study in 1992

7-18 Multifactor Models Limitations of CAPM: –Market Portfolio is not directly observable –Research shows that other factors affect returns

7-19 Fama French Three-Factor Model Returns are related to factors other than market returns: –Size –Book value relative to market value –Three factor model better describes returns

7-20 Arbitrage Pricing Theory Arbitrage - arises if an investor can construct a zero beta investment portfolio with a return greater than the risk-free rate If two portfolios are mispriced, the investor could buy the low-priced portfolio and sell the high-priced portfolio In efficient markets, profitable arbitrage opportunities will quickly disappear

7-21 APT and CAPM Compared APT applies to well diversified portfolios and not necessarily to individual stocks With APT it is possible for some individual stocks to be mispriced - not lie on the SML APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio APT can be extended to multifactor models