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CHAPTER 9 The Capital Asset Pricing Model Investments, 8th edition Bodie, Kane and Marcus Slides by Susan Hine McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Capital Asset Pricing Model (CAPM) • It is the equilibrium model that underlies all modern financial theory • Derived using principles of diversification with simplified assumptions • Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development 9-2 Assumptions • Individual investors are price takers • Single-period investment horizon • Investments are limited to traded financial assets • No taxes and transaction costs 9-3 Assumptions Continued • Information is costless and available to all investors • Investors are rational mean-variance optimizers • There are homogeneous expectations 9-4 Resulting Equilibrium Conditions • All investors will hold the same portfolio for risky assets – market portfolio • Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value 9-5 Resulting Equilibrium Conditions Continued • Risk premium on the market depends on the average risk aversion of all market participants • Risk premium on an individual security is a function of its covariance with the market 9-6 Figure 9.1 The Efficient Frontier and the Capital Market Line 9-7 Market Risk Premium •The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor: E (rM ) rf A M 2 where 2 M is the variance of the market portolio and A is the average degree of risk aversion across investors 9-8 Return and Risk For Individual Securities • The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio • An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio 9-9 Using GE Text Example • Covariance of GE return with the market portfolio: n n Cov(rGE , rM ) Cov rGE , wk rk wk Cov(rk , rGE ) k 1 k 1 • Therefore, the reward-to-risk ratio for investments in GE would be: GE's contribution to risk premium GE's contribution to variance wGE E (rGE ) rf E (rGE ) rf wGE Cov(rGE , rM ) Cov(rGE , rM ) 9-10 Using GE Text Example Continued • Reward-to-risk ratio for investment in market portfolio: Market risk premium E (rM ) rf M 2 Market variance • Reward-to-risk ratios of GE and the market portfolio: E (rGE ) rf E (rM ( rf ) Cov(rGE , rM ) M2 • And the risk premium for GE: E (rGE ) rf Cov(rGE , rM ) 2 M E (rM ) rf 9-11 Expected Return-Beta Relationship • CAPM holds for the overall portfolio because: E (rP ) wk E (rk ) and k P wk k k • This also holds for the market portfolio: E (rM ) rf M E (rM ) rf 9-12 Figure 9.2 The Security Market Line 9-13 Figure 9.3 The SML and a Positive-Alpha Stock 9-14 The Index Model and Realized Returns • To move from expected to realized returns— use the index model in excess return form: Ri i i RM ei • The index model beta coefficient turns out to be the same beta as that of the CAPM expected return-beta relationship 9-15 Figure 9.4 Estimates of Individual Mutual Fund Alphas, 1972-1991 9-16 The CAPM and Reality • Is the condition of zero alphas for all stocks as implied by the CAPM met – Not perfect but one of the best available • Is the CAPM testable – Proxies must be used for the market portfolio • CAPM is still considered the best available description of security pricing and is widely accepted 9-17 Econometrics and the Expected ReturnBeta Relationship • It is important to consider the econometric technique used for the model estimated • Statistical bias is easily introduced – Miller and Scholes paper demonstrated how econometric problems could lead one to reject the CAPM even if it were perfectly valid 9-18 Extensions of the CAPM • Zero-Beta Model – Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks • Consideration of labor income and nontraded assets • Merton’s Multiperiod Model and hedge portfolios – Incorporation of the effects of changes in the real rate of interest and inflation 9-19 Extensions of the CAPM Continued • A consumption-based CAPM – Models by Rubinstein, Lucas, and Breeden • Investor must allocate current wealth between today’s consumption and investment for the future 9-20 Liquidity and the CAPM • Liquidity • Illiquidity Premium • Research supports a premium for illiquidity. – Amihud and Mendelson – Acharya and Pedersen 9-21 Figure 9.5 The Relationship Between Illiquidity and Average Returns 9-22 Three Elements of Liquidity • Sensitivity of security’s illiquidity to market illiquidity: Cov(C , C ) i L1 M Var ( RM CM ) • Sensitivity of stock’s return to market illiquidity: Cov( R , C ) i L2 M Var ( RM CM ) • Sensitivity of the security illiquidity to the market rate of return: L3 Cov(Ci , RM ) Var ( RM CM ) 9-23