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 gives a precise prediction of the relationship that should be observed between the risk of an asset and its expected return. • Beneftis: – Provides benchmark rate of return for evaluating possible investments – Helps to make an educated guess as to the expected return on assets that have not yet been traded in the marketplace • It is the equilibrium model • Derived using principles of diversification with simplified assumptions • Markowitz, Sharpe, Lintner and Mossin 9-2 Assumptions • Individual investors are price takers: they act as though security prices are unaffected by their own trades (their wealth is small compared to the total wealth of all investors) • Single-period investment horizon: myopicshort-sighted behavior (ignores everything that might happen after the end of the single period horizon) • Investments are limited to traded financial assets: (traded financial assets –bonds and stocks) and risk-free borrowing or lending) 9-3 Assumptions Continued • No taxes and transaction costs • Information is costless and available to all investors • Investors are rational mean-variance optimizers: all investors use Markowitz Portfolio Selection Model (minimum-variance frontier, efficient frontier, CAL, optimal risky portfolio and optimal complete portfolio) • There are homogeneous expectations: all investors analyze securities in the same way and share the same economic view 9-4 Resulting Equilibrium Conditions • All investors will hold the same portfolio for risky assets – market portfolio • Market portfolio contains all securities (all traded assets) and the proportion of each security is its market value as a percentage of total market value • Market portfolio: – on the efficient frontier – The tangency portfolio to the optimal CAL 9-5 Figure 9.1 The Efficient Frontier and the Capital Market Line 9-6 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 9-7 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 M2 where 2 M X 0.01 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 wGE E (rGE ) rf E (rGE ) rf GE's contribution to variance 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 Market variance M2 • Reward-to-risk ratios of GE and the market Basic portfolio: Principle: all E (rGE ) rf E (rM ( rf ) Cov (rGE , rM ) 2 M • And the risk premium for GE: E (rGE ) rf Cov (rGE , rM ) 2 M E (rM ) rf investments should offer the same reward-to-risk raito. Otherwise investors will rearrange their portfolios. 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 PositiveAlpha Stock Alpha: the difference between the fair and the actual expected rates of return 9-14 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 9-15 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 9-16 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 9-17 Liquidity and the CAPM • Liquidity • Illiquidity Premium • Research supports a premium for illiquidity. – Amihud and Mendelson – Acharya and Pedersen 9-18 Figure 9.5 The Relationship Between Illiquidity and Average Returns 9-19 Three Elements of Liquidity • Sensitivity of security’s illiquidity to market illiquidity: L1 Cov(Ci , CM ) 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 ) 9-20