10-1 CHAPTER 10 The Capital Asset Pricing Model (CAPM) McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-2 Chapter Outline 10.1 Individual Securities 10.2 Expected Return, Variance, and Covariance 10.3 The Return and Risk for Portfolios 10.4 The Efficient Set for Two Assets 10.5 The Efficient Set for Many Securities 10.6 Diversification: An Example 10.7 Riskless Borrowing and Lending 10.8 Market Equilibrium 10.9 Relationship between Risk and Expected Return (CAPM) 10.10 Summary and Conclusions McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-3 10.1 Individual Securities The characteristics of individual securities that are of interest are the: Expected Return Variance and Standard Deviation Covariance and Correlation McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-4 10.2 Expected Return, Variance, and Covariance Rate of Return Scenario Probability Stock fund Bond fund Recession 33.3% -7% 17% Normal 33.3% 12% 7% Boom 33.3% 28% -3% Consider the following two risky asset world There is a 1/3 chance of each state of the economy and the only assets are a stock fund and a bond fund McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-5 10.2 Expected Return, Variance, and Covariance Scenario Recession Normal Boom Expected return Variance Standard Deviation McGraw-Hill/Irwin Corporate Finance, 7/e Stock fund Rate of Squared Return Deviation -7% 3.24% 12% 0.01% 28% 2.89% 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 1.00% 7% 0.00% -3% 1.00% 7.00% 0.0067 8.2% © 2005 The McGraw-Hill Companies, Inc All Rights 10-6 10.2 Expected Return, Variance, and Covariance Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock fund Rate of Squared Return Deviation -7% 3.24% 12% 0.01% 28% 2.89% 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 1.00% 7% 0.00% -3% 1.00% 7.00% 0.0067 8.2% E (rS ) = × ( −7%) + × (12%) + × (28%) 3 E (rS ) = 11% McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-7 10.2 Expected Return, Variance, and Covariance Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock fund Rate of Squared Return Deviation -7% 3.24% 12% 0.01% 28% 2.89% 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 1.00% 7% 0.00% -3% 1.00% 7.00% 0.0067 8.2% E (rB ) = × (17%) + × (7%) + × ( −3%) 3 E (rB ) = 7% McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-8 10.2 Expected Return, Variance, and Covariance Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock fund Rate of Squared Return Deviation -7% 3.24% 12% 0.01% 28% 2.89% 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 1.00% 7% 0.00% -3% 1.00% 7.00% 0.0067 8.2% − − (11% 7%) = 3.24% McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-9 10.2 Expected Return, Variance, and Covariance Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock fund Rate of Squared Return Deviation -7% 3.24% 12% 0.01% 28% 2.89% 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 1.00% 7% 0.00% -3% 1.00% 7.00% 0.0067 8.2% − (11% 12%) = 01% McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1010 10.2 Expected Return, Variance, and Covariance Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock fund Rate of Squared Return Deviation -7% 3.24% 12% 0.01% 28% 2.89% 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 1.00% 7% 0.00% -3% 1.00% 7.00% 0.0067 8.2% − (11% 28%) = 2.89% McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1034 return Market Equilibrium CM L 100% stocks Balanced fund rf 100% bonds σ Just where the investor chooses along the Capital Asset Line depends on his risk tolerance The big point though is that all investors have the same CML McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1035 return Market Equilibrium CM L 100% stocks Optimal Risky Portfolio rf 100% bonds All investors have the same CML because they all have the σ same optimal risky portfolio given the risk-free rate McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights The Separation Property return 1036 CM L 100% stocks Optimal Risky Portfolio rf 100% bonds The separation property implies that portfolio choice can be separated into two tasks: (1) determine the optimal σ risky portfolio, and (2) selecting a point on the CML McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights Optimal Risky Portfolio with a Risk-Free Asset return 1037 f f r r L CML CM 100% stocks First Optimal Risky Portfolio Second Optimal Risky Portfolio 100% bonds By the way, the optimal risky portfolio depends on the risk-free rate σ as well as the risky assets McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1038 Definition of Risk When Investors Hold the Market Portfolio Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (β)of the security Beta measures the responsiveness of a security to movements in the market portfolio Cov ( Ri , RM ) βi = σ2 ( RM ) McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights Estimating β with regression Security Returns 1039 ne i L c i t s i r e t ac r a h C Slope = βi Return on market % Ri = α i + β i Rm + e i McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1040 Estimates of β for Selected Stocks Stock Beta Bank of America 1.55 Borland International 2.35 Travelers, Inc 1.65 Du Pont 1.00 Kimberly-Clark Corp 0.90 Microsoft 1.05 Green Mountain Power 0.55 Homestake Mining 0.20 Oracle, Inc 0.49 McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1041 The Formula for Beta Cov ( Ri , RM ) βi = σ ( RM ) Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1042 10.9 Relationship between Risk and Expected Return (CAPM) Expected Return on the Market: R M = RF + Market Risk Premium Expected return on an individual security: R i = RF + β i × ( R M − RF ) Market Risk Premium This applies to individual securities held within welldiversified portfolios McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1043 Expected Return on an Individual Security This formula is called the Capital Asset Pricing Model (CAPM) Ri = RF + βi × ( RM −RF ) Expected return on a security Risk= + free rate Beta of the security ì Market risk premium Assume βi = 0, then the expected return is RF • Assume βi = 1, then Ri = RM McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights Relationship Between Risk & Expected Return Expected return 1044 Ri = RF + βi × ( RM −RF ) RM RF 1.0 McGraw-Hill/Irwin Corporate Finance, 7/e β © 2005 The McGraw-Hill Companies, Inc All Rights Relationship Between Risk & Expected Return Expected return 1045 13.5% 3% β i = 1.5 RF = 3% 1.5 β RM = 10% R i = 3% + 1.5 × (10% − 3%) = 13.5% McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1046 10.10 Summary and Conclusions This chapter sets forth the principles of modern portfolio theory The expected return and variance on a portfolio of two securities A and B are given by E (rP ) = wA E (rA ) + wB E (rB ) 2 σP = (wA σ A ) + (wB σB ) + 2(wB σB )(wA σ A )ρAB By varying wA, one can trace out the efficient set of portfolios We graphed the efficient set for the two-asset case as a curve, pointing out that the degree of curvature reflects the diversification effect: the lower the correlation between the two securities, the greater the diversification The same general shape holds in a world of many assets McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1047 10.10 Summary and Conclusions return The efficient set of risky assets can be combined with riskless borrowing and lending In this case, a rational investor will always choose to hold the portfolio of risky securities represented by the market portfolio L efficient frontier CM Then with borrowing or lending, the M investor selects a point along the CML rf σP McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 1048 10.10 Summary and Conclusions The contribution of a security to the risk of a well-diversified portfolio is proportional to the covariance of the security's return with the market’s return This contribution is called the beta Cov( Ri , RM ) βi = σ ( RM ) The CAPM states that the expected return on a security is positively related to the security’s beta: Ri = RF + βi × ( RM −RF ) McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights ... fund rf 100% bonds Now investors can allocate their money across the T-bills and a σ balanced mutual fund McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights... Expected Return Variance and Standard Deviation Covariance and Correlation McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-4 10.2 Expected Return, Variance,... state of the economy and the only assets are a stock fund and a bond fund McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc All Rights 10-5 10.2 Expected Return, Variance,