McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter 9 Capital Asset Pricing

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Capital Asset Pricing Model (CAPM) 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Assumptions Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes, and transaction costs Information is costless and available to all investors Investors are rational mean-variance optimizers Homogeneous expectations

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. E(r) E(r M ) rfrfrfrf M CML mmmm Capital Market Line 

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Slope and Market Risk Premium M=Market portfolio r f =Risk free rate E(r M ) - r f =Market risk premium E(r M ) - r f =Market price of risk =Slope of the CAPM M 

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Components of Risk Market or systematic risk: risk related to the macro economic factor or market index Unsystematic or firm specific risk: risk not related to the macro factor or market index Total risk = Systematic + Unsystematic

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Single Index Model Risk Prem Market Risk Prem or Index Risk Prem or Index Risk Prem i = the stock’s expected return if the market’s excess return is zero market’s excess return is zero ß i (r m - r f ) = the component of return due to movements in the market index movements in the market index (r m - r f ) = 0 e i = firm specific component, not due to market movements movements 

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Let: R i = (r i - r f ) R m = (r m - r f ) R m = (r m - r f ) Risk premium format R i =  i + ß i (R m ) + e i Risk Premium Format

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Estimating the Index Model Excess Returns (i) SecurityCharacteristicLine Excess returns on market index R i =  i + ß i R m + e i

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Expected Return and Risk on Individual Securities The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Examining Percentage of Variance Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk =  2 ß i 2  m 2 /  2 =  2  i 2  m 2 /  i 2  m 2 +  2 (e i ) =  2 This is useful information since it tells us how well B explains the security’s returns. Will be between 0 and 100%.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. E(r) E(r M ) rfrfrfrf SML M ß ß = 1.0 Security Market Line

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. SML Relationships  = [COV(r i,r m )] /  m 2 Slope SML =E(r m ) - r f =market risk premium SML = r f +  [E(r m ) - r f ]

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Sample Calculations for SML E(r m ) - r f =.08r f =.03  x = 1.25 E(r x ) = (.08) =.13 or 13%  y =.6 e(r y ) = (.08) =.078 or 7.8%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. E(r) R x =13% SML m m ß ß 1.0 R m =11% R y =7.8% 3% x x ß 1.25 y y ß.6.08 Graph of Sample Calculations

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. E(r) 15% SML ß 1.0 R m =11% r f =3% 1.25 Disequilibrium Example

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Disequilibrium Example Suppose a security with a  of 1.25 is offering expected return of 15% According to SML, it should be 13% Underpriced: offering too high of a rate of return for its level of risk

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Stock A has an estimated rate of return of 12% and a beta of 1.2. The market expected rate of return is 12% and the risk-free rate is 2%. The alpha of the stock is __________. A) 0% B) -2% C) 2% D) -4%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. You invest $8,000 in stock A with a beta of 1.4 and $12,000 in security B with a beta of 0.8. The beta of this formed portfolio is __________. A) 1.10 B) 1.20 C) 1.04 D) 2.20

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Which of the following is(are) correct according to the CAPM: A) There is a linear and positive relationship between a stock's beta and its required return. B) The expected return of a stock will be doubled if its beta increases from 1 to 2. C) There is a linear and positive relationship between a portfolio's standard deviation and its required return. D) All of the above are correct.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Which one of the following stocks is relatively more risky when held in a well-diversified portfolio? StockStandard DeviationBeta ABC35%1.2 XYZ30%1.6 A) ABC because its beta is lower. B) XYZ because its beta is higher. C) ABC because its standard deviation is higher. D) XYZ because its standard deviation is lower.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. The expected market rate of return is 14% while the risk-free rate expected return is 4%. If you expect stock A with a beta of 1.2 to offer a rate of return of 20%, then you should __________. A) buy stock A because it is overpriced B) buy stock A because it is underpriced C) sell short stock A because it is overpriced D) sell short stock A because it is underpriced

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. The slope of the Security Market Line is ____________. A) the beta B) the risk-free rate of return C) the market return D) the market risk premium

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. The expected return on the market is 12%. The expected return on a stock with a beta of 1.5 is 17%. What is the risk-free rate of return according to the CAPM? A) 2% B) 6% C) 8% D) 5%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. According to the CAPM, a stock with a high standard deviation must have a beta ________ that of a stock with a low standard deviation. A) higher than B) lower than C) the same as D) There is not sufficient information to determine.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. The expected risk-free rate of return is 4%. The expected return on a stock with a beta of 1.2 is 16%. What is the expected return on the market according to the CAPM? A) 12% B) 14% C) 18% D) 15%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. According to the systematic risk principle, which one of the following risks is rewarded? A) Unsystematic risk. B) Total risk. C) Systematic risk. D) Industry risk.