McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 9 The Capital Asset Pricing Model

9-2 It is the equilibrium model that is a centerpiece of modern financial theory. It gives us a precise prediction of the relationship between risk and return. Gives us a benchmark to make comparisons Gives us a way to evaluate non traded assets such as investment projects (use in Capital Budgeting) Derived using principles of diversification with simplified assumptions. Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development. Capital Asset Pricing Model (CAPM)

9-3 Individual investors are price takers. Single-period investment horizon. Investments are limited to traded financial assets. No taxes and transaction costs. Assumptions

9-4 Information is costless and available to all investors. Investors are rational mean-variance optimizers. There are homogeneous expectations. Assumptions (cont’d)

9-5 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. (What would happen if this were not true?) Resulting Equilibrium Conditions

9-6 Capital Market Line E(r) E(r M ) rfrf M CML mm  The CML is the CAL between the risk free asset and the Market Portfolio

9-7 Derivation of the CAPM

9-8 Recall the optimal choice equation Given that on balance, for every $1 borrower there must be $1 lent, we can plug y=1 into this equation and compute the market risk premium – it depends on variance of the market portfolio, and overall average risk aversion

9-9 Risk premium on the 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. i.e. the beta Resulting Equilibrium Conditions (cont’d)

9-10 Mutual Fund Theorem The passive investment strategy is efficient Another way of stating the “separation theorem” of last chapter Portfolio selection has two components First the technological to create a mutual fund of the market portfolio (index fund) Second to optimize to an individual, based on risk tolerance, how much of the risk free each person should hold

9-11 M=Market portfolio r f =Risk free rate E(r M ) - r f =Market risk premium E(r M ) - r f =Market reward to variability =Slope of the CAPM M  Slope and Market Risk Premium

9-12 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 (i.e. the beta). An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio.

9-13 Security Market Line (Graph of CAPM) E(r) E(r M ) rfrf SML    = 1.0

9-14  = [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 ] Beta m = [Cov (r m,r m )] /  m 2 =  m 2 /  m 2 = 1 SML Relationships

9-15 E(r m ) - r f =.08 (market risk premium) r f =.03  x = 1.25 E(r x ) = (0.08) =.13 or 13%  y =.6 E(r y ) = (0.08) =.078 or 7.8% These show, the expected return is a function of beta Sample Calculations for SML

9-16 Graph of Sample Calculations E(r) R x =13% SML  1.0 R m =11% R y =7.8% 3% 1.25  x.6  y.08

9-17 Suppose a security with a  of 1.25 is offering expected return of 15%. According to SML, it should be 13%. This security has an alpha of 2% Under-priced: offering too high of a rate of return for its level of risk. The price must rise, so that the expected return falls to 13% to regain equilibrium Disequilibrium Example

9-18 Disequilibrium Example (illustrate alpha) E(r) 15% SML  1.0 R m =11% r f =3% 1.25 “alpha” is the vertical distance from a point to the line

9-19 Adjustments to CAPM Black’s zero beta version if there is no risk free Adjustments to consider liquidity (require a reward for bearing illiquidity) Market to Book ratio’s seem to have empirical value (No theoretical basis)

9-20

9-21 Black’s Zero Beta Model Absence of a risk-free asset Combinations of portfolios on the efficient frontier are efficient. All frontier portfolios have companion portfolios that are uncorrelated. Returns on individual assets can be expressed as linear combinations of efficient portfolios.

9-22 Black’s Zero Beta Model Formulation

9-23 Efficient Portfolios and Zero Companions Q P Z(Q) Z(P) E[r z (Q) ] E[r z (P) ] E(r) 

9-24 Zero Beta Market Model CAPM with E(r z (m) ) replacing r f

9-25 CAPM & Liquidity Liquidity Illiquidity Premium Research supports a premium for illiquidity. Amihud and Mendelson

9-26 CAPM with a Liquidity Premium f (c i ) = liquidity premium for security i f (c i ) increases at a decreasing rate

9-27 Liquidity and Average Returns Average monthly return(%) Bid-ask spread (%)