McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Asset Pricing Models: CAPM & APT

9-2 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. 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. Resulting Equilibrium Conditions

9-6 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. Resulting Equilibrium Conditions (cont’d)

9-7 Capital Market Line E(r) E(r M ) rfrf M CML mm 

9-8 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  Slope and Market Risk Premium

9-9 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. Return and Risk For Individual Securities

9-10 Security Market Line E(r) E(r M ) rfrf SML    = 1.0

9-11  = [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 i,r m )] /  m 2 =  m 2 /  m 2 = 1 SML Relationships

9-12 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% Sample Calculations for SML

9-13 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

9-14 Disequilibrium Example E(r) 15% SML  1.0 R m =11% r f =3% 1.25

9-15 Suppose a security with a  of 1.25 is offering expected return of 15%. According to SML, it should be 13%. Under-priced: offering too high of a rate of return for its level of risk. Disequilibrium Example (cont.)

9-16 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.

9-17 Black’s Zero Beta Model Formulation

9-18 Efficient Portfolios and Zero Companions Q P Z(Q) Z(P) E[r z (Q) ] E[r z (P) ] E(r) 

9-19 Zero Beta Market Model CAPM with E(r z (m) ) replacing r f

9-20 CAPM & Liquidity Liquidity Illiquidity Premium Research supports a premium for illiquidity. Amihud and Mendelson

9-21 CAPM with a Liquidity Premium f (c i ) = liquidity premium for security i f (c i ) increases at a decreasing rate

9-22 Liquidity and Average Returns Average monthly return(%) Bid-ask spread (%)

9-23 Arbitrage Pricing Theory Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit. Since no investment is required, an investor can create large positions to secure large levels of profit. In efficient markets, profitable arbitrage opportunities will quickly disappear.

9-24 APT & Well-Diversified Portfolios r P = E (r P ) +  P F + e P F = some factor For a well-diversified portfolio: e P approaches zero Similar to CAPM

9-25 Portfolios and Individual Security F E(r)% Portfolio F E(r)% Individual Security

9-26 Disequilibrium Example E(r)% Beta for F Risk Free 4 A D C.51.0

9-27 Disequilibrium Example Short Portfolio C Use funds to construct an equivalent risk higher return Portfolio D. D is comprised of A & Risk-Free Asset Arbitrage profit of 1%

9-28 E(r)% Beta (Market Index) Risk Free M 1.0 [E(r M ) - r f ] Market Risk Premium »APT with Market Index Portfolio

9-29 APT applies to well diversified portfolios and not necessarily to individual stocks. With APT it is possible for some individual stocks to be mispriced - not lie on the SML. APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio. APT can be extended to multifactor models. APT and CAPM Compared