The Capital Asset Pricing Model Chapter 9

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)

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

Information is costless and available to all investors Investors are rational mean-variance optimizers Homogeneous expectations Assumptions (cont’d)

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

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 Resulting Equilibrium Conditions (cont’d)

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

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

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 Expected Return and Risk on Individual Securities

Security Market Line E(r) E(r M ) rfrf SML M ß ß = 1.0

 = [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

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

Graph of Sample Calculations E(r) R x =13% SML m ß ß 1.0 R m =11% R y =7.8% 3% x ß 1.25 y ß.6.08

Disequilibrium Example E(r) 15% SML ß 1.0 R m =11% r f =3% 1.25

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 Disequilibrium Example

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

Black’s Zero Beta Model Formulation

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

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

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

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

Illiquidity and Average Returns Average monthly return(%) Bid-ask spread (%)