The Capital Asset Pricing Model Chapter 9 Bodi Kane Marcus Ch 5

Capital Asset Pricing Model (CAPM) Irwin/McGraw-Hill 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

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

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

Resulting Equilibrium Conditions Irwin/McGraw-Hill 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

Resulting Equilibrium Conditions (cont’d) Irwin/McGraw-Hill Resulting Equilibrium Conditions (cont’d) 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

Capital Market Line E(r) CML M E(rM) rf  m Problem 9-7,8,9,12; p313 Irwin/McGraw-Hill E(r) E(rM) rf M CML m  Problem 9-7,8,9,12; p313

Slope and Market Risk Premium Irwin/McGraw-Hill Slope and Market Risk Premium M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk = Slope of the CAPM  M

Expected Return and Risk on Individual Securities Irwin/McGraw-Hill 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

Security Market Line E(r) SML E(rM) rf ß = 1.0 M Problem 9-6,10,11 Irwin/McGraw-Hill E(r) E(rM) rf SML M ß = 1.0 Problem 9-6,10,11

Bodi Kane Marcus Ch 5 6 E( rA ) < E( rB ) A > B impossible

Bodi Kane Marcus Ch 5 10 E( rA ) < E( rM ) A > M impossible

Bodi Kane Marcus Ch 5 11 E( rA ) < E( rM ) A M possible

SML Relationships = [COV(ri,rm)] / m2 Irwin/McGraw-Hill SML Relationships = [COV(ri,rm)] / m2 Slope SML = E(rm) - rf = market risk premium SML = rf + [E(rm) - rf] Betam = [Cov (ri,rm)] / sm2 = sm2 / sm2 = 1

Sample Calculations for SML Irwin/McGraw-Hill Sample Calculations for SML RPM=E(rm) - rf = .08 rf = .03 x = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% y = .6 e(ry) = .03 + .6 (.08) = .078 or 7.8%

Graph of Sample Calculations Irwin/McGraw-Hill E(r) Rx=13% SML m ß 1.0 Rm=11% Ry=7.8% 3% x 1.25 y .6 .08 Exercise 9.6 - 9.12

Disequilibrium Example Irwin/McGraw-Hill E(r) 15% SML ß 1.0 Rm=11% rf=3% 1.25

Disequilibrium Example Irwin/McGraw-Hill 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

Black’s Zero Beta Model p.301 Irwin/McGraw-Hill Black’s Zero Beta Model p.301 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 Irwin/McGraw-Hill Black’s Zero Beta Model Formulation

Efficient Portfolios and Zero Companions Irwin/McGraw-Hill Efficient Portfolios and Zero Companions Q P Z(Q) Z(P) E[rz (Q)] E[rz (P)] E(r) s

Zero Beta Market Model CAPM with E(rz (m)) replacing rf Irwin/McGraw-Hill Zero Beta Market Model CAPM with E(rz (m)) replacing rf

CAPM & Liquidity Liquidity Illiquidity Premium Irwin/McGraw-Hill CAPM & Liquidity Liquidity Illiquidity Premium Research supports a premium for illiquidity Amihud and Mendelson

CAPM with a Liquidity Premium Irwin/McGraw-Hill CAPM with a Liquidity Premium f (ci) = liquidity premium for security i f (ci) increases at a decreasing rate

Illiquidity and Average Returns Irwin/McGraw-Hill Illiquidity and Average Returns Average monthly return(%) Bid-ask spread (%)

Bodi Kane Marcus Ch 5 THank You