Capital Asset Pricing Model Investments 11 Capital Asset Pricing Model CAPM Security Market Line CAPM and Market Efficiency Alpha (a) vs. Beta (b)

CAPM Capital Asset Pricing Model Who developed it? An equilibrium model underlying modern finance theory Based on diversification principle and simplified assumptions Who developed it? Markowitz: Nobel Prize Sharpe: Nobel Prize Treynor, Lintner and Mossin Investments 11

CAPM Assumptions Individual investors are price takers Individual’s action inconsequential to stock prices Single-period investment horizon Investors maximize expected utility Homogeneous expectations Investors do not know the actual outcome Investors agree on the likelihood of each outcome Investors risk aversion may be different Market is frictionless No taxes, and transaction costs Investments 11

CAPM Resulting Equilibrium Outcome All investors will hold the same portfolio for risky assets – the 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 Investments 11

CAPM Capital Market Line E[rP] CML M E[rM] rf P M Investments 11

CAPM – a Single Factor Model CAPM is just a single factor model! Investments 11

CAPM Expected return on individual security The risk premium on individual securities is equal to its expected return above the risk free rate of return depends on its contribution to the risk of the market portfolio depends on its level of systematic risk The systematic risk is a function of the covariance of returns with the assets that make up the market portfolio is equal to one for market portfolio Investments 11

Security Market Line (SML) Math and Graphical Representation E(ri) SML E(rM) rf bi bM = 1.0 Investments 11

Security Market Line (SML) Sample calculations Market risk premium is 8%, risk free rate is 3%, security x and y have beta of 1.25 and 0.6, what is the expected return of each based on CAPM? Solution: Security x: Security y: Investments 11

Security Market Line (SML) Graph of Samples E(r) SML rx=13% rM=11% ry=7.8% Market risk premium: 8% rf=3%  y=0.6 M=1.0 x=1.25 Investments 11

CAPM Estimation How to find beta? Find the return data of individual stocks Find the market return data Find the T-bill data Calculate the excess return of Individual stocks Market Run the regression Investments 11

CAPM Estimation GM Example (is it such a good stock?) Investments 11

CAPM and Market Efficiency If markets are perfectly efficient, there would be no non-zero alphas! Did this stop people in search for alpha? Investments 11

CAPM, Alpha, and Market Efficiency Non-zero alphas show up as deviations from the SML for individual securities SML E[ri] 15%  = 2% rm=11% rf=3%  1.0 1.25 Investments 11

Investments - It Is All about Alpha! Investments – Active vs. Passive Alpha (a) vs. Beta (b) Beta is easy – it is the market Beta should be free! Alpha is hard, but does it require frequent trading? Not necessarily – it is about taking right long-term positions, and identifying underpriced factors Good old “Buy Low – Sell High” always works!!! Not having too many constraints helps Investments 11

Application - Disequilibrium Example Suppose a security with  = 1.25 is offering expected return of 15%, what’s your decision? Solution: According to SML (CAPM), it should offer 13%  = 15% – 13%=2% Under-priced: offering too high a rate of return for its level of risk, what to do? What is then over-priced? – It is the market index!!! Long a portfolio C of similar stocks and short a market portfolio! Investments 11

Arbitrage – How to Get It Done How does it work? Market portfolio: αM = 0, and βM = 1 If portfolio C has αC = 2%, βC = 1.25 Show me the money Long $100 of portfolio C Short $125 of the market portfolio Net payoff Risk-free two bucks? I’ll take it anytime! Investments 11

Application Graph of disequilibrium  SML E[ri] 15%  = 2% rm=11% rf=3%  1.0 1.25 Investments 11

Wrap-up What is CAPM? What does CAPM tell us? Market risk premium beta What does CAPM tell us? How to capture the excess risk adjusted return (non-zero )? Investments 11