Capital Asset Pricing Model CAPM Security Market Line

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

CAPM q Capital Asset Pricing Model Ø Ø q An equilibrium model underlying modern finance theory Based on diversification principle and simplified assumptions Who developed it? Ø Ø Ø Markowitz: Nobel Prize Sharpe: Nobel Prize Treynor, Lintner and Mossin Investments 11 2

CAPM q Assumptions Ø Individual investors are price takers q Ø Single-period investment horizon q Ø Investors maximize expected utility Homogeneous expectations q q q Ø Individual’s action inconsequential to stock prices Investors do not know the actual outcome Investors agree on the likelihood of each outcome Investors risk aversion may be different Market is frictionless q Investments 11 No taxes, and transaction costs 3

CAPM q Resulting Equilibrium Outcome Ø Ø 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 4

CAPM q Capital Market Line E[r. P] E[r. M] M CML rf M Investments 11 P 5

CAPM – a Single Factor Model q CAPM is just a single factor model! Investments 11 6

CAPM q Expected return on individual security Ø The risk premium on individual securities is equal to its expected return above the risk free rate of return q depends on its contribution to the risk of the market portfolio q depends on its level of systematic risk q Ø The systematic risk is a function of the covariance of returns with the assets that make up the market portfolio q is equal to one for market portfolio q Investments 11 7

Security Market Line (SML) q Math and Graphical Representation E(ri) SML E(r. M) rf i M = 1. 0 Investments 11 8

Security Market Line (SML) q Sample calculations Ø Ø 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: q Security x: q Security y: Investments 11 9

Security Market Line (SML) q Graph of Samples E(r) SML rx=13% r. M=11% ry=7. 8% Market risk premium: 8% rf=3% y=0. 6 M=1. 0 x=1. 25 Investments 11 10

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

CAPM Estimation q GM Example (is it such a good stock? ) Investments 11 12

CAPM and Market Efficiency q q If markets are perfectly efficient, there would be no non-zero alphas! Did this stop people in search for alpha? Investments 11 13

CAPM, Alpha, and Market Efficiency q Non-zero alphas show up as deviations from the SML for individual securities SML E[ri] 15% = 2% rm=11% rf=3% 1. 0 Investments 11 1. 25 14

Investments - It Is All about Alpha! q q Investments – Active vs. Passive Ø Alpha (a) vs. Beta (b) Beta is easy – it is the market Ø q Beta should be free! Alpha is hard, but does it require frequent trading? Ø Ø Ø 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 15

Application - Disequilibrium Example q q Suppose a security with = 1. 25 is offering expected return of 15%, what’s your decision? Solution: Ø Ø Ø 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 16

Arbitrage – How to Get It Done q How does it work? Ø Ø Market portfolio: αM = 0, and βM = 1 If portfolio C has αC = 2%, βC = 1. 25 Show me the money q Long $100 of portfolio C q Short $125 of the market portfolio q Net payoff q q Investments 11 Risk-free two bucks? I’ll take it anytime! 17

Application q Graph of disequilibrium SML E[ri] 15% = 2% rm=11% rf=3% 1. 0 Investments 11 1. 25 18

Wrap-up q What is CAPM? Ø Ø Market risk premium beta What does CAPM tell us? q How to capture the excess risk adjusted return (non-zero )? q Investments 11 19