Capital Asset Pricing Model

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

2. CAPM • Capital Asset Pricing Model • 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

3. 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

4. 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

5. CAPM • Capital Market Line E[rP] CML M E[rM] rf P M

6. CAPM – a Single Factor Model • CAPM is just a single factor model!

7. 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

8. Security Market Line (SML) • Math and Graphical Representation E(ri) SML E(rM) rf bi bM = 1.0

9. 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:

10. 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

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

12. CAPM Estimation • GM Example (is it such a good stock?)

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

14. 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

15. 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!

16. 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!

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

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