2. Capital Asset Pricing Model CAPM Security Market Line CAPM and Market Efficiency Alpha (  ) vs. Beta (  )

3. Investments 112 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

4. Investments 113 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

5. Investments 114 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

6. Investments 115 CAPM  Capital Market Line E[r P ] E[r M ] rfrfrfrf M CML MMMM PPPP

7. Investments 116 CAPM – a Single Factor Model  CAPM is just a single factor model!

8. Investments 117 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

9. Investments 118 Security Market Line (SML)  Math and Graphical Representation E(r i ) E(r M ) rfrfrfrf SML iiii MMMM = 1.0

10. Investments 119 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:

11. Investments 1110 Security Market Line (SML)  Graph of Samples E(r) r x =13% SML   M =1.0 r M =11% r y =7.8% r f =3%  x =1.25  y =0.6 Market risk premium: 8%

12. Investments 1111 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

13. Investments 1112 CAPM Estimation  GM Example (is it such a good stock?)

14. Investments 1113 CAPM and Market Efficiency  If markets are perfectly efficient, there would be no non-zero alphas!  Did this stop people in search for alpha?

15. Investments 1114 Investments - It Is All about Alpha!  Investments – Active vs. Passive  Alpha (  ) vs. Beta (  )  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

16. Investments 1115 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!

17. Investments 1116 Arbitrage – How to Get It Done  How does it work?  Market portfolio: α M = 0, and β M = 1  If portfolio C has α C = 2%, β C = 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!

18. Investments 1117 Application  Graph of disequilibrium E[r i ] 15% SML 1.0 r m =11% r f =3% 1.25  = 2% 

19. Investments 1118 Wrap-up  What is CAPM?  Market risk premium  beta  What does CAPM tell us?  How to capture the excess risk adjusted return (non-zero  )?