1. Capital Asset Pricing Model Applied covariance: Project Part 1

2. Review variance, covariance  Variance: square the deviations and take expectation.  Covariance: multiply the deviations and take expectation.

3. Application  Asset B is the market portfolio  Call it asset M.  Everyone prefers to hold M, in theory  Asset A is any asset.  Think of adding a little A to the market portfolio.

4. Question  does adding a little of asset A to the market portfolio increase the risk?  Yes if No if

5. Derivation

6. Beta measures risk  How much risk is added depends on the relation of sigma AM and sigma squared M  Define beta

7. Sum of squared errors Minimize it

8. Divide by T-1

9. The estimate of   Is the ratio of sample covariance over variance of the market.  It’s beta, except for using sample statistics instead of population values.

10. The story of CAPM  Investors prefer higher expected return and dislike risk.  All have the same information.  Two (mutual) funds are sufficient to satisfy all such investors:

11. The two funds:  1) The "risk-free" asset, i.e., Treasury Bills  2) The market portfolio consisting of all risky assets held in proportion to their market value.

12. The market portfolio  Its expected return is 8.5% over the T- Bill rate  It bears the market risk  Its beta is unity by definition.

13. Capital asset pricing model T-bill rate is known. Market premium is known, approximately 8.5%. Estimate beta as in the project

14. Security market line  It’s straight.  Risk-return relation is a straight line.

15. Why is it a straight line?  Beta is the measure of risk that matters.  Given beta construct a portfolio with the same beta by a mix of T-Bills (beta = 0) and the market portfolio (beta = 1)  Expected return on the portfolio is on the SML.  So any asset with the same beta must also be on the SML.

16. beta Rate of return expected by the market RfRf E[R M ] Security market line 1

17. Review item  Return on asset A has a std dev of.05  Return on asset B has a std dev of.07  Correlation of return on asset A with return on asset B is 1.  What is the covariance of the returns?

18. Answer:  Covar = corr*stdevA*stdevB=.0035