1. MFE 230G Section 1 Hari Phatak 14 August, 2008

2. Introduction Hari Phatak Office: F633 E-mail: nphatak@haas.berkeley.edunphatak@haas.berkeley.edu Web: http://faculty.haas.berkeley.edu/nphatak Sections: Thursdays 10:00am-11:00am Office Hours: Mondays 5:00pm-7:00pm in F621

3. Portfolio Math What is the risk of an equal-weighted portfolio consisting of five stocks, each with 35% volatility and a 50% correlation with all other stocks? How does volatility decrease as the portfolio increases to 20 stocks or 100 stocks?

4. Portfolio Math First solve for the base case of five stocks:

5. Portfolio Math Now generalize to n assets, assuming equal variances and covariances: Note the limiting case of zero correlation

6. Portfolio Math At this point, plug in n=20 and n=100 and solve for portfolio variance: More interestingly, note the limit as n goes to infinity:

7. BLUE Given information about the current performance of GM (-5%) an analyst believes Ford will fall by 3%. If the analyst believes the long-term return on Ford is 3%, what is the analyst’s implied expected return to GM?

9. BLUE What pieces of information are missing?

10. BLUE Suppose the covariance of GM and Ford is 0.015 and the volatility of GM is 20%. Solve for the implied expected return to GM.

11. The Fundamental Law Suppose a portfolio manager is considering a switch from evaluating 100 stocks annually to evaluating them quarterly. What will be the change in the manager’s information ratio?

12. The Fundamental Law(II) Suppose manager A evaluates 500 stocks quarterly and manager B evaluates 1000 stocks annually. Both managers have transfer coefficients of 0.90. If manager A has an IC of 0.03, what is his IR? What IC must manager B attain to match manager A’s information ratio?