Problem Four (15 points): Suppose that the actual rate of return on the S&P 500 index from December 17, 2001 (today) to December 17, 2002 (12 months hence) is 9.0%, including dividends paid by companies in the index. You are given the following information about the performance of mutual funds X Y and Z. Each mutual fund invests only in common stocks. R2 .92 .88 .65 ) Fund manager X (Gladys Friday) Y (Gene Pool) Z (Hugh Betcha) Rate of return 9.8% 9.0% 13.4% Alpha (SE) +.48% (1.0%) -,65% (3.0%) +.50% (3.1%) Beta (SE) 1.05(.05) 1.10(.07) 1.60(.09) Alphas and betas are estimated from 52 weekly returns from December 2001 to December 2002. Returns and alphas are given above as annual percentage returns. SE means standard error. The start-of-year risk-free rate is 2.5%. Based on these statistics, what can you say about the investment strategy and performance of each of the three managers? Explain. Consider risk as well as return before answering