A client invested $100 at the start of the month. Assume that the manager tracks an assigned benchmark index. The benchmark is at 100 at the start of the period. After 10 days the portfolio gained 10% (value ? $110), just like the index, and the client added an extra $20 (total portfolio value ? $130). From day 10 to 30, the portfolio, and the index, lost 9.09% [final portfolio value of $130 (1-0.0909) ? $118.18].
a. What are the rates of returns using the various methods outlined in the text?
b. Which rate should you use to evaluate the performance of the manager relative to its benchmark?