《《Investment 8th Chap024》.docVIP

CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION PROBLEM SETS 1. As established in the following result from the text, the Sharpe ratio depends on both alpha for the portfolio (( P) and the correlation between the portfolio and the market index (ρ): Specifically, this result demonstrates that a lower correlation with the market index reduces the Sharpe ratio. Hence, if alpha is not sufficiently large, the portfolio is inferior to the index. Another way to think about this conclusion is to note that, even for a portfolio with a positive alpha, if its diversifiable risk is sufficiently large, thereby reducing the correlation with the market index, this can result in a lower Sharpe ratio. 2. The IRR (i.e., the dollar-weighted return) can not be ranked relative to either the geometric average return (i.e., the time-weighted return) or the arithmetic average return. Under some conditions, the IRR is greater than each of the other two averages, and similarly, under other conditions, the IRR can also be less than each of the other averages. A number of scenarios can be developed to illustrate this conclusion. For example, consider a scenario where the rate of return each period consistently increases over several time periods. If the amount invested also increases each period, and then all of the proceeds are withdrawn at the end of several periods, the IRR is greater than either the geometric or the arithmetic average because more money is invested at the higher rates than at the lower rates. On the other hand, if withdrawals gradually reduce the amount invested as the rate of return increases, then the IRR is less than each of the other averages. (Similar scenarios are illustrated with numerical examples in the text, on page 824, where the IRR is shown to be less than the geometric average, and in Concept Check 1, where the IRR is greater than the geometric average.) 3. It is not necessarily wise to shift resources to timing at the expense of security selection. There is al