# SolCh24 - CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION...

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CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION 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 α ) and the correlation between the portfolio and the market index (ρ): M P P P f P S r r E ρ σ + = - ) ( 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 If the amount invested also increases each period, and then all of the proceeds are withdrawn at the end of several periods, the IRR is greater than either the geometric or the arithmetic average because more money is invested at the higher rates than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, 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 also tremendous potential value in security analysis. The decision as to whether to shift resources has to be made on the basis of the macro, compared to the micro, forecasting ability of the portfolio management team. 24-1

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CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION 4. a. Arithmetic average: % 10 r ABC = ; % 10 r XYZ = b. Dispersion: σ ABC = 7.07%; σ XYZ = 13.91% Stock XYZ has greater dispersion. (Note: We used 5 degrees of freedom in calculating standard deviations.) c.Geometric average: r ABC = (1.20 × 1.12 × 1.14 × 1.03 × 1.01) 1/5 – 1 = 0.0977 = 9.77% r XYZ = (1.30 × 1.12 × 1.18 × 1.00 × 0.90) 1/5 – 1 = 0.0911 = 9.11% Despite the fact that the two stocks have the same arithmetic average, the geometric average for XYZ is less than the geometric average for ABC. The reason for this result is the fact that the greater variance of XYZ drives the geometric average further below the arithmetic average. d.In terms of “forward looking” statistics, the arithmetic average is the better
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## This note was uploaded on 12/06/2011 for the course FINANCE EF4320 taught by Professor Wuxueping during the Spring '09 term at City University of Hong Kong.

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SolCh24 - CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION...

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