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Answer: The Modigliani-squared measure, which shows that Manager 2 outperforms Manager 1 by 2%
B is correct. When comparing the performances of portfolios that are not fully diversified, the appropriate measure to use is Sharpe or M2; Sharpe to rank the performance of the portfolios, M2 to calculate by how much one portfolio outperforms/underperforms the market or the other portfolio. Treynor ratio is appropriate to use when we are comparing many portfolios to form an overall portfolio. Because the number of portfolios combined is high, nonsystematic risk is largely diversified away and beta (rather than standard deviation) can be used to measure risk. This is not the case here. The investor in the question is interested in total risk. According to the provided data, Manager2 has a higher Sharpe ratio (1.79) compared to Manager1 (1.61) and an M2 measure of -0.01 compared to Manager1's -0.03, indicating that Manager2 outperforms Manager1 by 2%. Therefore, the Modigliani-squared measure shows that Manager 2 outperforms Manager 1 by 2%.
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To comprehensively evaluate the performances of two portfolio managers, each allocated the same amount of investment capital and operating under identical strategies and constraints with undiversified portfolios, consider the following context: Both managers have provided data on their respective average returns, betas relative to the market index, standard deviations of returns, and tracking errors, while the risk-free rate of interest is 3%. Given this information, which performance metric should be employed, and what is the correct inference to draw from the comparison?
A
The Modigliani-squared measure, which shows that Manager 1 outperforms Manager 2 by 2%
B
The Modigliani-squared measure, which shows that Manager 2 outperforms Manager 1 by 2%
C
Treynor's measure, which shows that Manager 1 outperforms Manager 2 by 6%
D
Treynor's measure, which shows that Manager 2 outperforms Manager 1 by 6%