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Answer: The Modigliani-squared measure, which shows that Manager 2 outperforms Manager 1 by 2%
## Explanation When comparing the performances of portfolios that are **not fully diversified**, the appropriate measure to use is either the **Sharpe ratio** or the **Modigliani-squared (M²) measure**. ### Key Points: - **Treynor's measure** is appropriate when comparing many portfolios to form an overall portfolio, where nonsystematic risk is largely diversified away and beta can be used to measure risk. - **M² measure** is used to calculate by how much one portfolio outperforms/underperforms the market or another portfolio when portfolios are not fully diversified. ### Calculations: Based on the provided data table in the explanation: - **Manager 1 M²**: -0.03 (underperforms market) - **Manager 2 M²**: -0.01 (underperforms market but less than Manager 1) - **Difference**: Manager 2 outperforms Manager 1 by approximately 2% ### Why Other Options Are Incorrect: - **A**: Incorrect - Manager 1 does not outperform Manager 2 - **C & D**: Incorrect - Treynor's measure is not appropriate for undiversified portfolios Therefore, the Modigliani-squared measure correctly shows that Manager 2 outperforms Manager 1 by 2%.
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An investor is comparing the performances of two portfolio managers who have been allocated an equal amount of investment funds. The managers apply the same strategy with the same constraints, and their portfolios are not diversified. The investor gathers the following data about the two managers and the market index:
| Manager 1 | Manager 2 | Market index | |
|---|---|---|---|
| Average return | 32% | 28% | 22% |
| Beta with respect to market index | 1.2 | 1.4 | 1.0 |
| Standard deviation of returns | 18% | 14% | 10% |
| Tracking error | 8% | 6% | 0% |
The risk-free rate of interest is 3%. Which of the following is an appropriate measure to use and the correct conclusion to reach when comparing the performances of the two managers?
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%
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