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Answer: The Treynor measure of performance
## Explanation The **Treynor measure** is the most appropriate performance measure in this scenario because: 1. **Beta information is provided** - All three portfolio managers have beta values (1.35, 1.95, 2.10), indicating we have systematic risk data 2. **Risk-adjusted performance comparison** - The Treynor ratio specifically measures excess return per unit of systematic risk (beta) 3. **Formula**: Treynor Ratio = (Portfolio Return - Risk-Free Rate) / Beta ### Why not other measures: - **Sharpe ratio**: Uses total risk (standard deviation) rather than systematic risk - **Jensen's alpha**: Requires risk-free rate data which is not provided - **Sortino ratio**: Focuses on downside risk only and requires minimum acceptable return Since we have beta values and want to compare performance relative to systematic risk exposure, the Treynor measure is the optimal choice for this analysis.
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Donaldson Capital Management, a regional money management firm, manages nearly $400 million allocated among three investment managers. All portfolios have the same objective, which is to produce superior risk-adjusted returns (by beating the market) for their clients. You have been hired as a consultant to measure the performance of the portfolio managers. You have collected the following information based on the last ten years of returns.
| Portfolio Manager | Mean Annualized Rate of Return | Beta | Standard Deviation of Return |
|---|---|---|---|
| a | 0.18 | 1.35 | 0.24 |
| b | 0.21 | 1.95 | 0.25 |
| c | 0.24 | 2.10 | 0.22 |
During the same time period the average annual rate of return on the market portfolio was 13% with a standard deviation of 19%. In order to assess the portfolio performance of the above managers, you should use:
A
The Treynor measure of performance
B
The Sharpe measure of performance
C
The Jensen measure of performance
D
The Sortino measure of performance
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