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Answer: The Treynor measure of performance
## Explanation The **Treynor measure** is most appropriate here for several reasons: **Why Treynor over other measures:** 1. **Beta information is provided** - All three managers have different betas (1.35, 1.95, 2.10), indicating different levels of systematic risk 2. **Client context** - The firm manages $400 million allocated among multiple managers, suggesting clients likely hold diversified portfolios where unsystematic risk is minimized 3. **Systematic risk focus** - When evaluating professional managers for institutional clients, systematic risk is typically the primary concern since unsystematic risk can be diversified away 4. **Different betas** - The managers have substantially different betas, making the Treynor ratio ideal for comparing risk-adjusted performance across different systematic risk levels **Treynor Ratio Formula:** \[\text{Treynor Ratio} = \frac{R_p - R_f}{\beta_p}\] Where: - \(R_p\) = Portfolio return - \(R_f\) = Risk-free rate - \(\beta_p\) = Portfolio beta While we don't have the risk-free rate in the data, the Treynor measure is still the conceptually correct choice given the context and available information.
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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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