Answer-first summary for fast verification
Answer: 1, 2, 3
## Explanation The Treynor measure is calculated as: \[\text{Treynor Ratio} = \frac{R_p - R_f}{\beta_p}\] Where: - \(R_p\) = Portfolio return - \(R_f\) = Risk-free rate (6%) - \(\beta_p\) = Portfolio beta **Calculations:** - **Portfolio 1:** \(\frac{14\% - 6\%}{1.15} = \frac{8\%}{1.15} = 6.96\%\) - **Portfolio 2:** \(\frac{16\% - 6\%}{1.00} = \frac{10\%}{1.00} = 10.00\%\) - **Portfolio 3:** \(\frac{20\% - 6\%}{1.25} = \frac{14\%}{1.25} = 11.20\%\) **Ranking from lowest to highest Treynor ratio:** - Portfolio 1: 6.96% - Portfolio 2: 10.00% - Portfolio 3: 11.20% Therefore, the correct ranking from lowest to highest is **1, 2, 3**. **Key Points:** - The Treynor measure evaluates risk-adjusted performance using only systematic risk (beta) - Higher Treynor ratios indicate better risk-adjusted performance - Portfolio 3 has the highest return but also the highest beta, resulting in the best Treynor ratio - Portfolio 1 has the lowest Treynor ratio despite having moderate returns due to its high beta
Author: Tanishq Prabhu
Ultimate access to all questions.
No comments yet.
A 10-year research on 3 distinct portfolios and the market reveals the following information:
| Portfolio | Average Annual Return | Standard Deviation | Beta |
|---|---|---|---|
| 1 | 14% | 21 | 1.15 |
| 2 | 16% | 24 | 1.00 |
| 3 | 20% | 28 | 1.25 |
| S&P500 | 12% | 20 | — |
If the risk-free rate is 6%, then use the Treynor measure to rank the portfolios from the lowest to the highest.
A
1, 2, 3
B
2, 3, 1
C
3, 2, 1
D
1, 3, 2