Financial Risk Manager Part 1
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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.
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TTanishq
Explanation:
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
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