Answer-first summary for fast verification
Answer: 1, 2, 3
## Explanation The Sharpe ratio is calculated using the formula: $$ S_p = \frac{E(R_p) - R_f}{\sigma_p} $$ Where: - $E(R_p)$ = Expected portfolio return - $R_f$ = Risk-free rate (6%) - $\sigma_p$ = Portfolio standard deviation Let's calculate the Sharpe ratios for each portfolio: **Portfolio 1:** $$ S_1 = \frac{14\% - 6\%}{21} = \frac{8\%}{21} = 0.3809 $$ **Portfolio 2:** $$ S_2 = \frac{16\% - 6\%}{24} = \frac{10\%}{24} = 0.4167 $$ **Portfolio 3:** $$ S_3 = \frac{20\% - 6\%}{28} = \frac{14\%}{28} = 0.5000 $$ **Ranking from lowest to highest Sharpe ratio:** - Portfolio 1: 0.3809 - Portfolio 2: 0.4167 - Portfolio 3: 0.5000 Therefore, the correct ranking from lowest to highest is **1, 2, 3**, which corresponds to option D. **Note:** The beta values and S&P 500 information are not needed for Sharpe ratio calculations, as Sharpe ratio uses total risk (standard deviation) rather than systematic risk (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&P 500 | 12% | 20 | — |
Given that the risk-free rate of return is 6%, use the Sharpe measure to rank the portfolios from the lowest to the highest.
A
1, 3, 2
B
2, 3, 1
C
2, 1, 3
D
1, 2, 3