An adviser is comparing four funds over the same three-year period, during which Treasury bills yielded 3%. Based on the data shown, which fund delivered the highest excess return per unit of total risk?
| Fund | Return | Standard deviation | Beta |
|---|---|---|---|
| Fund W | 8% | 6% | 0.6 |
| Fund X | 14% | 18% | 1.0 |
| Fund Y | 10% | 9% | 0.5 |
| Fund Z | 12% | 10% | 1.2 |
Show answer & explanation
Answer: D
- Sharpe = (Rp − Rf) ÷ σp
- W: (8 − 3) ÷ 6 = 0.83; X: (14 − 3) ÷ 18 = 0.61
- Y: (10 − 3) ÷ 9 = 0.78; Z: (12 − 3) ÷ 10 = 0.90
- Fund Z has the highest Sharpe ratio. Beta is not used because the question asks about total risk
Fund W: Fund W has the lowest volatility, but (8 − 3) ÷ 6 = 0.83, below Fund Z's 0.90.
Fund X: Fund X has the highest raw return, but (14 − 3) ÷ 18 = 0.61, the lowest risk-adjusted result.
Fund Y: Fund Y has the best Treynor ratio, (10 − 3) ÷ 0.5 = 14, but Treynor uses beta (systematic risk). Its Sharpe ratio is (10 − 3) ÷ 9 = 0.78.
Fund Z: Correct — Fund Z's Sharpe ratio is (12 − 3) ÷ 10 = 0.90, the highest of the four, so it earned the most excess return per unit of total risk (standard deviation).
Sharpe = (Rp − Rf) ÷ σp measures excess return per unit of total risk. Treynor divides by beta instead and measures systematic risk only.