gen-define-the-sharpe-ratio-and-give-one-short-worked-example-686c

Define the Sharpe ratio and give one short worked example.

# Sharpe Ratio The **Sharpe ratio** measures the excess return per unit of risk for an investment. It's calculated as: $$\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}$$ Where: - **R_p** = Average return of the portfolio - **R_f** = Risk-free rate of return - **σ_p** = Standard deviation of the portfolio's returns A higher Sharpe ratio indicates better risk-adjusted performance. ## Worked Example Suppose you're evaluating a mutual fund with the following annual data: - Average return: 12% - Standard deviation: 15% - Risk-free rate (Treasury bills): 2% $$\text{Sharpe Ratio} = \frac{0.12 - 0.02}{0.15} = \frac{0.10}{0.15} = 0.67$$ **Interpretation**: The fund generates 0.67 units of excess return for each unit of risk taken. This can be compared to other investments—a fund with a Sharpe ratio of 1.0 would be preferable, as it delivers more return per unit of risk.