Sharpe Ratio

Sharpe Ratio is a financial metric used to measure the risk-adjusted return of an investment. It helps investors understand how much excess return they are earning for the additional risk taken compared to a risk-free asset.

Definition

The Sharpe Ratio is calculated as:

• Sharpe Ratio = (R_p - R_f) / σ_p

where:

• R_p – Return of the portfolio.
• R_f – Risk-free rate (e.g., U.S. Treasury rate).
• σ_p – Standard deviation of the portfolio's return (risk).

Interpretation

• Sharpe Ratio greater than 1 – Indicates a good risk-adjusted return.
• Sharpe Ratio between 0 and 1 – Suggests that returns may not be significantly better than the risk-free rate.
• Negative Sharpe Ratio – The investment underperforms compared to the risk-free rate.

Example Calculation

Suppose:

• Portfolio return (R_p) = 12%
• Risk-free rate (R_f) = 3%
• Portfolio standard deviation (σ_p) = 10%

The Sharpe Ratio is:

• (12% - 3%) / 10% = 0.9

Advantages

• Compares different investments – Helps assess performance across assets.
• Considers risk – Accounts for volatility, unlike raw returns.
• Widely used – Standard benchmark in portfolio management.

Limitations

• Assumes normal distribution – May not be accurate for highly skewed assets.
• Sensitive to inputs – Different risk-free rates or time periods can affect results.
• Does not capture downside risk separately – Unlike the Sortino Ratio.

Applications

• Portfolio optimization in asset management.
• Comparing mutual funds, hedge funds, and ETFs.
• Evaluating risk-adjusted returns in quantitative finance.

Variations

• Sortino Ratio – Focuses only on downside risk.
• Treynor Ratio – Uses beta instead of standard deviation.

See Also

• Risk-Adjusted Return
• Sortino Ratio
• Treynor Ratio
• Volatility (Finance)
• Modern Portfolio Theory
• Efficient Frontier