The Sharpe ratio measures how much excess return (above the risk-free rate) an investment earns for each unit of total risk (standard deviation). It was developed by Nobel laureate William Sharpe.
Formula: > Sharpe Ratio = (Portfolio Return − Risk-free Rate) ÷ Standard Deviation
Interpretation: - A higher Sharpe ratio = better risk-adjusted performance. - A ratio above 1.0 is generally considered good; above 2.0 is very good; above 3.0 is exceptional. - Negative Sharpe ratio = the investment underperformed the risk-free rate.
Example: - Portfolio return: 12% - Risk-free rate: 4% - Standard deviation: 10% - Sharpe ratio = (12% − 4%) ÷ 10% = 0.8
Sharpe vs. Treynor vs. Jensen:
| Metric | Denominator | Best for | |---|---|---| | Sharpe | Standard deviation (total risk) | Comparing non-diversified portfolios | | Treynor | Beta (systematic risk) | Comparing fully diversified portfolios | | Jensen's alpha | CAPM expected return | Absolute excess return |
Limitations: - Assumes returns are normally distributed (doesn't capture skewness/kurtosis). - Uses standard deviation, which penalizes upside volatility equally with downside volatility. - More appropriate for comparing portfolios with similar objectives.
> Exam tip: Sharpe uses standard deviation (total risk). Treynor uses beta (systematic risk). If a portfolio is well-diversified, Sharpe ≈ Treynor ranking. Both are risk-adjusted return measures — higher is better.