📐 Sharpe Ratio
The Sharpe ratio is the most widely used risk-adjusted return metric. It measures how much excess return you receive per unit of total volatility.
🔢 Formula
where:
- \(R_p\) = portfolio return (annualized)
- \(R_f\) = risk-free rate (e.g., Treasury bill rate)
- \(\sigma_p\) = portfolio standard deviation (annualized)
💡 Interpretation
| Sharpe Ratio | Quality |
|---|---|
| \(< 0\) | Portfolio underperformed the risk-free rate |
| \(0 - 0.5\) | Suboptimal risk-adjusted return |
| \(0.5 - 1.0\) | Acceptable |
| \(1.0 - 2.0\) | Good |
| \(> 2.0\) | Excellent (rare for long periods) |
Numerical example
Portfolio return: 12%, Risk-free rate: 3%, Volatility: 15%
For every 1% of volatility, the portfolio earned 0.60% of excess return.
⚙️ Annualization
When computed from daily returns:
where 252 is the typical number of trading days per year. This assumes returns are IID (independent and identically distributed) — an approximation that breaks down for autocorrelated returns.
⚠️ Limitations
📊 Symmetric Penalty
The Sharpe ratio penalizes upside volatility as much as downside volatility. An asset that frequently spikes upward (highly desirable!) will have a lower Sharpe ratio than one with the same return and less upside movement.
→ For asymmetric return distributions, prefer the Sortino Ratio.
📈 Sensitivity to Outliers
A few extreme returns can significantly distort the standard deviation, making the Sharpe ratio unstable for short time periods.
🔄 Time-Period Dependency
The Sharpe ratio can vary dramatically depending on the lookback window. A strategy with an excellent 5-year Sharpe may have a poor 1-year Sharpe (or vice versa).
🔗 Related
- 📊 Sortino Ratio — Downside-only variant
- 📊 Volatility — The denominator of the Sharpe ratio
- 📈 Returns — The numerator of the Sharpe ratio