The Sharpe ratio, developed by Nobel laureate William Sharpe in 1966, measures the excess return per unit of risk in an investment or portfolio. It is one of the most widely used metrics for comparing risk-adjusted performance.
The Sharpe ratio formula
Sharpe Ratio = (Rp - Rf) / Sp
Where:
- Rp = portfolio return
- Rf = risk-free rate (typically the yield on government treasury bills)
- Sp = standard deviation of portfolio returns (a measure of volatility)
The numerator captures how much extra return you earn above the risk-free rate. The denominator measures how much volatility you endured to achieve that return.
How to interpret the Sharpe ratio
| Sharpe ratio | Interpretation |
|---|---|
| Below 0 | The portfolio underperformed the risk-free rate |
| 0 to 0.5 | Poor risk-adjusted returns |
| 0.5 to 1.0 | Acceptable |
| 1.0 to 2.0 | Good |
| 2.0 to 3.0 | Very good |
| Above 3.0 | Excellent (rare over long periods) |
A Sharpe ratio of 1.0 means the portfolio earned one unit of excess return for every unit of risk taken. Most well-diversified equity portfolios achieve Sharpe ratios between 0.4 and 0.8 over long periods.
Worked example
Portfolio A returned 12% over the past year. The risk-free rate was 4%. The standard deviation of monthly returns, annualised, was 16%.
Sharpe Ratio = (12% - 4%) / 16% = 0.50
Portfolio B returned 9% with a standard deviation of 8%.
Sharpe Ratio = (9% - 4%) / 8% = 0.625
Despite Portfolio A having a higher absolute return, Portfolio B delivered better risk-adjusted performance. An investor in Portfolio B took less risk per unit of return earned.
Comparing investments with the Sharpe ratio
The Sharpe ratio is most useful when comparing:
- Two mutual funds or ETFs in the same category
- A portfolio against its benchmark index
- Different asset allocation strategies over the same period
It allows fair comparison between investments with very different risk profiles. A bond fund returning 6% with low volatility may have a higher Sharpe ratio than a stock fund returning 15% with high volatility.
Choosing the risk-free rate
The risk-free rate should match the investment period and currency. Common choices include:
- US: 3-month Treasury bill yield
- UK: 3-month gilt yield
- Eurozone: 3-month German Bund yield or ECB deposit rate
Using an inappropriate risk-free rate will distort the Sharpe ratio and make comparisons unreliable.
Limitations
- Assumes normally distributed returns. The Sharpe ratio treats upside and downside volatility equally. An investment that frequently delivers large positive surprises is penalised the same as one that delivers large negative surprises.
- Sensitive to the measurement period. A Sharpe ratio calculated over 1 year can differ significantly from one calculated over 5 years. Always compare ratios over the same timeframe.
- Does not capture tail risk. Strategies that rarely lose money but occasionally suffer catastrophic losses (such as option-selling strategies) can display artificially high Sharpe ratios.
- Backward-looking. Past Sharpe ratios do not guarantee future risk-adjusted performance.