This guide explains the formulas, how to calculate both ratios from daily or monthly returns, worked examples, what good values look like and the limits of both measures.
The Sharpe ratio
The Sharpe ratio was introduced by William F. Sharpe in 1966:
Sharpe ratio = (strategy return − risk-free rate) ÷ standard deviation of returns
- Strategy return: the average return over the period.
- Risk-free rate: the return on a near risk-free investment, such as Indian government Treasury bills.
- Standard deviation: how much the strategy's returns vary.
A higher Sharpe ratio means more excess return per unit of volatility.
The Sortino ratio
The Sortino ratio replaces the standard deviation with the downside deviation, which only counts returns below a target, usually zero or the risk-free rate:
Sortino ratio = (strategy return − risk-free rate) ÷ downside deviation
Traders usually do not mind volatility on the upside. The Sortino ratio does not penalise a strategy for large gains, only for losses.
Annualising
Ratios are usually quoted on an annual basis:
- From daily returns: multiply the daily ratio by the square root of 252, the approximate number of trading days in a year.
- From monthly returns: multiply the monthly ratio by the square root of 12.
A worked example
A strategy's monthly returns over three years average 1.5%, with a standard deviation of 4%. Its downside deviation is 2.5%. Assume a risk-free rate of 6.5% a year, or about 0.54% a month.
- Monthly excess return: 1.5% − 0.54% = 0.96%.
- Monthly Sharpe ratio: 0.96% ÷ 4% = 0.24.
- Annual Sharpe ratio: 0.24 × √12 ≈ 0.83.
- Monthly Sortino ratio: 0.96% ÷ 2.5% = 0.38.
- Annual Sortino ratio: 0.38 × √12 ≈ 1.33.
The Sortino ratio is higher because part of the strategy's volatility comes from good months.
What is a good Sharpe ratio?
As a rough guide for a trading strategy after costs:
| Annual Sharpe ratio | Typical reading |
|---|---|
| Below 0 | Earns less than the risk-free rate |
| 0 to 0.5 | Weak |
| 0.5 to 1 | Reasonable |
| 1 to 2 | Good |
| Above 2 | Excellent, and worth checking for errors or overfitting |
A backtest with a very high Sharpe ratio is more often a sign of a mistake than a sign of genius. Check for look-ahead bias, unrealistic fills and overfitting before trusting it. See avoiding overfitting.
Comparing strategies
| Strategy A | Strategy B | |
|---|---|---|
| Annual return | 30% | 18% |
| Annual volatility | 40% | 12% |
| Sharpe ratio (risk-free 6.5%) | 0.59 | 0.96 |
Strategy A earns more, but Strategy B earns more per unit of risk. With leverage or larger size, B could match A's return with less volatility. That is the comparison the Sharpe ratio makes possible.
Limits of the Sharpe and Sortino ratios
- They assume volatility captures risk. Option-selling strategies can show smooth returns and a high Sharpe ratio for years, then lose heavily in one event. The ratio does not see that tail risk until it happens.
- They depend on the period. A ratio calculated over a calm period can look much better than the strategy's long-run behaviour.
- They ignore drawdown depth and length. Look at the maximum drawdown as well.
- They can be gamed. Smoothing returns, for example by valuing positions infrequently, lowers measured volatility.
- Few data points make them noisy. A ratio from 12 monthly returns has a wide margin of error.
Using the ratios in strategy development
- Compare versions of a strategy on the same period.
- Compare with a benchmark, such as buying and holding Nifty.
- Use out-of-sample results, not the best backtest.
- Adjust for the number of versions tried. The deflated Sharpe ratio corrects for selection bias when many versions were tested.
QuantPower's backtesting engine reports the results of each strategy so you can compare them. Our guide on how to backtest trading strategies explains which other metrics to read alongside these ratios.
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Frequently asked questions
What does the Sharpe ratio tell you?
How much return above the risk-free rate a strategy earned for each unit of volatility.
What is the difference between Sharpe and Sortino?
Sharpe counts all volatility as risk. Sortino counts only downside volatility, so it does not penalise large gains.
What risk-free rate should I use in India?
Traders commonly use the yield on government Treasury bills of a similar horizon. Use the rate for the period you are measuring.
Can a strategy with a high Sharpe ratio still lose a lot?
Yes. Strategies with hidden tail risk, such as naked option selling, can show high Sharpe ratios until a large loss occurs.
Sources
- Sharpe, W. F. (1966). Mutual Fund Performance. Journal of Business, 39(1), 119–138
- Sortino, F. A. and Price, L. N. (1994). Performance Measurement in a Downside Risk Framework. Journal of Investing, 3(3), 59–64
- Bailey, D. H. and López de Prado, M. (2014). The Deflated Sharpe Ratio. Journal of Portfolio Management, 40(5), 94–107