Sharpe Ratio Explained: Formula, Examples and Limits
The Sharpe ratio measures how much return an investment or strategy earned above a risk-free rate for each unit of volatility it carried. The formula is (return − risk-free rate) ÷ standard deviation of returns. A higher Sharpe ratio means a better risk-adjusted return; a value around 1 or above is commonly treated as good for a strategy after costs.
What is the Sharpe ratio?
The Sharpe ratio was developed by Nobel laureate William F. Sharpe. It answers one question: was the return worth the ups and downs it took to get it?
It needs three numbers:
| Input | What it is | Example |
|---|---|---|
| Return | Average return of the strategy over a period, usually annualised | 14% a year |
| Risk-free rate | What you could earn with almost no risk, such as government treasury bills | 6% a year (example rate) |
| Standard deviation | How much returns swing around their average: the strategy's volatility | 10% a year |
With the numbers above: (14% − 6%) ÷ 10% = 0.80. For every 1% of volatility, the strategy earned 0.8% above the risk-free rate.
Comparing two strategies
The Sharpe ratio is most useful for comparing options that take different levels of risk:
Hypothetical figures. B earns less in total but much more per unit of risk
That last point shows a useful property: changing position size scales both excess return and volatility, so the Sharpe ratio stays roughly the same. That makes it a measure of the quality of a strategy's returns, and it's also why Sharpe alone can't tell you whether a strategy is sized too large for your account.
How to calculate the Sharpe ratio for an algo strategy
Strategies usually produce daily P&L, so you calculate on daily returns and then annualise:
- Convert daily P&L into daily returns on the capital used: ₹1,200 on ₹5,00,000 is 0.24%.
- Average the daily returns and calculate their standard deviation.
- Subtract the daily risk-free rate (annual rate ÷ 252) from the average.
- Divide by the standard deviation to get the daily Sharpe.
- Annualise: multiply by √252, about 15.9, using roughly 252 trading days a year.
Note that volatility scales with the square root of time, not with time itself. That's why you multiply the daily Sharpe by √252 rather than by 252.
What is a good Sharpe ratio?
| Sharpe ratio | Common reading |
|---|---|
| Below 0 | Did worse than the risk-free rate |
| 0 to 1 | Positive, but modest for the risk taken |
| Around 1 to 2 | Commonly treated as good |
| Above 2 | Very strong; check it carefully, especially on short backtests |
These bands are rules of thumb, not standards. A very high Sharpe from a short backtest is more often a sign of overfitting or a calm test period than of an exceptional strategy. See backtesting mistakes to avoid.
The limits of the Sharpe ratio
- It treats gains and losses alike. A big up day raises volatility and lowers Sharpe, even though you'd welcome it.
- It assumes returns are roughly normal. Trading returns often have fat tails: rare, large moves the standard deviation understates.
- It depends on the period. The same strategy can show very different Sharpe ratios in different years.
- It depends on how it's calculated: daily or monthly data, annualised or not, which risk-free rate.
Related ratios: Sortino and Calmar
| Ratio | Formula | Fixes |
|---|---|---|
| Sharpe | (Return − risk-free) ÷ total volatility | Baseline risk-adjusted return |
| Sortino | (Return − risk-free) ÷ downside volatility only | Doesn't penalise big up days |
| Calmar | Annual return ÷ maximum drawdown | Focuses on the worst fall from peak, which traders feel most |
Using all three, plus maximum drawdown, gives a much fuller picture than Sharpe alone. How to evaluate a strategy's performance covers the rest of the metrics.
Frequently asked questions
What does the Sharpe ratio tell you?
It tells you how much return above a risk-free rate an investment or strategy earned for each unit of volatility. It's used to compare investments that take different amounts of risk.
How do you calculate the Sharpe ratio?
Subtract the risk-free rate from the return, then divide by the standard deviation of returns. For example, a 14% return, a 6% risk-free rate and 10% volatility give (14 − 6) ÷ 10 = 0.8.
What is a good Sharpe ratio?
A Sharpe ratio around 1 or above is commonly treated as good, and above 2 as very strong. Compare values only when they're calculated the same way, and be cautious of very high ratios from short backtests.
How do I annualise a daily Sharpe ratio?
Multiply the daily Sharpe ratio by the square root of the number of trading days in a year, about √252 ≈ 15.9.
What is the difference between the Sharpe and Sortino ratios?
The Sharpe ratio divides by total volatility, both up and down. The Sortino ratio divides only by downside volatility, so it doesn't penalise a strategy for large gains.
Can a negative Sharpe ratio happen?
Yes. It means the strategy returned less than the risk-free rate over the period, so the risk taken wasn't rewarded.
