What the two ratios measure
The Sharpe ratio is return per unit of risk: the average return above the risk-free rate, divided by the standard deviation of returns. The Sortino ratio divides by downside deviation instead, counting only returns below the target, on the argument that nobody minds volatility on the way up.
Sharpe = (mean return − risk-free per period) ÷ standard deviation × √periods per year
Sortino = (mean return − risk-free per period) ÷ downside deviation × √periods per year
Both are annualised by multiplying by the square root of the number of periods in a year: √252 for daily returns, √52 weekly, √12 monthly.
A worked example
The figures loaded above are twelve monthly returns with a 4% risk-free rate.
- The average month returned 0.63%, about 7.6% a year, with a monthly standard deviation of 2.02%, about 7.0% a year.
- The Sharpe ratio is (0.633% − 0.333%) ÷ 2.023% × √12 = 0.51.
- The Sortino ratio is 0.77, higher because only the down months count against it.
What is a good Sharpe ratio?
As rough guides, a Sharpe ratio below 0.5 is weak, around 1 is good, and above 2 is unusual over long periods. A broad stock index has historically run somewhere around 0.4 to 0.6 over decades. Very high figures from short records are more often luck, a short sample or a strategy with hidden tail risk than genuine skill.
That is what the confidence range is for. With only twelve observations, the standard error of this Sharpe ratio is about 1.0, so the 95% range runs from about −1.5 to +2.5. Twelve months cannot distinguish this record from one with no edge at all. With 36 monthly returns the range would narrow by about 40%; even so, years of data are needed before a Sharpe ratio means much.
Common mistakes
- Mixing frequencies. A daily Sharpe multiplied by 12 instead of √252 is wrong by a large factor.
- Returns, not P&L. Enter percentage returns on the capital at risk, not dollar profits, or the ratio depends on account size.
- Strategies that sell options often show high Sharpe ratios for years and then lose several years of gains in a month. Standard deviation does not see a risk that has not happened yet.
- Survivorship. Ratios computed only on the strategies or months you kept look better than the ones you would have got.
For a trade-level view of the same record, use the profit factor and expectancy calculators, and see the worst stretch with the drawdown recovery calculator.