What this calculator does
The Sharpe ratio treats all volatility as risk, including the upside kind. Most investors do not mind a portfolio that occasionally jumps sharply in their favour, and the Sortino ratio reflects that by measuring only the downside.
The difference shows up most in strategies with asymmetric returns. A series averaging 1.63 per cent a period with a downside deviation of 1.32 per cent gives a Sortino ratio of 1.08, where total volatility would have produced a noticeably harsher figure.
The formula
The average period return has the risk-free rate subtracted, then is divided by the downside deviation, which is the root mean square of the negative returns only, with positive periods counted as zero.
| Term | Meaning |
|---|---|
| Downside deviation | Volatility calculated from losing periods alone. |
| Sortino ratio | Excess return per unit of downside risk. Above 1 is generally considered good. |
| Asymmetry | The reason the measure exists: upside and downside volatility are not equally unwelcome. |
The inputs explained
| Field | What to enter |
|---|---|
| Period returns (%, comma separated) | Period returns as percentages, comma separated, in order. |
| Risk-free rate per period (%) | The risk-free rate per period, matching the frequency of the returns. |
When to use it
Assessing a strategy with skewed returns
Where gains and losses are not symmetric, the Sortino ratio is the fairer measure.
Comparing against a Sharpe ratio
A Sortino ratio much higher than the Sharpe ratio means most of the volatility was upside.
Evaluating a drawdown-sensitive portfolio
For investors who care mainly about losses, downside deviation is the relevant risk.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How do different return patterns score?
Three series with progressively worse downside.
| Return series | Sortino ratio | Downside deviation |
|---|---|---|
| No losing periods | not defined: no downside volatility in this period | 0.000% |
| Mild losses | 1.08 | 1.32% |
| Severe losses | -0.02 | 3.81% |
Questions
How does this differ from the Sharpe ratio?
Only in the denominator. Sharpe uses the standard deviation of all returns; Sortino uses the deviation of negative returns only. A strategy with volatile gains and steady small losses scores much better on Sortino.
What happens with no losing periods?
Downside deviation is zero, which would make the ratio infinite. The calculator reports it as undefined instead, which is the honest answer: there is no downside in the sample to measure against.
Which ratio should be used?
Sortino is generally more informative for strategies with asymmetric returns, and Sharpe is more widely quoted and easier to compare across sources. Looking at both is more useful than choosing.
Does a short return series give a reliable figure?
No. Downside deviation from a handful of losing periods is a very rough estimate, and a single extra bad period can move it substantially. Longer series give more dependable figures.
For the total-volatility version, see the Sharpe ratio calculator. For the worst decline rather than average volatility, see the maximum drawdown calculator.