Sortino ratio from returns
How is the Sortino ratio computed when few returns fall below the target?
Subtract the target from each return, average the result, and divide by the square root of the mean squared shortfall over all observations, with gains counted as zero shortfall. For 4%, -2%, 3% and -1% with a zero target, that gives 1% / sqrt(1.25)% = 0.894.
This calculator averages squared shortfalls over all observations; some published variants divide by the number of shortfalls, which gives a smaller ratio.
Compute mean excess return over target divided by downside deviation from pasted observations. The denominator uses the full-sample lower partial moment.
Four observed returns
For returns 4%, −2%, 3%, −1% and target zero, the mean is 1%, downside deviation is sqrt(1.25)% and the Sortino ratio is 0.894427.
The denominator is the root mean square shortfall relative to a minimum acceptable return. It differs from the standard deviation used by Sharpe because returns above the target contribute zero downside. The numerator remains the ordinary arithmetic mean minus the target. Keeping all observations in the denominator means the output corresponds to the discrete lower partial moment of order two, with each observation equally weighted. A target of zero has a different economic meaning from a target equal to a financing or hurdle rate; the target should be fixed before inspecting the statistic. If all sampled returns clear the target, the denominator vanishes and the reported ratio is undefined. It does not assign a large arbitrary number, because such a number would dominate rankings for a reason that is entirely sample dependent. Use the companion drawdown and Omega tools if the path or full distribution is the actual concern.
Lower partial moment
All returns refer to equal observation intervals and the target is on the same scale. Downside deviation divides by all observations, including those above the target.
Sortino = mean(r−target) / sqrt(mean(min(0,r−target)^2))Shortfall below the target determines the denominator. A large value can reflect a short sample with no observed adverse returns, so the observation count remains central to interpretation.
No observed shortfall
There is no finite ratio when downside deviation is zero. This is an in-sample description and can become unstable with few losses; it is not an annualized estimate or a confidence bound.
The original downside-risk article
Sortino, F. A. and van der Meer, R. (1991), Downside Risk: Capturing What's at Stake in Investment Situations, Journal of Portfolio Management 17(4), 27–31. The page specifies its discrete lower-partial-moment convention. Publisher record (DOI) · Institutional copy.
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</script>Cite this calculator
To cite the Sortino ratio from returns in a paper, a report or a post, copy the reference below. Its address is https://stochastly.com/tools/sortino-ratio-returns-calculator.
Stochastly (2026). Sortino ratio from returns [web calculator]. https://stochastly.com/tools/sortino-ratio-returns-calculatorThe method behind the Sortino ratio from returns comes from the paper below: cite that paper for the method, and the reference above for the Sortino ratio from returns itself.
Sortino, F. A. and van der Meer, R. (1991). Downside Risk: Capturing What's at Stake in Investment Situations. Journal of Portfolio Management 17(4), 27-31.