What is the Sortino ratio?

How to calculate a Sortino ratio

1. Choose a target return, and write it down

   Zero, the risk-free rate, or a required return. Any of them is defensible; leaving it unstated is not, because the choice moves the answer and nobody downstream can reconstruct it.

2. Compute the shortfall for every period

   For each period, take the return minus the target. Where the result is positive, replace it with zero — upside is not being measured here. Where it is negative, keep it.

3. Square the shortfalls and average over all periods

   Sum the squared shortfalls, then divide by the total number of observations — including the periods you just set to zero. Dividing by the count of losing periods instead is the error that makes two Sortino ratios for the same strategy disagree.

4. Take the square root

   That is the downside deviation, the denominator. It is always smaller than the standard deviation of the same series, so a Sortino ratio is essentially always larger than the corresponding Sharpe ratio.

5. Divide, then annualize once

   Mean return above the target, divided by downside deviation. Multiply by the square root of the periods in a year — about 252 for daily, 12 for monthly — and only once, at the end.

What is downside deviation?

It is the standard deviation calculated on only the returns that fell below a target, with everything above the target treated as zero rather than dropped.

That last detail is what people get wrong, and it matters. The squared shortfalls are averaged over every period in the sample, not only over the losing ones. Averaging over just the losing periods produces a much larger denominator and a much smaller ratio, and both versions circulate under the same name.

The reasoning behind the convention is that a period which did not lose money contributed no downside risk, so it should pull the average down — it is evidence of the thing being measured, not a missing observation.

What does it mean if the Sortino ratio is much higher than the Sharpe ratio?

It means the volatility in the return series is mostly upside. The two ratios share a numerator, so the gap between them is entirely a statement about the denominators, and a large gap says the big moves were disproportionately gains.

That is usually a genuine and favorable property — it is exactly what the Sortino ratio was built to detect. But two other explanations produce the same signature, and both are less pleasant.

• Very few losing periods. If a strategy fell below the target only a handful of times, the downside deviation is estimated from a handful of observations and is correspondingly unstable. A dramatic Sortino ratio computed from six losing months is not a finding.
• The losses have not happened yet. Strategies that collect small premiums and rarely lose a great deal — selling options, carry, most short-volatility exposure — post outstanding Sortino ratios for years, because the shape of their loss is a rare large one that the sample may not contain.

So the gap is informative, and it is not self-interpreting. Check how many observations went into the denominator before reading much into it.

What target return should you use?

There is no universal answer, which is precisely why the choice has to be published alongside the number.

• Zero is the most common and the easiest to compare across sources, because it removes one free parameter. It also treats any positive return as acceptable, which is generous.
• The risk-free rate makes the Sortino ratio directly comparable to the Sharpe ratio, since both then measure the same excess. This is the cleanest choice when the two figures are being reported together.
• A required return — the rate below which the strategy has failed for your purposes — is the most meaningful and the least comparable. Raising the target increases the number of periods counted as shortfalls and lowers the ratio, sometimes dramatically.

Because the target is a free choice that moves the result in a predictable direction, an unstated target is functionally an invitation to pick the flattering one.

Does the Sortino ratio fix the Sharpe ratio’s problems?

It fixes one of them, cleanly. It leaves the largest one entirely untouched.

The fix is real: treating a large gain as risk is a genuine defect of the Sharpe ratio, and the Sortino ratio removes it. For strategies with asymmetric return distributions that is a meaningful correction rather than a cosmetic one.

What it does not touch is selection. A Sortino ratio computed on the best of fifty thousand backtested variants is exactly as selected as the Sharpe ratio would have been, and the arithmetic gives no hint of it. Switching measures changes what counts as risk; it does not change the fact that the number is the winner of a search.

It also inherits two of the Sharpe ratio’s other limits: it says nothing about the path of a loss or how long you would have been underwater, and its annualization assumes returns are independent from one period to the next.

Backtested and hypothetical results are not indicative of future performance. Nothing here is investment advice.

Common questions