The Sortino ratio is your average return above a minimum acceptable return, divided by downside deviation: how far your returns fall below that target. Only the shortfalls count as risk, so a big winning day does not hurt the score. It is the Sharpe ratio with the denominator changed to measure only the swings a trader dislikes. Frank Sortino and Robert van der Meer introduced the idea in 1991. This page works the Sortino and Sharpe ratios on the same ten trading days, then on two other traders who finish with identical profit, to show where the two ratios disagree.
The Sortino ratio formula
Sortino ratio = (average return − MAR) ÷ downside deviation
Downside deviation = √( Σ min(return − MAR, 0)² ÷ N )
- MAR (minimum acceptable return): the return you must beat for a period to count as a good one. Common choices are 0%, or the risk-free rate converted to the same period. You choose it, and it moves the answer.
- Downside deviation: for each period, take how far the return fell below the MAR (zero if it was at or above), square it, average the squares, then take the square root.
- N is every period, not just the losing ones. Sortino and Price (1994) define downside deviation this way: a winning day contributes a shortfall of zero but still counts in the average. Some tools divide by the number of below-target days, or take the standard deviation of only the negative returns. Those give different, usually lower, ratios, so confirm which variant a tool uses before comparing numbers.
The original sources are Sortino and van der Meer, Downside Risk (Journal of Portfolio Management, 1991), and Sortino and Price, Performance Measurement in a Downside Risk Framework (Journal of Investing, 1994).
A Sortino ratio worked example with 10 trading days
These are the same ten daily returns used in the Sharpe ratio example, as a percentage of the balance at the start of each day. The MAR is the 4% annual risk-free rate used there, which is 4% ÷ 252 = 0.016% a day. Four days finish below it, including day 7, which was flat. The shortfalls are 0.416, 0.916, 0.016 and 0.516 points below the MAR; the last column squares them.
| Day | Return | Shortfall squared |
|---|---|---|
| 1 | +0.8% | 0 |
| 2 | −0.4% | 0.173 |
| 3 | +1.2% | 0 |
| 4 | +0.3% | 0 |
| 5 | −0.9% | 0.839 |
| 6 | +0.6% | 0 |
| 7 | 0.0% | 0.000 |
| 8 | +1.1% | 0 |
| 9 | −0.5% | 0.266 |
| 10 | +0.7% | 0 |
- Average daily return above the MAR: 0.29% − 0.016% = 0.274%
- Sum of squared shortfalls: 1.278
- Divide by all 10 days: 1.278 ÷ 10 = 0.128. Square root: downside deviation = 0.358%
- Daily Sortino: 0.274 ÷ 0.358 = 0.77
- Annualised: 0.77 × √252 = 12.2
The Sharpe ratio on the same days is 6.1: the standard deviation of all ten returns is 0.72%, twice the downside deviation, so Sortino comes out about twice as high. Neither number is a forecast. Both rest on ten days, and the Sortino rests on four losing ones.
Sortino vs Sharpe on the same profit
Here are three traders who each made +2.9% over ten days, an average of 0.29% a day. The table shows annualised ratios, with the MAR at 0.016% a day.
- Trader A is the series above: small moves, a worst day of −0.9%. Standard deviation 0.72%, downside deviation 0.36%, four days below the MAR.
- Trader B reached the same total with big swings both ways: +2.4%, −1.8%, +3.0%, −0.6%, −2.7%, +1.9%, −1.2%, +2.8%, −1.6%, +0.7%. Standard deviation 2.13%, downside deviation 1.23%, five days below the MAR.
- Trader C lost a little most days and won big twice: +3.2%, −0.3%, −0.2%, −0.5%, +2.6%, −0.4%, −0.3%, −0.2%, −0.5%, −0.5%. Standard deviation 1.39%, downside deviation 0.36%, eight days below the MAR.
| Trader | Sharpe | Sortino |
|---|---|---|
| A | 6.1 | 12.2 |
| B | 2.0 | 3.5 |
| C | 3.1 | 12.2 |
A and B differ the way you would expect: B's losing days are far deeper, and both ratios fall. A and C are the interesting pair. C's two big winners push its standard deviation to nearly twice A's, so Sharpe halves from 6.1 to 3.1. Its downside deviation is the same 0.36%, so Sortino stays at 12.2. Sharpe reads C as a much bumpier account than A. Sortino says the bad days were equally mild, and only the good days differ.
Sortino is not simply kinder, though. C lost on 8 of 10 days, which feels very different from A's 4 of 10, and the Sortino ratio is blind to that. It measures how deep the losses were, not how often they came.
One more pattern. If returns were symmetric around the MAR, downside deviation would be the standard deviation divided by √2, which makes Sortino about 1.41 times Sharpe. A sits at 2.0 times and C at 3.9 times because their large moves are on the winning side. When the Sortino-to-Sharpe gap is wide, your volatility is mostly upside. When it narrows toward 1.4 or below, more of it is downside.
How to annualise the Sortino ratio
Multiply the daily ratio by √252, about 15.9, as in the Sharpe ratio. For monthly returns use √12. The reasoning: the average return grows with the number of periods, and downside deviation grows with its square root, so the ratio grows with the square root.
The caveat is the same one that applies to Sharpe. The scaling assumes each day is independent of the last. A strategy that trades streaks, or that averages down after losses, breaks that assumption, and annualising will flatter it. Annualising also hides sample size: 12.2 looks like a measurement, but it came from ten days.
What is a good Sortino ratio?
There is no official threshold, and I could not trace the "above 2 is good, above 3 is excellent" scales that circulate online to a primary source, so treat them with suspicion. Three reasons a single cutoff does not exist:
- It depends on your MAR. On trader A's ten days, a MAR of 0% gives 13.2, the 4% risk-free MAR gives 12.2, a MAR of 0.1% a day gives 7.5, and 0.2% a day gives 3.1.
- It depends on the formula variant. Dividing trader A's squared shortfalls by the 4 below-target days instead of all 10 gives 7.7 rather than 12.2.
- It usually reads higher than Sharpe for the same returns, so a Sharpe rule of thumb is too strict for it.
A more useful benchmark is your own history. Pick one MAR and one formula, then watch how your Sortino moves from quarter to quarter and between strategies. A fall from 4 to 1 means something. Below about 60 trading days the number moves too much to read; the sample-size problem is the same as for Sharpe, and is covered in how many trades before you can trust a statistic.
Where the Sortino ratio misleads traders
- The downside rests on few observations. Trader A's denominator comes from four days. Add one −1.5% day as an eleventh day and the Sortino drops from 12.2 to 3.1. A handful of bad days decides the whole ratio.
- The MAR is a free parameter. A higher target turns more ordinary days into shortfalls. Quote the MAR next to every Sortino, or the number cannot be compared.
- It rewards a few big winners without asking how they came. If C's two winning days were luck, Sortino still gives full credit. The gain to pain ratio and a longer sample are the checks on that.
- Daily returns hide intraday pain. A day that dips 3% and recovers to flat counts as a zero-shortfall day. If you trade a prop firm account with a daily loss limit, the max drawdown and Calmar ratio cover what Sortino cannot see.
- It is built on account returns, not R-multiples. A day where you risked 2% and a day where you risked 0.5% both feed in as percentages, so changing position size changes the ratio without changing your skill. For per-trade quality, use expectancy and profit factor.
Sortino ratio vs the other trading ratios
- Sharpe ratio: same numerator idea, but divides by all volatility. Use it to see how smooth the whole curve was; see the Sharpe ratio guide.
- Gain to pain ratio: total return divided by total losses, with no standard deviation and no MAR. Easier to compute by hand, and it counts every loss, not only those below a target.
- Expectancy and profit factor: measure the average and the balance of your trades, not the path of your account.
- Calmar ratio: return against the single worst drawdown, the stricter test for funded accounts; see the Calmar ratio guide.
No single ratio is enough. A trader with a high Sortino, a deep max drawdown and 40 days of data has learned very little yet.
Your own Sortino ratio, without the spreadsheet
ExpectancyIQ's Performance report shows an annualised Sortino ratio next to Sharpe and Calmar, built from your daily returns (each trading day's P&L divided by the balance going into that day). It uses the formula above over every trading day in the range, with a MAR of 0, so the ten days above show 13.2 rather than 12.2. A trading day follows the 17:00 CT session roll described in the methodology. The trading dashboard shows how it sits with the rest of the numbers, and the glossary defines each metric in short.