Sortino ratio
The Sortino ratio divides the average return of a series by its downside deviation, the dispersion of results below a target that is usually zero. It penalizes losses but not large gains, so it measures average result per unit of harmful volatility rather than per unit of all volatility.
Senzoukria · Glossary · Updated September 2026
At a glance
- Formula
- (mean return − target) ÷ downside deviation
- Downside deviation
- √[(1/N) × Σ min(0, rᵢ − target)²], divided by ALL observations
- Usual target
- 0 for trade results; a minimum acceptable return for fund returns
- In Senzoukria
- Sortino / trade, not annualized, ∞ when no trade lost
Definition and formula
The ratio is associated with Frank Sortino, who argued that investors do not experience upside dispersion as risk. It keeps the numerator of the Sharpe ratio, the mean excess over a target, and replaces the standard deviation with the downside deviation: the square root of the average squared shortfall below the target.
Two details decide whether a published figure is comparable. First, the shortfall of an observation above the target is counted as zero, not dropped, so the sum is divided by the total number of observations. Dividing by the number of losing observations only would punish a strategy that rarely loses as if it lost on every trade. Second, the target must be stated: zero, a risk-free rate or a minimum acceptable return give different values on the same series.
A worked example
Take five trade results in dollars: +300, −100, +200, −200, +100. The mean is 300 ÷ 5 = 60. The squared shortfalls below zero are 10,000 and 40,000, the other three are zero; their average over five trades is 10,000, and the square root is 100. The Sortino ratio is 60 ÷ 100 = 0.60.
The population standard deviation of the same five results is about 185.5, so the Sharpe ratio is 60 ÷ 185.5 ≈ 0.32. The gap exists because the two large winners add to the standard deviation but not to the downside deviation. For a symmetric distribution centered on the target, the downside deviation equals σ ÷ √2, so the Sortino is roughly 1.4 times the Sharpe; a much wider gap points to right skew, a narrower one to a heavy left tail.
In Senzoukria
The Performance panel of the Replay screen lists Sortino / trade in its System quality section, next to Sharpe / trade and SQN, and the automatic backtest shows it for each walk-forward phase. It is computed per trade on net trade results with a target of zero, the downside sum is divided by the total trade count, and it is deliberately not annualized. When no trade lost, the downside deviation is zero and the panel shows ∞, the mathematically correct value rather than a capped placeholder; the hint reads that the ratio penalizes downside dispersion only.
Common mistakes
- Dividing the downside sum by the number of losing trades instead of all trades.
- Comparing a per-trade Sortino with an annualized figure from a fund factsheet.
- Reading a high value built on three or four losing trades: the denominator rests on almost no data.
- Forgetting to state the target, which makes two Sortino ratios on the same record disagree.
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Frequently asked questions
- Is a higher Sortino ratio always better than a higher Sharpe ratio?
- They answer different questions. The Sortino ignores upside dispersion, so it favors strategies with occasional large winners. The Sharpe treats all dispersion as risk. Reading both together tells you whether the volatility of a record comes mostly from its gains or from its losses.
- Why does the desktop show an infinite Sortino ratio?
- Because no trade in the sample lost money, so the downside deviation is zero and the ratio has no finite value. It is a signal to look at the sample size, not a measure of quality: a handful of winning trades produces the same infinity.
- What target should be used for trade-level results?
- Zero is the usual choice for per-trade futures results, since each result is already a profit or loss net of costs. For monthly or annual account returns, a minimum acceptable return such as a cash rate is more common. Whatever the choice, state it.