Skewness of returns and trade results
Skewness measures the asymmetry of a distribution. Negative skew means frequent small gains and rare large losses; positive skew means frequent small losses and rare large gains. Two strategies with the same average and volatility can have opposite skew and very different risks.
Senzoukria · Glossary · Updated September 2026
At a glance
- Formula
- g₁ = m₃ ÷ m₂^(3/2), third standardized moment
- Negative skew
- Long left tail: many small wins, rare large losses
- Positive skew
- Long right tail: many small losses, rare large wins
- Normal distribution
- Skewness 0
A high win-rate example
Ten trades: nine winners of +100 dollars and one loser of −800. The win rate is 90% and the average trade is (900 − 800) ÷ 10 = +10. The deviations from the mean are +90 nine times and −810 once. The second central moment is (9 × 8,100 + 656,100) ÷ 10 = 72,900, so the standard deviation is 270. The third central moment is (9 × 729,000 − 531,441,000) ÷ 10 = −52,488,000. Dividing by 270³ = 19,683,000 gives a skewness of about −2.67.
The record looks excellent most of the time and depends on a single large loss not getting larger. That profile is typical of strategies that sell insurance in some form: fading moves with wide stops, collecting small targets, or short option premium.
Why skew matters beyond the average
- Negative skew hides risk in small samples: a short record may contain no large loss at all, and every ratio will look better than the strategy is.
- Positive skew hides edge in small samples: long losing streaks come before the rare large winners, and strategies are abandoned during them.
- The Sharpe ratio treats both shapes alike; the Sortino ratio and a look at the worst trades separate them.
- Prop firm rules interact with skew: a daily loss limit caps the left tail of a negatively skewed strategy only if the stop is respected; a consistency rule can penalize a positively skewed record whose profit comes from one day.
In Senzoukria
The indicator catalogue's Skewness study plots the skewness of the last N bar returns, 50 by default, with population moments and no value when the window is flat; it describes the shape of recent price changes, not of your trades. For strategy evaluation, the Gauntlet computes the skewness of daily results and uses it in the probabilistic and deflated Sharpe ratios, which require a negatively skewed record to show a higher Sharpe before it passes. The Replay report shows Best trade and Worst trade, and the Performance panel warns when the best trade is 50% or more of the net profit, a simple sign of a record carried by its right tail.
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Frequently asked questions
- Is negative skew bad?
- It is a risk profile, not a verdict. Negatively skewed strategies can be profitable for long periods, but their risk is concentrated in rare large losses that small samples may not contain. They need sizing that survives the tail, not just the average.
- How many trades are needed to estimate skewness?
- Many, because the measure is dominated by the few largest observations. With a few dozen trades, the estimate can change sign when one trade is added. Treat skewness from small samples as a warning to look at the extreme trades directly.