Do fat tails mean a strategy is risky?

They mean that the strategy's large outcomes are more frequent than its standard deviation suggests. Whether that is bad depends on the side: fat left tails mean occasional large losses; fat right tails can mean occasional large gains, as in trend following.

Why is kurtosis sometimes reported as 3 and sometimes as 0 for a normal distribution?

Because two conventions exist. Pearson kurtosis gives 3 for a normal distribution; excess (Fisher) kurtosis subtracts 3 and gives 0. Check which one a tool reports before comparing values.

Fat tails (excess kurtosis)

A distribution has fat tails when extreme values occur more often than a normal distribution with the same mean and standard deviation would predict. Returns and trade results usually do, which makes models built on the normal curve understate the frequency of large moves and large losses.

Senzoukria · Glossary · Updated September 2026

At a glance

Measure: Kurtosis m₄ ÷ m₂²; normal = 3
Excess kurtosis: Kurtosis − 3; > 0 means fatter tails than normal
Normal |z| > 4: About 1 in 15,800 observations
In Senzoukria: Kurtosis indicator (excess); DSR corrects for kurtosis

How rare a large move should be

Under a normal distribution, a move larger than three standard deviations in either direction happens about once every 370 observations, and a move larger than four standard deviations about once every 15,800. On daily data, that second figure means roughly once in 63 years of trading days. Market returns and intraday futures moves show such events far more often, which is what fat tails mean in practice: the middle of the distribution is narrower and the extremes are more frequent than the bell curve implies.

Measuring it

Kurtosis is the fourth standardized moment: the average of (x − mean)⁴ divided by the squared variance. A normal distribution has kurtosis 3, so excess kurtosis subtracts 3 to center the normal on zero. Positive excess kurtosis signals fat tails. Like every higher moment, it is dominated by a few observations and needs a large sample to be stable; a single crash day can double it.

Consequences for trading statistics

A standard deviation computed on a calm sample understates the risk of the next large move.
Parametric VaR based on the normal curve underestimates tail losses; expected shortfall and historical methods fare better.
The Sharpe ratio ignores the shape of the distribution; two strategies with the same Sharpe can have very different crash exposure.
Significance tests that assume normality overstate confidence when results are fat-tailed.
Stops protect less than they seem: fat-tailed moves are often gaps or fast markets where stops slip.

In Senzoukria

The indicator catalogue has a Kurtosis study that plots the excess kurtosis of the last N returns in a separate pane, with population moments and a default window of 50, and returns no value when the window is flat rather than a misleading zero. It is designed to be read with the Skewness study. For strategy evaluation, the Gauntlet's probabilistic and deflated Sharpe ratios take the skewness and the kurtosis of daily results into account, so a fat-tailed return series needs a higher Sharpe to pass than a normal one.

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Frequently asked questions

Do fat tails mean a strategy is risky?: They mean that the strategy's large outcomes are more frequent than its standard deviation suggests. Whether that is bad depends on the side: fat left tails mean occasional large losses; fat right tails can mean occasional large gains, as in trend following.
Why is kurtosis sometimes reported as 3 and sometimes as 0 for a normal distribution?: Because two conventions exist. Pearson kurtosis gives 3 for a normal distribution; excess (Fisher) kurtosis subtracts 3 and gives 0. Check which one a tool reports before comparing values.

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