Kurtosis describes how much probability mass a distribution places in its tails and center relative to a normal distribution.

Kurtosis describes how much probability mass a distribution places in its tails and center relative to a normal distribution. For a normal distribution, kurtosis is 3. Excess kurtosis is kurtosis minus 3, so a normal distribution has excess kurtosis of 0.

In market data work, kurtosis matters because it helps describe how often returns depart sharply from their typical range. A return series with high kurtosis has heavier tails than a normal curve. That means extreme observations occur more often than a Gaussian model would imply. In practical risk modeling, this is important because models that assume normality can understate the frequency of large moves.

The mechanism is straightforward. If return observations are more concentrated near the center but also produce more extreme realizations in the tails, the distribution becomes more peaked and more heavy tailed than a normal curve. That combination raises kurtosis. In financial time series, this can arise from volatility clustering, regime changes, jumps, and market microstructure effects that create more unusually large returns than a constant variance Gaussian process would generate.

The Sonar Sciences glossary on the deflated Sharpe ratio explicitly defines kurtosis as a measure of the heaviness of the tails of the return distribution and notes that excess kurtosis is common in return series. It also states that excess kurtosis can affect statistical inference for performance metrics, which is one reason higher moment properties matter in quantitative research.

Covered in depth in the Strategy research fundamentals pillar hub.