BacktestFolio · Glossary
Kurtosis
In plain language
A normal distribution assumes crashes of −5% or worse are rare. Real markets have high kurtosis — crashes occur more often than the bell curve would suggest. This is why historical VaR and CVaR (based on actually observed returns) are more reliable than models assuming normality.
Technical definition
Statistical measure of the 'heaviness' of the tails of a return distribution relative to the normal distribution (kurtosis = 3). Positive excess kurtosis (kurtosis − 3 > 0) indicates fat tails (leptokurtic): extreme events occur more frequently than the normal model predicts. Real financial returns are almost always leptokurtic.