Measure the tail weight of a distribution relative to a normal distribution.
A normal distribution has kurtosis of exactly 3, so excess kurtosis measures deviation from it. Positive excess kurtosis means extreme values occur more often than a normal model would predict. Financial returns have strong positive excess kurtosis, which is why normal-distribution risk models systematically underestimate the frequency of crashes.
Kurtosis
Kurtosis = fourth central moment ÷ σ⁴; excess kurtosis subtracts 3
Kurtosis = fourth central moment ÷ σ⁴; excess kurtosis subtracts 3 A normal distribution has kurtosis of exactly 3, so excess kurtosis measures deviation from it. Positive excess kurtosis means extreme values occur more often than a normal model would predict.
Financial returns have strong positive excess kurtosis, which is why normal-distribution risk models systematically underestimate the frequency of crashes.
This calculator takes 3 inputs: Fourth central moment, Standard deviation, Sample size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.