Term Glossary

Metrics, Models & Concepts

Kurtosis


Return kurtosis characterizes the relative peakedness or flatness of a given distribution compared to a normal distribution: \begin{equation} \kappa=\frac{E(r-E(r))^{4}}{\sigma^{4}} \end{equation}

\(r\)
asset return
\(\sigma\)
standard deviation of asset returns (square root of variance)

The kurtosis for the normal distribution is 3. Often, instead of kurtosis, researchers talk about excess kurtosis which is defined as kurtosis minus 3 so that in a normal distribution excess kurtosis is zero. Distributions with an excess kurtosis value greater than 0 are frequently referred to as having fat tails.


Function Reference
portfolio_kurtosis, position_kurtosis