sigmaquant.performance.metrics.excess_kurtosis#

sigmaquant.performance.metrics.excess_kurtosis(returns)#

Compute the excess kurtosis of a return series.

Excess kurtosis measures the degree of tail heaviness of a distribution relative to a normal distribution. A normal distribution has zero excess kurtosis.

Parameters:

returns – Sequence of periodic returns or PnL values.

Returns:

Excess kurtosis of the input series.

Return type:

float

Notes

  • A normal distribution has zero excess kurtosis.

  • NaN values are ignored. No finite-sample bias correction is applied.

The excess kurtosis estimator is:

\[\widehat{\kappa} = \frac{1}{T} \sum_{t=1}^{T} \left( \frac{r_t - \bar{r}}{s} \right)^4 - 3\]