Return kurtosis describes how heavy or light the tails of a return distribution are relative to a reference distribution.
Higher kurtosis is associated with more probability mass in the tails and more extreme observations than a Normal model would suggest.
Pearson kurtosis and excess kurtosis use different conventions
Under the Pearson convention, a Normal distribution has kurtosis of 3. Under excess kurtosis, the same Normal distribution has value 0 because three is subtracted.
That convention matters in systematic research. The Grizzly Bulls Deflated Sharpe Ratio implementation accepts Pearson kurtosis, not excess kurtosis.
Kurtosis complements return skewness and effective sample size. The first describes asymmetry, the second dependence-adjusted information, and kurtosis describes tail weight.
For Sharpe inference that explicitly uses higher moments, see the Probabilistic Sharpe Ratio and Deflated Sharpe Ratio tools.
Kurtosis does not summarize every tail risk
Two return series can have the same kurtosis while differing in drawdown path, asymmetry, clustering, and dependence.
It is a distribution-shape statistic, not a complete risk model.
Sources: NIST, Measures of Skewness and Kurtosis and Bailey and López de Prado, Deflated Sharpe Ratio.
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Continue from the concept into the Grizzly Bulls research surface that best matches the next question. These links are research continuations, not recommendations or required steps.
Test Sharpe uncertainty
Use sample length, skewness, kurtosis, and a benchmark Sharpe to evaluate uncertainty around one observed Sharpe ratio.
Deflate selected Sharpe evidence
Include non-Normal return shape when judging a selected Sharpe against a search-aware benchmark.
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