Kurtosis
Kurtosis measures the heaviness of a distribution's tails relative to a normal distribution. Excess kurtosis above zero means heavier tails than normal, implying more frequent extreme values — a concern in financial risk modelling.
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A normal distribution has excess kurtosis of zero. Daily financial returns typically show positive excess kurtosis — a leptokurtic shape with fatter tails than the bell curve implies, so sharp crashes and rallies occur more often than normal theory predicts. Negative excess kurtosis instead means thinner tails and fewer outliers.
Where it fits
TopicDescriptive StatisticsAdvancedSubjectData Analysis & StatisticsAdvanced
The formula
LaTeX
Variables
- Individual observation
- Sample mean
- Number of observations
- Sample standard deviation
Excess kurtosis of zero matches a normal distribution. Positive values (leptokurtic) indicate heavier tails and more frequent extreme values than normal.