Kurtosis

The kurtosis or leptokurtosis (literally, ‘fat tails’) of a distribution is a measure of
the frequency of large positive or negative asset returns. Specifically, it measures the
frequency of large squared deviations from the mean. The distribution of asset
returns will show high kurtosis if asset returns which are far above or below the
mean occur relatively often, regardless of whether they are mostly above, mostly
below, or both above and below the mean return.
Kurtosis is measured in comparison with the normal distribution, which has a
coefficient of kurtosis of exactly 3. If the kurtosis of an asset return distribution is
significantly higher than 3, it indicates that large-magnitude returns occur more
frequently than in a normal distribution. In other words, a coefficient of kurtosis well
over 3 is inconsistent with the assumption that returns are normal. Figure 1.2
compares a kurtotic distribution with a normal distribution with the same variance.