Kurtosis

Kurtosis is a measure of the combined weight of the tails of a distribution relative to the rest of the distribution.

leptokurtic: fatter tails than the normal distribution

platykurtic: thinner tails than the normal distribution

mesokurtic: identical to the normal distribution

For all normal distributions, kurtosis is equal to 3.

Excess kurtosis: kurtosis minus 3. (Normal or other mesokurtic=0. Leptokurtic > 0, Platykurtic < 0.)

[Practice Problems] A portfolio has excess kurtosis of 6.2. Compared with a normal distribution, the distribution of returns for this portfolio most likely:

A.  has less weight in the tails.

B.  has a greater number of extreme returns.

C.  has fewer small deviations from its mean.

[Solutions] B

The portfolio has positive excess kurtosis, which indicates that its return distribution is leptokurtic and has fatter tails than the normal. The fatter tails mean the portfolio has a greater number of extreme returns.