What is Skewness?

What is skewness?

Skewness, a measure of a distribution’s symmetry, is the standardised third moment. We standardise it by dividing it by the standard deviation cubed. It is unaffected by differences in the random variable’s mean or variance because we subtract the mean and divide by the standard deviation cubed. This enables us to compare the skewness of two different distributions directly.

A completely symmetric distribution has skew = 0.

Example of Skewness:

The third central moment of a distribution is:

Skewness = E{[X − E(X)]^3} = E[(X − μ)^3]

Why is skewness important?

The fundamental reason for skew is that normal distribution analysis wrongly calculates expected returns and risk. According to Harvey (2000) and Bekaert and Harvey (2002), skewness is a significant risk factor in developed and emerging markets.