The skewness and kurtosis statistics determine whether returns are normally distributed.
Skewness reflects the degree of asymmetry of a distribution. If the distribution has a longer left tail, the function has negative skewness. Otherwise, it has positive skewness. A normal distribution is symmetric with skewness 0. In lognormal case, the curve has a long right tail so the skewness is positive.
Kurtosis provides an idea whether dispersions in returns are mostly due to moderate deviations or are driven by outliers. Kurtosis indicates the peakedness of a distribution. For normal distribution, Kurtosis is 0.
The following formulas are used to calculate skewness and kurtosis:
