Detecting non-normality using skewness and kurtosis

Returns are most often non-normal in nature. Two metrics key to understanding the distribution of non-normal returns are skewness and kurtosis. The skewness will help you identify whether or not negative or positive returns occur more frequently. Negative skewness indicates that large negative returns occur more often than large positive ones, and vice versa.

Kurtosis will be positive if there are fat tails in your distribution. This means that large positive or negative returns will happen more often than can be assumed under a normal distribution.

The histograms in the plot environment compare the daily and monthly returns of the S&P 500 over the period of 1986 until today. There seems to be a negative skewness() in these plots, and a somewhat greater than normal kurtosis(). Note that, by default, kurtosis() reports the excess kurtosis (that is, the kurtosis minus three). Let's see if the numbers match our observations!

The objects sp500_daily and sp500_monthly are already loaded in your workspace.