Python Tutorial : Skewness and Kurtosis

Key Takeaways

daily volatility and mean give you a good indication of daily risk in return but skewness kurtosis and scaled volatility will help you build a more holistic view of risk the third moment skewness can be thought of as a measure of how much a distribution leans to the left or the right negative skew is a right leaning curve while positive skew is a left leaning curve in finance you would tend to want positive skewness with a higher probability of significantly good returns on the right-hand side of the distribution and the compressed predictable left-hand distribution of negative returns to calculate the skewness of a return distribution simply call the skew function after importing skew from scipy dot stats be sure to drop any n/a values using the drop and a method skewness above zero indicates possible non normality which once again you can expect to find in financial returns kurtosis is a measure of the thickness of the tails of a distribution which can be used as a proxy for the probability of outliers if you recall normal distributions tend to have a kurtosis near 3 most financial returns are leptokurtic which simply means that they tend to have a positive excess kurtosis or kurtosis greater than 3 since kurtosis is so often compared to a normal distribution many functions in Python will automatically return excess kurtosis which is essentially the sample kurtosis minus 3 which helps demonstrate whether the probability of outliers is higher or lower than a normal distribution if excess kurtosis is higher than 0 the kurtosis is higher than a normal distribution inside pi for example the kurtosis function is actually computing excess kurtosis if you wanted to calculate the true sample kurtosis you would actually need to add 3 to the result but for most cases you're going to be interested in excess kurtosis anyways so this functionality is fine as long as you are aware of it in hi excess kurtosis is an indication of high risk when large movements in returns happen often this can be a very bad thing for your portfolio if it moves in the wrong direction high kurtosis distributions are said to have thick tails which means that outliers such as extreme negative and positive returns are more common before we move on let me briefly add one final tool to your arsenal if the kurtosis of a distribution is greater than 3 and the skewness is nonzero the data is most likely non normal but what if the values are close to but not quite normal you can use the Shapiro well Casta tist achill test to estimate the probability that the data is normally distributed the null hypothesis of the Shapiro will test is that the data are normally distributed and when the p-value returned is less than or equal to 0.05 that means you can safely reject the null hypothesis and assume that the data are non normal now it's your turn