Skewness and Kurtosis of Hedge Funds| In a number of previous post I wrote that learning how to program has loads of benefits. I have started to do a lot of backtesting and research in matlab lately. I haven’t left excel and it will probably take me a long time to go from excel to matlab. I have noticed that Matlab is blazing fast; I mean as fast as the marvel comic book character “Flash”! Who doesn’t love the flash?
So I fired up excel again and wanted to compare the skewness – a measure of symmetry, or really a lack of symmetry for a data set and the Kurtosis – a statistical measure used to describe the distribution of observed data around the mean.
The formula used for Skewness.
The formula used for Excess Kurtosis.
I plotted all the hedge fund strategies standardized z scores based on a normal distribution- a probability distribution that plots all of its values in a symmetrical fashion and most of the results are situated around the probability’s mean. They are below in chart A.
Next in chart B is a comparison of the skewness and kurtosis for a number of hedge fund strategies a risk averse investor or institution wouldn’t like negative skewness. A negative skewed distribution has thicker left tails than right, which increases the chance of fat tails. Gaussian distribution is expected to follow a normal bell curve; fat tails are often an unexpected and unwelcomed result. A positive skewed distribution has thicker right tails than left.
Kurtosis is the measurement of the fat tails. I have used excess kurtosis to make it simpler to understand as it adjusted the value to zero. A risk averse investor or institution should prefer a lower kurtosis. The images below will give a better sense of why investors and institution prefer higher kurtosis.
There are a number of ways to look at chart B. I ranked the hedge fund strategies by positive skew and lower excess kurtosis. The hedge fund strategies that rank in the top three are Long/Short, Global Macro and IASG Systematic Index in that order. The test was all done with monthly returns from 1997 to 2011.