Misc System Statistics Issues

I thought I would chime in with a couple of things related to system statistics. Please forgive me if what I say is repeated elsewhere on these boards; this thread was recommended to me and I have not visited this site is many months.

First, I enjoyed Jules’s post earlier on system statistics; I can only assume you are very well respected around here.

With regards to the normality arguement, I wholeheartedly agree with avoiding the assumption of normal distributions whenever possible, especially when discussing returns in financial markets. In fact, when discussing common global financial markets, returns are most certainly not normal. There is usually very significant leptokurtosis on high-frequency data; as the frequency increases, the kurtosis usually does as well. Also, stock market returns usually have significant skewness.

As an example, I did a very quick and crude test on weekly spot SP 500 data. The data showed kurtosis of 10 and skewness of -.33, with a Jarque-Berra normality statistic of 82 (1% critical value is 9.21).

Trading systems can be all over the spectrum with regards to return distributions. A very consistent mean-reversion strategy may have very strong kurtosis. A long term trend system, on the other hand, may have less kurtosis but very strong skewness. Either way they’re not normal.

I really think Sortino ratios are a far better choice. The point of using a Sharpe ratio is to assess the return/risk tradeoff; any application of the ratio when the distribution of returns is not symmetrical is misleading.