As of this afternoon, a total of 1149 of approximately 2,500 hedge funds have reported data for October, 2009; so it's now time to update our data and forecasts for the dynamic trading risk factor. This gives us an early estimate of a number that is not much likely to change during the rest of the month.

Out-of-sample, our final forecast of the return for September, 2009, was 1.10% (our early forecast was 1.11%), and the realization was a substantial 3.25%. Our final forecast for October, 2009, was 1.61%, yet our current estimate of the performance for the most recent month is a loss of −0.20%. As a result we are forcasting a 0.30% return for November, 2009. These forecasts represent an a priori expected monthly return for any fund or firm that makes it's living by trading.

We have a new month and new data for the dynamic trading risk factor. Last month's forecast was for a profit of 1 %; the realization was a profit of 5.20 %. This month we are forecasting a profit of 2.17% for May, 2009. (Note that the underlying charts for the prior posts have been replaced by the newer versions.)

On the chart above I have, arbitarily, identified the start of the crisis as October, 2007; and, the end of the crisis as November, 2008. (The three regions are labelled pro articulus; per articulus; and, secundum articulus; repsectively.) This identification was done by "eyeballing" the peak and trough of the cumulative factor series without reference to any other criteria. Although this uses up two degrees of freedom, since we are choosing part of the data according to some criteria of our choice, I wasn't trying to choose regions according to the underlying properties of the data and I've not varied these choices to emphasis any statistic. I think, on this basis, I can legitimately use the two sample Kolmogorov-Smirnov test without violating the criteria regarding its validity. I'm not 100% confident of that, but I'm over 99% confident!

Without making any distributional assumptions, we can ask whether the pro articulus data set and the sec. articulus dataset are consistent with being drawn from the same underlying distribution. The two sample K-S test allows us to compare the empirical distribution function for two data samples and assess whether they are consistent with eachother without every having to specify the underlying population distribution. It is a truly remarkable tool.

The chart above presents the results of this analysis, including a chart comparing both empirical distribution functions. The Dmax statistic is 0.27901 with a sample of 81 months pro art. and 5 months sec. art. The test indicates that the distributions agree, with a p-Value of 0.91453 (indicating the probability of obtaining a larger Dmax by chance with samples this size). Again, the similarity of the two samples was not the criteria used to choose the samples — which is why I believe that this is an unbiased use of the test.

In plain terms, the data does not contradict the assumption that the returns are distributed as they were before.