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(Note that the underlying charts for the prior posts have been replaced by the newer versions.)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.