Attached is a histogram of the time taken to close my winning trades vs. the time to close losing trades (the bottom axis is in seconds), it is obvious that the losers and winners have different distributions and that my trading could benefit from adopting a time limit on open trades. My question is to the math guys, given this information how would you systematically decide the length of a time based stops given the overlap and the non-Gaussian nature of the distributions?
Just looking at your densities (which might not be stationary... but let's assume that) 5000 seconds looks like a good point to cut it off since from that point on the winners decay just as fast as losers (and losers are much more frequent the longer the trade takes). Did you try to put that time stop around that time and see if it improves your results? The caveat is that these densities are absolute (not relative to the time of exit...). It's a natural desire to try to optimize exits but one needs to realize that without considering the structure of the trade itself, one would have to introduce additional edge (alpha) to achieve a better exit that the original one. If your strategy is some sort of momentum based one (as the densities suggest), then the time exit may introduce that additional alpha. Let us know if you could find an improvement of any kind considering time exit. In one of my strategies, I found that tightening my stop to a well defined location AFTER a certain amount of time has passed introduces additional alpha to the trade. That however depends on the strategy itself.