I posted some results for Trend Plays #1 on my blog and they seem to indicate a declining but highly insignificant alpha over time. I’m planning to look at some more systems over the next few days, and see if I can find any indications of regression to the mean.
"So that does not explain why systems at the right side are vertically in the middle."
Well - the more trades the higher probability that the system has been abandoned.
I think the only real way to approach this issue is the way Science Trader is - find all the systems with a large number of trades and see what the Sharpe Ratio is for them. Otherwise you are just making guesses.
Steve
Otherwise you are just making guesses.
You forget that my explanation is not a guess. It is a mathematical necessity, stated before the observation. It a logical consequence of the fact that the statistical estimates become more reliable when the number of observations grows. The alternative explanations, on the other hand, are guesses.
So even if you find empirical support for alternative explanations, these can only come on top of the statistical explanation but they cannot replace it (i.e the statistical effect will still be true too). Furthermore, note that the statistical explanation, even with this simple model, predicts the present pattern quite accurately (see the plot in my previous post). If there are also additional effects such as selective abandonment, then the pattern should be even stronger than it is now . An alternative explanation should also explain why this doesn’t happen.
In other words, my explanation is by far the simplest explanation. It may not sound simple to you if you aren’t used to statistical reasoning, but it needs less assumptions. Basically, the only assumption that it needs is that most trading systems have a probabilistic component. From there it follows that a pattern like this must happen.
With respect to the specific points you raised:
Well - the more trades the higher probability that the system has been abandoned.
That cannot explain it either, because the total number has no effect on the variance, as I already pointed out to ST. Remember that the observation is not that the mean changes, but that the variance decreases. If the abandonment of systems is to explain this, you must assume much more than the abandonment of more systems. You must assume that profitable systems are abandoned too, which is inconsistent with your previous explanation. And you must also explain why the neutral systems are not abandoned, or less likely to be abandoned.
I think the only real way to approach this issue is the way Science Trader is …
That method has the same amount of limitations. My method was “cross-sectional” and the other method is “longitudinal”, as I explained in the beginning of this thread. Both are generally open to alternative explanations. It is true though that doing them both will eliminate more alternative explanations.
Please note that the graph was only about forex systems, not stock systems. A similar pattern can be expected for stock systems, but the limit need not be 0. Also, the statistical theory does not imply that the performance statistics of every system will decrease, only that the performance statistics of most above-average systems will decrease.
I’m closing this thread to keep the length manageable, but please feel free to continue the discussion in a new thread.
