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Using the same example above where I got 0.28 score, your formula yields 58.81. I'm not sure how to interpret the results, more research is needed here it seems. Is 58.81 saying there is a 58% chance of positive performing results?
The 58.81 means something like:
- if you keep the same win/loss ratio, and the same average winners/losers, you'll win $58.81 per trade.
Your formula make sense, but why not dividing by the the average winner, for example.
Anyway, the thing is to compare in using the same criteria, and understand the meaning of used criteria.
Yes I agree with you on both counts. And because of this, I see no real advantage of having it divide out that last part. So I removed it from the version I am using now in my MC.
Thanks for raising the question of expectancy optimisation / custom fitness functions for MC.
My interpretation of expectancy is closer to Mike's original. It is a measure of risk adjusted returns when you include the average losing trade in the denominator.
As such the 0.28 reflects an expectation of 28c return for every dollar risked, where risk is defined as the average losing trade size.
Van Tharp amends the risk denominator to be his 'R' being the actual dollar amount risked per trade (assuming it is predefined), but this usually requires an array to capture the risk per individual trade, and so it is often expressed as average losing trade as the risk denominator. As such, when using the array approach, I usually find it ends up being dumped to excel for comparison, whereas the average trade denominator makes it possible to use it as an optimisation fitness function in MC. So thanks for putting the optimisation code together.
The interpretation of the 0.28 is such that the system is expected to return 28c per dollar risked. A negative number reflects a negative expectancy, ie a truly losing system. Anything greater than 0 has a positive expectancy, even if it is only 0.01. How much more than 0 you will accept as reasonable is a judgement call.
Yes there are systems that have expectancies > 1 as calculated originally by BM, but they are few and far between, and they are surprisingly not always the most tradeable systems psychologically, as I have found that the highest expectancy systems are often in the 20-40% win percentage range.
The reason for including the risk denominator is so that it is a normalised fitness function that allows comparisons across systems. From the perspective of optimising one system at a time, you can argue that removing the denominator doesn't make much difference, but by taking it away you are essentially optimising of average trade value (or average trade net profit / ATNP), which is what the formula usually reduces to. This is the classic definition of expectation: Netprofit / no trades. How much does your system make per trade. If positive, you have a winning system / backtest. If negative a losing system / backtest. I prefer the risk adjusted version with average losing trade as the denominator.
The utility of expectancy as a custom fitness function depends upon its predictive value in a walk forward sense, and my research suggests that it is a pretty reasonable fitness function, and I do tend to incorporate some weighting for expectancy in my fitness functions, but it is not the only component.
