Registered: Mar 2003
03-08-05 08:19 PM
Any probability distribution of trades (gaussian or not) will yield a gaussian distribution of results after N trades, as long as N is high enough and the trades are independent (central limit theorem). So if you want to compare the mean and variance of of your live trading results with that of your backtested results, you have two problems:
(1) You need a large number of trades N to generate your gaussian distribution of results.
(2) If the trades are not independent in the first place, you have to be careful with how you interpret "mean" and "variance". Your distribution of results is not gaussian.
Using a monte carlo, you get rid of both of these problems at once.
(1) Many less trades are required, since you can now compare distributions directly. By using a set of 100,000 traders, you can see how likely it would be to achieve a certain result with only 10-20 trades.
(2) Since you are not using "mean" and "variance" to compare your results anymore, it is a moot point whether your results are independent or not. You are comparing distributions directly.
This all makes sense to me now... but i'm open to re-education if neccesary.