Ok, here's an example how to do #1 in excel. Enter your returns/trade in column B. You'll find a random sample of these trades (40 in the current sheet) in column G, and its average in column I. The monte carlo runs are shown (100 in the current sheet) in column L, using Excel's Datatable function. A distribution is obtained in column O, and plotted on the chart. You can modify the sheet if you want to enter a larger/smaller number of trades, do more replications etc. Be careful with the interpretation: What you see is the distribution of your *expected* (i.e. average) return, NOT the distribution of the individual returns.
I think if you're just interested if the strategy has a positive expectancy, you don't need to build a distribution of the trades. You just sample from the actual returns/trade.
No. It means that 68.3% of closed position P/Ls will fall somewhere between -2.5 points and 9.3 points, 95.4% of them between -8.4 points and 15.2 points and 99.7% of them between -14.3 points and 21.1 points. The higher the standard deviation the higher the strategy risk. In absolute terms this means nothing. It only means something when compared to an alternative strategy with a lower/higher standard deviation. Ron
Eric, A quick eyeball will give you a rough idea of how normal they are. Or, as I suggested skew and kurtosis will help. If you are using targets and/or stops fat tails shouldn't really be an issue - but it is wise to check. You could also do a rough non-parametric VaR. That is, sort your daily returns in ascending sequence. Divide the number of samples by 20. Find the sample number that corresponds. That is your 1 day VaR @ 95%. You should only have a bigger losing day on average once every month. although they may be somewhat clustered. If you have outliers more frequently than this stop trading and figure out what was wrong with your testing or is wrong with your trading model. As for books - try some high school stats primers like the series by Schaum. Hope this helps. All the best, bolter
Sample size: 150 Average trade: 3.4 Standard deviation of trades: 5.9 Based on the above data, elementary computation of a confidence interval suggests: with 95% probablility you can expect that in the future your average trade will be in the interval [2.4, 4.4] points. t-statistic will give very similar results. But be aware, this is only theory and there are a lot of ifs behind.
careful with that - with a 'loosey-goosey' "system" like that it's very easy to curve fit - i can show you the same data points every month for the next year, and I guarantee you that youre 'observations' of them will differe almost every time. (unless your observations are hard and concrete, like if a> b then buy a at b/2.
this is a neat spreadsheet, thanks - would someone enlighten me, pls, if this approach is what is referred to in statistics as "bootstrapping"? it looks like it, based on what i have read...except that perhaps you bootstrap from a portion of the sample, not the entire sample. or how is bootstrapping different from this exercise? thanks a lot.
As a5519 suggested in theory the estimation of this system's true average is between [2.4, 4.4] points with 95% confidence. Your average trade will be between [-2.5,9.3] with 68% confidence and between [-8.4,15.2] with 95% confidence assuming of cource a normal distribution for your returns..
Thanks everyone for your input. Although sometimes ET can be very childish the information provided here and in other threads have been very helpful to me. thanks Eric