dom, would I average the median/std dev then across the Monte Carlo simulations?
Otherwise the variance would be way too wide to be meaningful since there aren't that many live trades yet but there are over 49.000 backtested ones.
As I mentioned in the previous post, the median is 47.8, the std dev is ~ 480. (on a full position size [10k margin] based on the backtest results across the entire distribution, no monte carlo here).
The live trades are half the position size [5k margin] the median is 45 and the std dev is 138. There's only 7 live trades as of now.
1. You should normalize everything to a standard position-size
2. Ignore the backtest & live stdev
3. Using the backtest trades distribution, run MC sim for the number of live trades you currently have, and take
that stdev
4. Divide your normalized live avg/trade by the stdev just computed : that's how far your current live avg/trade is vs. what you expect it to be based on the backtest.
Given the very small live sample-size, the stdev should be sky-high, and the current distance as a result should be close to zero - that's my point : with such a small sample size, you can't conclude anything, unless your live results are really way far off.
In the long run, I would consider live-results to be "as expected" as long as that distance is less than 2 stdev. (at some point, you will want to use the last N months of live trade data for this - even though lower sample size means higher stdev, it is also faster to detect a degradation into "unexpected" territory).
As for your current live slippage being better than the backtest assumption, that's a good thing & I would not change the backtest assumptions - my experience is that once in a while, you experience a large unfavorable slippage which will eat a lot of the prior small favorable slippage.