The correlation calculation here is straight forward. With correlation tho, I presume that the objective would be that as more systems were added, ideally the N systems would have ZERO pairwise correlation. Otherwise, for highly correlated systems, it would simply be better to opt for the highest performing system. Given the sample size of returns (several months), is it introducing any sample errors? What I mean is that if I were to assess the correlation matrix of N systems, should I be taking a random sample from the population, as opposed to a biased sample of the most recent months, of the system's returns and then evaluating the correlation or does it all just collapse to this reduced form?... To elaborate a bit, what is being sampled is returns, across the board of all systems, at a specific point in time. Systems with high correlation are possibly variants of a fundamental form, I admit this is an iffy statement that I just made... A non-zero correlation value would indicate that a larger proportion of N systems have performance that are materially related to one of the other systems. Optimally, no one system should have performance correlated to another so as to limit the variance of the sum of the returns of all N systems. Actually, I have to think about this some more... Very interesting stuff... For sure! I do have a moderate quant background but have kept much of this stuff separated from trading (well actually all aspects separate from trading). It is a knowledge and application weakness that I am attempting to overcome in order to integrate the best of both worlds... Kindest Regards, MAK!
For this run I believe there were 37 samples that were averaged. I chose 48 months minimum because you need 12 before you can do a rolling average. Then at least 30 more to get some sort of base close to a normal distribution. Of course there is sampling error introduced with such small numbers but it's the best I can do. I could add more periods but it doesn't change the correlations much. What I was trying to do is assess the overall correlation (average) and the distribution (std. deviation). If you have models that trade on a daily basis it would probably work better to do the test on daily results instead of monthly. These models are pretty selective so their trade frequency isn't anything special. In a practical sense what I'm interested in is the average correlation + 1 std. dev. being below .5. I have a program around here somewhere where I processed trades at different correlations and found that below +.5, it's better to trade separately. Above +.5 it's better to save the better model and either combine the second model with it or discard it if it can't be integrated.
Absolutely agree here... Negative correlations would state that the two systems would have a cancelling result on the aggregate of their returns. NEAT! Thanks. At the moment, I have several automated systems and prob a dozen others scattered across several dozen notebooks of scribbling and rambling. When I get better organized, I'll dig up some results to contribute and evaluate within the confines of the material presented. Thanks Again, MAK!
Here's the money management sim for the two combined models. I ran the report once and it hit the profit objective so I cut back the % risk per-trade to 3/4%. Notice the contract multiplier is the same as on the weighting report. With the addition of the second system the expected return moved up to 49.6%, the expected drawdown dropped to 9.8%, and the profitable months moved up to 74.9%. The combination of two uncorrelated systems has helped. One thing to note about Monte-Carlo tests is they tend to offer pessimistic results as compared to the real-world trades. This happens because when two models are structurally non-correlated the chances both are in drawdown at the same time are virtually nil. Monte-Carlo assumes both are just as likely to be in drawdown at the same time as any other outcome. Since the objectives aren't met, it's on to using 3 models.
Here's the 3 model weighting report. The third model I added is the same as the first one except it is run on the NQ market instead of ES. It also is at a higher timeframe so it trades less often. I added it to show that by changing markets and timeframe but using the same methodology you can sometimes get good results. Notice the reduced modified sharpe ratio on model 3. This is what happens when the trading frequency declines. Also notice that the overall correlation between 1 and 3 is slightly correlated. Also notice the standard dev on the correlation moves the correlation +1 standard dev. up to +.32. While it's ok, if I was looking to trade in realtime, I'd look to see if I have another model with better correlation stats. In the big picture the 3 model test shows the modified sharpe ratio is moving up, so I expect the number of winning months to go up as well.
With the 3 models the projected profits moved up past the profit target using .75% risk per-trade but the max dd was above the goal. I reran the mmgt test dropping the fixed % to risk per-trade to .6%. The result was all three of the performance goals came closer. The projected average return moved up to 58.9%, the average drawdown dropped to 9.1%, and the per-cent of profitable months moved up to 79.4%. Notice how every time I hit the performance goal I reduce the risk per-trade. This is done to lower the expected drawdown. In testing I've found if you use fixed % risk per-trade the best way to lower the drawdown is to lower the average losing trade. At this level the only tool is the % risked. I'll need a fourth model to see if we can meet the goals. I'm going to get something to eat and be back.
Now we're up to 4 models. Here's the weighting report. I love to look at these reports when they start getting up in numbers of systems because it tells you so much about how your portfolio is being managed. Once again the test reveals the best combination of models is using all 4 models. I like to look at the 12 month rolling correlation with +1 std. dev. in the two model results and also the two model modified sharpe ratio's to get ideas on what I need to work on to improve my performance.
Once again, here's the 4 model mmgt report. I once again lowered the % risked on each trade. This time down to .5%. The projected returns stayed about the same with lower drawdowns and more months projected to be profitable. The projected return was 58.1%, with expected average drawdown to be 7.7%, and expected per-cent months profitable to be 83.6%.
I realize not everyone will have the talent or desire to develop software to do these types of tests. Because I do want to help individual traders, I'm willing to have these tests run on your stuff on up to 5 models (I have a helper that's pretty bored right now). To do this I'd need the following for each model. 1). A monthly total profit/loss for at least 48 months. 2). A trade list with date followed by a comma and the total closed profit. I'll setup a email account somewhere where anyone that wants this done can send the files as attachments. If I get too many requests, I'll let you know. I'll post the files from model131 as examples. Here's the monthly file.