Hi, I mean re-sampling by MonteCarlo. Not doing actual generation of price paths at all - thats for options pricing. I would be curious if you can write in detail your methodology. What do you mean by 2-dimensional re-sampling? What are the two dimensions here? How are you accounting for correlation between different strategies? Also, what do you mean by boolean re-sampling? Does it mean you are re-sampling just the signs of trade results + or - or you mean something else? Thanks.
Kevin, It will be great if you can explain in detail this problem of hidden or unaccounted for risk factors. What is "alpha alignment problem"? Thanks.
The two dimensions of re-sampling are (a) boolean 1/0 for each strategy for each day (b) the sequential position of a particular day on the joined equity curve For example, assume that I have two strategies, A and B, with 100 co-linear days of p&l each. I would first generate N combinations of these two strategies where I am randomly including only A for any given day, only B for any given day or both: for(n in 1:N) ..for(t in 1:days) ....Q[N,t] = sample(1,0) * A[t] + sample(1,0) * B[t] Now, I would run a M-times re-sample on each one of these joined paths: for(n in 1:N) ..for(m in 1:M) ....wdd = push worst_dd(Q[N, sample(seq(1,M))) After that you can look at mean wdd (expectation) or Xth percentile of worst draw down. Does that make sense?
I am not sure that's the right approach. Lets imagine that you have two strategies, one buys S&P 500 when Obama farts and another that sells DAX when Merkel smiles. The two strategies are hedging each other rather well, so you should be more comfortable trading on Obama system when you already have a position based on the Merkel system, do you agree?
Thank you very much! Yes, it seems like a nice approach. Biggest advantage is its simplicity. Another advantage is its numerically very much solvable. Even with 10 strategies, if you use N = 1000 and M = 100, its just 100k simulations/re-samples. Thus, using some ingenuity, you have managed to overcome the problem of 10 billion computations that I talked about. Since you are generating the boolean matrix - stating which strategies trade on a particular day in one go. If N = 1000, you generate 1000 boolean matrices, and M = 100 then resample 100 times in each matrix. Do I understand you correctly? I guess that when you are generating your boolean condition for say Strategy A to trade on a particular day, you are using the boolean function in such a way that it makes the total number of trades equal to that observed in strategy A. So, in 3rd line of your code, sample(1,0) function should have an input stating total number of trades in this strategy so that you can force total number of 1s equal to this input (you sample 1/0 such that you get same number of trades as actually observed). Correct? The shortcoming of this approach is that it ignores correlation between systems. In fact, it assumes correlation of 0 among systems. The approach of sampling from a joint distribution will overcome this precise shortcoming. However, it is more complex to implement. Also, as of now I am not sure how much extra value implementing that approach will result into compared to your approach. I think I will know only after I implement it and compare the results with your approach.
Continuing reply from above to sle (as the Edit time line expired) : It just occurred to me that most of my strategies trade like 30 to 100 days in a year. So, on most of the days, I have only 1 or 2 strategy trades. Probably only on 40-50 days a year or so, I will have 3-5 trades in a day. So, on most of the days, I won't really encounter the problem of allocation. Which means, I am mostly concerned with my worst DD and for that your simpler approach might be enough. I might not do this correlation thing at all unless my strategies start to trade much more frequently. However, I might sample based on volatility.
1 system: PEP three apps as they are now called. PVT, SCT and SSR. See one pagers. The four price drivers: anxiety, fear, anger and hope.
You could maybe use the correlation for the Q[N,t] calculation, like this: - calculate the correlation matrix for the strategies. - for every strategy, rank the days A(t), B(t) - or the trades, dependent on what you're using - by their return. - calculate Q[N,t] by a function that assigns higher probability to combinations that match the correlation. For instance, if A and B have a negative correlation, then combinations of a high rank of A(t) with a low rank of B(t) - or vice versa - should occur more frequently. This would keep the correlation info in the resulting DD.
So where does anxiety, anger and hope drive price? My guesses are, sideways, up and down, respectively.