I've recently begun to use MC simulation to study Max DD and profit levels. In doing so, I have come across an issue that I would be curious to get opinions on. From what I understand, most who use MC simulation have their MC program select trades randomly from a list of actual historical returns (in accordance w/their relative probabilities) and then observe how reordering and/or excluding certain past returns affects DD and Equity. While I certainly see the value in this and the guidance it provides for pos sizing, I am curious to hear if anyone feels the following procedure is better or worse than the above, and why. In my MC program I can define variables according to a certain distribution. So given a list of historical returns, once I calculate the Mean and Std Dev of Winners and the Mean and Std Dev of losers, I can input it into the MC program and it will generate values according to the distribution I select for each run (for simplicity's sake let's assume I choose Normal). The program will generate a winning and losing return for each potential trade, all I need to do is have the program signal which of the two returns to record. This is accomplished by defining a binary variable for each trade that has the same probability as the Win%. From that point forward, the rest of the metrics are calculated just as they are in the aformentioned procedure. I hope this is clear, please question me if it is not. Anyway, I was wondering if a continous set of trade results generated according to a distribution might give a slightly more realistic picture. After limited testing, I have noticed that the results I get from this procedure tend to be more pessimistic than those from the process described in the first paragraph above. I would appreciate anyone's thoughts on the matter. As a side note, if I decided to go with this method, I would likely stick to a normal distribution for the winning trades, but use an alternative that captures fat tails on the losers.
I also fit a distribution to my trade results and monthly returns and make draws from that distribution in MC simulations. I like BestFit by Palisade Decision Tools for quickly picking the correct curve and parameters. I also use @Risk from the same company. I also found that a normal distribution wasn't fitting the fat tails well. Welcome to Elite Trader, BJS, and good trading! Aaron Schindler Schindler Trading
I am having trouble understanding the results you get for the first option vs the second option. In the second option are you getting an entire equity curve constructed by randomly drawing from your distribution and in the first you are only getting a single value? I would prefer the second approach. I am new to this too though. I recently finished some monte carlo testing on money management compounding strategies. I wrote a small paper detailing the results. PM me if you want to see it.
Aaron- I appreciate the welcome and vote of confidence in the method. Opm- For both methods, I get a complete equity curve, but the data that was used to construct the curves differs, so I end up with different results (i.e. the 10th percentile DD in Method 1 differs from the 10th percentile DD in Method 2). The key difference in the data used is that Method 1 continually reuses only the discrete values that you have provided from historical results. While Method 2 constructs a nearly continous set of data points (based upon the discrete set of historical results) that ranges between a few standard deviations above and below the mean. That said, both methods conduct the same number of trades per trial and calculate equity and DD for each trial in the same manner. I hope this answers your question, please let me know if it doesn't...this is the type of thing thats easy to demonstrate looking at a screen, but more difficult to articulate in this format. Thanks again for the input.
I resample the original (discrete) distribution. However, because there appears to be serial correlation in the data, I don't take 1-day samples of the original equity curve. Instead I grab 2-7 day pieces (#days is a random number with exponential distribution). This is for position trading with average trades held approx 100 days, using a diversified portfolio of 50 futures markets. I like to plot the cumulative distributions of (longest drawdown) and (2nd longest drawdown) and (3rd longest drawdown) on the same graph. Shows me how bad things might get.