I know what MC is supposed to mean in general backtesting terms, so I’m confused as to how it is applied to the equity curve.
This is what I would expect it to mean:
It’s supposed to reflect what would have happened to the equity curve if there had been an element of randomness in the opening and closing of trades. The randomness can come in terms of price and/or time changes.
What isn’t clear to me is what are the ranges of price and time that are assumed in the random test? Is it 10% of open position time, and 10% of opening and closing of position price? Is it only price? Would you be able to give a distribution curve for the randomness of either price or time?
Finally, and most importantly, I’d like to be sure as to how to interpret the MC curve itself. If the randomness implied within it is rather huge, then that means any system where the real equity curve is below or at the mean MC curve is running on luck and it’s just a matter of time before luck runs out. Am I right?
Let me try to shed some light here.
The Monte Carlo method (http://en.wikipedia.org/wiki/Monte_Carlo_method) is a rather general matematical/statistical method to tackle problems which are otherwise hard to solve. It involves the use of a random number generator to find some “approximate” solution to a difficult problem.
What C2 does with the equity curves is better named a “Bootstrap method” (http://en.wikipedia.org/wiki/Bootstrapping_(statistics)).
This method helps to fond the “true expected result” in cases where we have only a limited number of observations.
If applied to the “expected” equity curve of a trading system, the thinking goes as follows:
Question: Given a set of trades with their observed outcomes (some wins, some losses), what is a probable equity curve, and therefore a probable expected drawdown?
Method: Take all the outcomes of individual trades/days/weeks, mix them randomly and generate a large number of “possible” equity curves. [This is the bootstrap]
Answer: From all these “probable” equity curves with their “probable” drawdowns you may calculate some average (or “expected”) equity curve with some “expected” drawdown and more important: You see immediately the “range” of these results.
These calculated numbers are “better” then the actual numbers measured form the only true one past run.
Because we have just this single one past run and its hard to tell if this run is the result of pure (bad or good) luck.
With the bootstrap we get a large number of possible results and this makes it possible to judge the range of possible outcomes.
If you look at C2’s so called MC results you see a broad band of “possible” equity curves. The “expected” outcome is the curve in the middle. If the true curve is far below, this shows “bad luck”, if the real curve is in the upper half you see a good result due to “luck”.
I think the most interesting feature of this bunch of curves is the following:
As long as a large part of all “possible” curves is below zero, the system is not mature enough to show any reliable profits.
OK thanks for that wonderful and detailed explanation. It makes sense completely, and the interpretation you mentioned is quite important. Risk management should be much easier with this knowledge.