Monte Carlo Simulation Definition

Monte Carlo Simulation is a method of stress-testing a trading strategy.   The general idea is to use random data to construct a larger sample space built according to the same results distribution as the original sample.   This more clearly shows the effects of chance on potential outcomes and gives a broader set of data to make decisions.

Monte Carlo methods may be applied at different places in the trading strategy development progress.

One way to apply Monte Carlo methods to backtesting results is to randomly re-sample trades.  Start with the distribution of results for a backtest.  Rather than go  trade to see what happens next, we can run simulated trades.  Tens of thousands of simulated trades.  The result of each simulated trade is generated randomly according to the actual distribution found in the backtesting run.  Then plot the results distribution of all the Monte Carlo simulations to see the broad range of possible outcomes for the trading strategy.

Monte Carlo simulation may also be used to assess the statistical significance of backtesting results.  The process is advocated in Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signalsand described in detail in this paper by Dr. Timothy Masters.  

Extra Insight:

Rather than try to digest the raw results of 100,000+ trades, set boundaries on potential outcomes and use the Monte Carlo method to assess the likelihood of a trading strategy producing those results.   For example, if we define a catastrophic loss as 50% of account value, we can keep track of the number times that happens in 10,000 runs of 1,000 trades each, for example.    That’s one estimate of the probability that the trading strategy will “blow up” in the future.

Of course, the market in the future may not follow the same probability distribution as our initial sample!   Also, we backtest stocks one at the time but a portfolio holds multiple stocks which may move together so the method described above doesn’t exactly model real life.    It is a useful approximation, however.  

For a more comprehensive definition see Wikipedia for Monte Carlo Method and Monte Carlo applied to finance.    For motivation in very accessible terms see Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

(Backtesting Blog is an Amazon Associate.)

Updated 11/12/08.

Tags: backtesting, data, loss, monte carlo simulation, probability, statistics, strategy, technical, trading