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Perform Monte Carlo analysis on your existing trading system or method to improve the accuracy of your system testing and to help prevent curve-fitting. Market System Analyzer (MSA) is a stand-alone Windows application that includes an easy-to-use Monte Carlo simulation feature. The software can be applied to any trading system or method regardless of market or time frame. When combined with the position sizing features of Market System Analyzer, Monte Carlo analysis can substantially improve the estimate of your system's likely rate of return and drawdown.

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What is Monte Carlo Analysis?

Monte Carlo analysis is a computational technique that makes it possible to include the statistical properties of a model's parameters in a simulation. In Monte Carlo analysis, the random variables of a model are represented by statistical distributions, which are randomly sampled to produce the model's output. When using Monte Carlo analysis to simulate trading, the trade distribution, as represented by the list of trades, is sampled to generate a trade sequence. Each such sequence is analyzed, and the results are sorted to determine the probability of each result. In this way, a probability or confidence level is assigned to each result.

Monte Carlo analysis is particularly helpful in estimating the maximum peak-to-valley drawdown. Generating a better estimate of the drawdown makes it possible to better evaluate the risk of a trading system or method. In using a Monte Carlo approach to calculate the drawdown, the historical sequence of trades is randomized, and the rate of return and drawdown are calculated for the randomized sequence. The process is then repeated several hundred or thousand times. Looking at the results in aggregate, we might find, for example, that in 95% of the sequences, the drawdown was less than 30% when 4% of the equity was risked on each trade. We would interpret this to mean that there's a 95% chance that the drawdown will be less than 30% when 4% is risked on each trade.

Monte Carlo Analysis is Easy to Apply in Market System Analyzer...

In Market System Analyzer, the Monte Carlo analysis is performed when the Monte Carlo Analysis command is selected from the Analysis menu.

The Analysis menu contains the Monte Carlo Analysis command.

The analysis is performed on the current sequence of trades using whatever analysis options and setting have been applied to the current sequence, including position sizing settings, dependency rules, and so on. The number of samples for the analysis can be entered in the Options tab of the Analysis Setup dialog box. In this context, "sample" means a randomly selected sequence of trades. The default is 1000 samples, which means that the Monte Carlo results will be based on 1000 random trade sequences. The results will be displayed in the Monte Carlo Results window at the confidence level entered in the Options tab. An example is shown below.

Example of Monte Carlo analysis results generated by Market System Analyzer.

In this example, the starting account equity was $50,000, and 5% of equity was risked on each trade ("Fixed Fraction: 5.00%"). The section labeled "Key Results at Select Confidence Levels" lists the rate of return, worst-case drawdown, return-drawdown ratio, and modified Sharpe ratio at a range of confidence levels. Notice, for example, that if you demand a higher confidence level, the predicted rate of return will be lower and the worst-case drawdown will be higher. The bottom section lists the Monte Carlo simulation results at the user-selected confidence level of 95%. For example, the results indicate a return on starting equity of 918% with 95% confidence and a profit factor of 1.31 with 95% confidence.

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For a general article on Monte Carlo analysis, click here. For a full list of available trading articles, select the Article Library link at left.