# Monte Carlo Analysis

The method called Monte Carlo Analysis has been around for 70 years, since it was formalized during research into the atomic bomb. While many testing methods, such as back testing to optimize variables, use a set of historical data and investigate different outcomes, the Monte Carlo method makes no such assumptions about what values should occur. The weakness of back testing is of course that previous results are no guarantee of future performance, so it is easy to be caught up in the exercise of over-optimizing variables based on specific history.

This analysis has many applications in business and commerce, and is generally applicable anywhere that you have a variable input that can be defined by a statistical function. The point is that you do not need to use “average” or previous values, with the uncertainty that they entail, and if you do you are introducing some errors in your work. Monte Carlo analysis allows you to input statistical variables, and to get statistical variables as an output. In the context of money management for your trading, it allows you to run more accurate simulations of the effect that, for instance, changing your fixed fraction size will have on your drawdown and profit.

For instance, say that you have a spread betting strategy that you have tested to be right 40% of the time, and wrong 60% of the time, but when it works produces twice as much in average profit as the average loss. With a profit of 40% x 2 compared with a loss of 60% x 1, this sounds like a winning system, but what you might do to discover how much drawdown you can expect is a back test over a few years’ results. If this is the best you have available, it is certainly much better than trading blindly, but you will finish up with one result, telling you what it would have done if you had been applying it over that time. You might want to think of this as the “average” result, but in truth it may not be the most likely outcome, and you have no way of knowing how variable it may be. It may depend on whether the test starts or finishes with a series of losses, which may distort the results, even if the number of wins and losses complies with the percentages.

The Monte Carlo method gets around this limitation by providing you with a probability of results. Put simply, this philosophical tenet holds that there is no such thing as a “perfect system” for beating games that produce outcomes through independent events. Taking the starting point of a probability of input, the analysis will examine many different series of events, complying with your parameters such as the percentage of wins and losses, and the answer is another probability curve – think for example of the  “normal distribution” Bell curve – which will give you much more accurate information. Simply by looking at the area under the probability curve, you will be able to say that the probability of an account going below “X” is 20%, for example.

In case you think that this sounds useful, but you are not up to the mathematics, you should know that there are commercially available programs and add-ons for Excel spreadsheets which make it relatively easy to try out the Monte Carlo analysis.