Monte Carlo Analysis
What is Monte Carlo Analysis?
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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.
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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