Introduction

In the realm of trading, Monte Carlo simulations involve applying random modifications to past trades, resulting in multiple different equity curves. These revised equity curves serve as a means to assess the trading strategy's resilience against unpredictable variations. For example, simulations can be used to evaluate the performance of a trading strategy under hypothetical circumstances, such as suboptimal entry or exit points, or the omission of profitable trades. For a more comprehensive review of how Monte Carlo simulations can be used to assess a strategy’s robustness, please refer to our article on best practices for backtesting.

In this brief article, we delve into the use of Monte Carlo simulations to set realistic or conservative expectations for a trading strategy’s maximum drawdown.

The benefits

Employing Monte Carlo simulations allows traders to gain insights into the potential maximum drawdown that may be encountered. For instance, while you may have encountered a modest drawdown of just 10% in your backtest, this is only a single metric obtained from a single historical path - a desirable low drawdown figure could easily be the result of luck. Monte Carlo simulations could unearth a high probability of facing a 30% drawdown at some point in the future. Being aware of this in advance has four main benefits:

1. It allows for mental preparedness, facilitating adherence to your trading plan when such a situation arises and navigate the uncertainties of short-term results with greater confidence;

2. Armed with a better understanding of your strategy, traders can make informed decisions on which strategies to deploy and which ones to discard;

3. Position sizes and allocation to strategies within a portfolio can be adjusted in a way that is commensurate to your risk tolerance;

4. Having more realistic expectations for maximum drawdown empowers traders to explore opportunities for optimising your trading strategy further to minimise the expected maximum drawdown.

The resample Monte Carlo simulation method

One of the simplest Monte Carlo methods involves simply reordering historical trade results, allowing for the creation of hundreds of different equity curves through repeated simulations. Since only the order of the trades is being varied but the profits and losses generated from said trades remain the same, we obtain hundreds of equity curves that end at the same level. But the drawdowns will vary for every simulation.

If we accept that there’s nothing inherently special about the order of the trades, then observing the probability distribution generated from the aforementioned simulations can allow us to set more realistic expectations for drawdowns we’re likely to encounter in live trading. Notably, the average drawdown tends to surpass that of the original backtest.

Extracting the maximum drawdown from the probability distribution

As mentioned previously, the Monte Carlo simulation exercise not only assists in quantifying the potential risks associated with a new trading strategy but also aids in determining the appropriate size for the strategy. This is achieved by studying the probability distribution derived from the simulations based on which we can assign a certain level of confidence to the assumed risk levels within the new trading strategy. This method can be broken down into the following steps:

1. Run the resample Monte Carlo simulations (typically between a few hundreds to one thousand).

2. Record the maximum drawdowns as a percentage of the initial capital.

3. Plot the frequency distribution of the maximum drawdowns from all the simulations.

4. Trace the cumulative distribution function.

5. Find the value on the X-axis (drawdown percentage value) that aligns with the 95% value of the cumulative distribution function on the Y-axis.

In this particular example, it can be concluded that 95% of all the Monte Carlo simulations result in a drawdown below 40%. Said differently, there is a 5% chance of experiencing a drawdown exceeding 40%. Traders who feel uncomfortable with these numbers have the option to either revise their strategy to mitigate the downside or discard it altogether.

Properly sizing a trading strategy based on drawdown data enables traders to make informed decisions rooted in calculated risk. By analysing the results, traders can determine whether to continue with the new trading strategy or promptly discontinue it.

The limitations of Monte Carlo simulations

In trading, the use of Monte Carlo simulation analysis provides traders with valuable insights into the strength of their trading strategy in the context of future market changes and risks. However, the accuracy of model results is heavily dependent on the quality of the historical data utilised. When comprehensive historical data is employed in the analysis model, and market conditions remain relatively stable, the Monte Carlo simulation analysis results tend to be more reliable. Indeed, it is important to acknowledge that unexpected real-life trading events or radically different market regimes not encountered in the backtest data will not be accounted for by the simulations. This is why such an analysis should ideally be complemented by a more qualitative market regime conditional analysis to help traders anticipate when a strategy will underperform given a shift in the market regime. Armed with these insights, traders can make informed investment decisions promptly, including knowing when to discontinue poor trading strategies or halt live trading of underperforming systems.

Furthermore, some may criticise the practice of randomising the order of trades as being a technique that is only relevant for a trading strategy exhibiting low serial autocorrelation. Otherwise, in cases where the results of one trade is correlated to the result of the next trade, the order of the trades is actually important and should not be randomised. The important point to keep in mind here is that the purpose of the exercise is to set conservative expectations for the maximum drawdown. So in the rare chance that the maximum drawdown obtained from the single backtest exceeds that obtained from the probability distribution of Monte Carlo simulations, the former should be selected.

Conclusion

Traders can utilise a Monte Carlo simulation analysis as a valuable tool to evaluate the risks of their trading strategies, including the maximum drawdown. This assessment aids in making informed investment decisions. Armed with this knowledge, traders have enhanced control over their trading activities and can decide which strategies to deploy and which ones to discontinue with greater confidence.