Backtesting is an important step when testing a trading strategy to assess its profit potential.
However, it is not enough to limit yourself to the total return of a strategy in backtesting.
There are many metrics that should be studied to assess the viability of a strategy and whether it will achieve its goals.
Monte Carlo simulation is a mathematical technique that can be used to stress test trading strategies. It runs backtest results through hundreds or even thousands of possible scenarios, helping traders discover weaknesses and potential problems.
I found Monte Carlo simulations to be very useful. This article explains how a Monte Carlo simulation works, how to run a simulation, and how to use the data from the simulation to make trading decisions.
Fundamentals of Monte Carlo Simulation
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Here we provide historical background and important elements of how the simulation works.
These will help you understand their value and how to use them in your backtesting process.
historical overview
There is much debate about who created this method and when it was developed.
Some historians believe that similar methods were used as far back as ancient Babylon.
If you think about it, this process is pretty normal.
Therefore, it makes sense that it has been used for a long time, not just in modern times.
However, the name “Monte Carlo Simulation” seems to have been developed in the 1940s and is named after the famous Monte Carlo Casino in Monaco, due to the element of chance and randomness.
statistical principles
The core of Monte Carlo simulation relies on the law of large numbers.
This is used to generate large random samples that represent statistical distributions.
In theory, as the number of simulations increases, the results converge to the expected value.
We assume the following:
- Actual results are usually determined by probabilities obtained through many simulations.
- statistical properties (mean, variance, etc.) is known
- Probability density functions (PDFs) represent the underlying conditions well
algorithm component
Implementing a Monte Carlo simulation involves the following steps:
- Define your domain. Identify inputs that can affect your model. When using simulation with backtest data, the domain is the actual backtest trade.
- Generate input randomly. Create random variables that mimic the behavior of real-world data. In backtesting, the random variable is usually the order in which trades are executed. However, other variables can also be used, such as overall win rate or randomly skipped trades.
- Compute the simulation: Run the simulation model using these inputs and produce results.
- Aggregate results: Run the simulation multiple times to create a distribution of possible outcomes. Computer programs can run simulations thousands of times to narrow down the most likely outcomes.
By employing these components, Monte Carlo simulation can provide insightful data about the risks and uncertainties of financial models. This is essential for robust backtesting.
Application in backtest
Monte Carlo simulation is a powerful tool for backtesting trading strategies, allowing you to understand potential risks and rewards by simulating different market conditions.
Setting parameters
First, we need to define the variables that will affect our trading strategy.
These include initial capital, position sizing, stop loss levels, and profit targets.
By setting these parameters, Monte Carlo simulations can help you test your strategy against different outcomes and evaluate its effectiveness.
Modeling market scenarios
It then uses historical price data to generate a number of hypothetical market scenarios.
This step involves randomizing trading orders and considering volatility/correlation between different instruments.
You can then apply your trading strategy to these simulated scenarios and measure its performance under various hypothetical market conditions.
Risk assessment and management
Finally, simulation provides a distribution of potential profits and helps assess the risks associated with a strategy.
Here we examine key metrics such as:
- Maximum drawdown: The largest decline in the value of a portfolio from peak to trough.
- Value at risk (VaR): The potential loss in value of a portfolio over a defined period of time within a specified confidence interval.
- Probability of profit/loss: The likelihood that your strategy will result in a profit or loss.
These insights allow you to refine your strategy, improve your risk management practices, and adjust your expectations to the simulated reality of your strategy.
How to run a Monte Carlo simulation after backtesting
As mentioned earlier, software makes it easy to run simulations.
First, backtest your trading strategy.
This can be automatic or manual backtesting.
We then instruct the simulation software to run X number of simulations based on actual backtest trades.
I typically use 1,000 simulations, but you can use more or less depending on your goals.
There are many software platforms that can do this, but I use NakedMarkets.
It strikes a good balance between ease of use and useful information.
Just tell the software the parameters of your test and this is the report it generates.
Click on the graph to see a screenshot in a separate tab.
As you can see, you can randomize skipped positions, slippage, and the order of trades.
Skipping random trades is a good way to account for trades you might miss because you’re away from your computer, on vacation, etc.
The fact that all the above simulations show very similar results is a good sign.
But that’s just the tip of the iceberg in terms of analysis.
Analysis of simulation results
Completing a Monte Carlo simulation provides a wealth of data.
It is important to systematically analyze this information to determine the effectiveness of your strategy.
capital curve
First, look at the equity curve.
A consistently upward trending curve indicates that the strategy is likely to be successful.
As we saw above, if the simulations are very similar, that’s a good sign.
If the results are very different, it is probably a risky strategy because the results are less reliable.
performance indicators
To quantify the potential of your strategy, focus on specific metrics.
- expected return: Calculate the average of the simulation results to measure the expected performance.
- Maximum drawdown: Check the maximum drawdown across all simulations. This will give you the worst case scenario.
- Average win and average loss: This is very important. Are the winners making up for the losers? This indicator tells you how much profit you can expect.
These metrics give you a factual understanding of your strategy’s strengths and weaknesses.
Best practices and limitations
Applying Monte Carlo simulation to backtesting can provide valuable insight into your financial models.
However, careful implementation and awareness of its limitations are required to ensure effectiveness.
Ensure model accuracy
To improve the accuracy of Monte Carlo simulations during backtesting, you need to input high-quality data.
data quality It is the most important as it directly affects the reliability of the simulation.
Try to get the cleanest data possible from the source.
This means you get it directly from an exchange or broker.
Trusted third-party data providers are also good data sources.
hire next cross validation Techniques for testing model robustness.
This involves splitting the data into an optimization set and a validation set to prevent overfitting.
Backtesting on data that was not used in the optimization process can help you understand how well your strategy handles unexpected situations.
Common pitfalls
One of the pitfalls of using Monte Carlo simulation is underestimating the role of: market anomalyResults may be skewed.
be careful overfitting, Models that perform very well on historical data do not necessarily accurately predict future scenarios due to their complex nature.
Also, double check if your trading strategy is being implemented consistently.
If you change your strategy mid-test, your results will not accurately represent your strategy and you will most likely fail.
Finally, make sure that costs such as commissions, commissions, spreads, swaps, and slippage are properly accounted for.
Advanced simulation technology
As computational power increases, Monte Carlo simulation techniques can be improved by integrating: machine learning algorithms Detect complex patterns in your data.
Under experiment parallel computing Simulations can be significantly faster, allowing for a wider range of scenarios and increasing the number of iterations for more comprehensive backtesting.
Please note that Monte Carlo simulations are powerful tools but are subject to error and results are dependent on the validity of your assumptions and the extent of your data.
Stay informed about the latest advances in simulation technology to keep your backtesting robust and useful.
conclusion
Adding Monte Carlo simulation protocols to your backtesting process makes it easy to understand the risks of your trading strategies.
Since backtesting yields only one result per market and time frame, randomizing trades in a Monte Carlo simulation effectively generates hundreds or even thousands of backtests using the same trading strategy and the same historical data. You will get a test session.
This allows you to see how much difference there is between each simulation and what the worst-case maximum drawdown will be.
You can also run Monte Carlo simulations on live trading results.
This is a very powerful tool that should be in every trader’s toolbox.