Monte Carlo Analysis:  Introduction. Monte Carlo analysis (or simulation) is a statistics-based technique that can be used in trading to help you estimate the risk and profitability of your trading strategy more realistically.

Monte Carlo Analysis: Uncertainty in Predicting Future Trading Performance

MOnte Carlo Analysis: what is ? Historical results of a trading strategy tell us only how the strategy performed in the past. When forecasting the strategy performance into the future we are faced with uncertainty. No matter how much historic information we have, we cannot know with certainty what the future will be. We can only draw an estimate, based on historical results, expertise in the field, or past experience. While this estimate is useful, we have no way to know how much the prediction will correspond to the real future results.
Monte Carlo (MC) simulation allows us to have a probabilistic interpretation of our future prediction. To put it simply – Monte Carlo simulation results will give us an estimated performance of the trading strategy based on statistics. It can help you decide if your strategy is robust, what profit / drawdown you can expect from your strategy and if you should trade this strategy at all.

What is Monte Carlo Analysis?

Monte Carlo simulation builds a list of models of possible results by randomising model parameters with a given probability distribution. It then calculates the results over and over, each time using a different set of random values in the model.
To give a very simple explanation – the basis of the Monte Carlo method is running the same simulation a number of times, each time with small random changes. The higher the number of repetitions, the greater is the statistical significance of the results.

An Example of Monte Carlo Analysis – Changing the Order of Trades

A strategy back test is usually a simple list of trades. What can be randomised about that? For example, the order of the trades. The order of trades in the past is relatively random. If your system has profitability of 60 per cent then you can expect that 60 per cent of the trades will be profitable and 40 per cent will be losing, but you cannot expect the order in which they will come. By simply reshuffling the trades your final profit will stay the same, but your drawdown can change a lot. Instead of a drawdown of ten per cent you might end up with a 30 per cent drawdown just by changing the order of the trades. So which value should you trust? What should you expect in the future?
The answer lies in statistics, which is the basis of Monte Carlo. You can let a programme run this reshuffling a hundred times and you will see what the best, worst and average drawdown achieved during these random runs is. In Figure 1 you can see the system.In Figure 3 you can see 100 different equities using the same system. All we did was change the order of the trades.

 F1 us equity drawdown


F1 us equity drawdown

 F2 MONTE CARLO ANALYSIS US EQUITY DRAWDOWN


F2 MONTE CARLO ANALYSIS US EQUITY DRAWDOWN

F3 MONTE CARLO SIMULATION CONFIDENCE LEVELS

F3 MONTE CARLO SIMULATION CONFIDENCE LEVELS

How are these Values Computed in Monte Carlo Analysis ?

It is quite simple. The first line is the result for the original strategy, the rest are confidence (or probability) levels computed using Monte Carlo analysis.  Numbers  on the left are confidence levels – they tell us with what confidence (probability) we can expect the results to be same or better than in a respective line.

For example, values at 95 per cent confidence level mean that from all the 100 random simulations we did, 95 of them (95 per cent) had the same or better values than the confidence level values.

Or, in other words, there is only five per cent probability that drawdown will be worse than 30.07 per cent. 95 per cent is the usual confidence level to consider. You could realistically expect that your system results will be same or better than values in this confidence level.

What Properties Can be Randomised in the Monte Carlo Analysis?

When we work with historical or back test trading results all we have is a list of trades in the past. What can we do with them?

1. Changing Trades Order. There are two possibilities: In one variation we only randomly shuffle the order of the trades. In a more random resampling variation of this test the trades are not just shuffled. Instead the program randomly picks total number of trades from the pool of all trades historically. The difference is that in this method the list of trades might not be the same. It can pick one trade multiple times and some other trade might not be picked at all.

2. Skipping Trades. We can make a result  where  some trades will be randomly missed (with given probability). In real trading you can often miss a trade because of platform or internet failure, or simply because you stopped trading for some time. This test will give you an idea of how the equity curve might look if some trades are randomly skipped.

Practical Use of Monte Carlo Analysis

This analysis should be one of the final steps in the strategy development. Before you start trading any strategy you should  run  a  Monte  Carlo  simulation to estimate more realistic drawdown and profit expectations.

Expectancy level and number of simulations – it is a good rule of thumb to watch 95 per cent expectancy level and run at least 100 simulations. More simulations will give you more statistical significance and at 95 per cent level means that there is only five per cent chance that results will be worse than simulated.

Drawdown and Net Profit values – you should look   at the values generated by Monte Carlo simulation as something that might happen – and consider if you would be willing to trade the strategy with such profit and risk expectations. «

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Emilio Tomasini is Chief Editor of the Italian edition of TRADERS’ MAGAZINE (www.traders-mag.it), the leading monthly publication in Europe for trading and investment, and since 1999 he organizes the TRADERS’ CUP the most important real money European trading competition (www.traders-cup.it). His personal weekly free newsletter L’Indipendente di Borsa (www.indipendentediborsa.it) is one of the most reputable Italian financial media and counts more than 100.000 readers. His website in English is www.emiliotomasini.com

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