Monte Carlo and drawdown ranges

By Otto Research 3 min read Article 50 of 95

The maximum drawdown a strategy has shown is one outcome. The same trades in a different order would have produced a different one, larger or smaller, depending on where the losers clustered. Monte Carlo analysis asks what the range of outcomes looks like, by reshuffling the trade sequence many thousands of times and recording the drawdown each time.

The method

Take the list of a strategy's trade results, in R or in money. Shuffle their order at random and compute the equity curve and its maximum drawdown. Repeat several thousand times. The results form a distribution: a most common value, a spread, and a tail. The point below which 95 per cent of the simulated maximum drawdowns fall is often quoted as DD95, and it is a more careful planning figure than the single historical maximum. Some services also report the probability of a drawdown deeper than a given level, and the range of returns over a period.

Reading it

If a strategy's historical maximum drawdown is 14 per cent and its DD95 is 23 per cent, the history was, in this respect, somewhat kinder than average, and a drawdown in the low twenties is within the ordinary range of the strategy's own trades. Plan for that. If the DD95 is close to the historical maximum, the history was already unkind, and the estimate is more stable. If the DD95 is far above the level at which you would stop, the risk setting is too high.

Limits

Reshuffling assumes the trades are independent of one another and that the future will draw from the same set of results. Neither is quite true. Losing trades cluster in bad markets more than random shuffling implies, so real drawdowns can run deeper than the simulation. And a strategy's future trades are not a reshuffle of its past ones; the market will produce results the history does not contain. Monte Carlo widens the estimate in the right direction. It does not bound it.

Worked example

A strategy has 400 trades over three years with a maximum drawdown of 12 per cent at one per cent risk. Ten thousand reshuffles give a median maximum drawdown of 15 per cent, a DD95 of 21 per cent, and a one-in-a-hundred outcome of 27 per cent. The trader was about to run it at two per cent risk on the strength of the 12. At two per cent the DD95 is around 38 per cent. They run it at one.

What this means when an EA is trading

Where an EA's record is published with a DD95 or similar figure, use it, at the risk setting you intend, as the drawdown to plan for. Where it is not, the historical maximum from a long record is a weaker substitute and a short record gives almost nothing. Either way the answer to "how much could this lose" is "more than it has so far", and Monte Carlo is the method that puts a rough number on the "more".

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