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Peering into the Future with Monte Carlo Simulations

February 28, 2005

 

Armed with 5 to 10 years of hypothetical data and a few months to a full year of actual trading results, many investors believe they have enough data to get a good feeling of what is going to occur with their trading system investment. The fact of the matter is that they only know what DID happen (in past tense) instead of what COULD happen (future tense).

The problem, as we all know, is that moving forward into the future introduces the element of randomness. Past performance does not guarantee future results is not just a clever phrase the lawyers make brokers use, it is a fact of life. The fact that the future will not look the same as the past is as certain as death and taxes. Random events will happen, causing trading systems to experience smaller or larger returns and drawdowns than were expected. While getting larger returns than expected in the future would be welcome, larger drawdowns than expected can be deadly to an investors psyche and ability to stick with a particular system.

So how do you get a better idea of what COULD happen, rather than being mesmerized by what did happen?

Monte Carlo Simulation

The crux of the problem in predicting future returns is that the only available data is past data. You can "make up" future data, or test your system on the data of another market to simulate future returns, but neither of those really show you how the system works on the market you wish to trade.

The answer for some is to take the historical return data, mix it up, then put it back together randomly. This is commonly referred to as a Monte Carlo simulation. To understand the premise of a Monte Carlo simulation, imagine a case in which all of the historical monthly results of a particular trading system are tossed into a hat. We then shake the hat around, and samples of those results are drawn out of the hat at random. One sample may include all winning trades, while another has all losing trades; but most will include a mixture of winners and losers roughly proportionate to what happened in real time.

While the data is the exact same as the actual trading performance, the order in which that performance occurred has changed. This introduces randomness into the results, and can cause drastic differences from the system's backtesting. Looking at these differences begins to show you what COULD happen, instead of what DID happen.

To run a Monte Carlo simulation, all the trades of a system (or profit and loss per day for long and swing trading systems) are compiled, then a set number of trades(or days) are pulled out and put together in a time series 'return stream'. The table below shows the actual return stream of the Compass system's eight trades this month (through Fri., Feb. 25th).

The actual results are in the far left column, and show a gross return of $4,367.50 with a max drawdown of -$800. This is a quite impressive month, and an investor using only this as her barometer for investing would expect a similar return and drawdown. However, the next four columns of the table show return streams using random samplings of the actual data, and you will quickly see that the possible drawdowns looking ahead may be much more than $800. In fact, 2 out of 4 random tests - which represents 50% of future return streams (in this case, future months) - produced drawdowns of -$1,035 or greater. And 1 out of 4 future return streams produced a drawdown of -$1,437.50, which is nearly twice the DD of what was experienced in real time.

The dollar amounts shown below represent the actual profits and losses achieved on a single contract basis in client accounts trading the Compass SP system from 2/01/05 - 2/25/05. The colored columns show the trade results in a randomized order, which makes them hypothetical. Please see the important disclaimer regarding hypothetical results at the bottom of this newsletter.

 

This example used only four future return streams, and is therefore not a very robust sampling. True Monte Carlo simulations are run with as many data points (trades or days) as you have, and are run thousands of times. Attain usually runs its Monte Carlo simulations across 5,000 to 100,000 trials, meaning the table above would have up to one hundred thousand columns showing different return and drawdown combinations.

In reviewing such large numbers of simulations, investors must understand the concept of percentiles. While percentiles are most often used to describe ones score on tests, it has a valid use when analyzing results. A percentile is simply a value between 1 and 100 indicating the percent of samples (return streams) taken form all results that is equal to or below the given value. For example, a 25% Drawdown at the 99th percentile level means 99% of the returns streams in the simulation had drawdowns below 25%.

Example: Helix SP

Attain Capital ran a Monte Carlo simulation on the 5.5 year historical track record of the Helix SP ending in March of 2004. This was just about the time Helix was ranked #1 in Futures Truth, and everyone and their brother was calling in wanting to trade the system. The backtesting showed a historical drawdown of about $20,000, which was large to be sure, and led the developer to recommend an initial capital level of $70,000. Several Monte Carlo simulations were run then, showing what COULD happen, and to demonstrate the power of the Monte Carlo engine in predicting what COULD happen - we've pasted the results of those March 2004 Monte Carlo simulations below.

Using the hypothetical trading performance of the Helix SP trading system between 1998 and March of 2004, we plugged 1000 trades into the simulator. Returning to our example, we then took 1000 trades "out of the hat" of all trades, and saw what the returns and drawdowns were given different equity levels, from $25,000 to $125,000. We repeated this 10,000 times per each equity level, running a total of 50,000 simulations across 500 million trades. You gotta love computers.

You will see that the brokers who recommended trading that system with as little as $25,000 to $50,000 were after nothing but your commission dollars for a few months until you lost all of your money. The simulator tells us that utilizing the system with $50,000 or less COULD result in some drawdowns over 100% of initial equity. In fact, only 50% of the samples had drawdowns less than 22%, and 10% had drawdowns greater than 41%. Are you ready for those extremes.?

For those looking at getting a good feel for possible drawdowns, this tool is very useful. I would recommend looking at both the DD99 and DD100 columns. The DD99 columns shows the level at which 99% of the simulations had drawdowns below that level. For whatever reason, this level meshes best with what really happens in the future, and for that reason is the level Attain uses as the best measuring stick for what COULD happen in the future.

DD100 shows a number which all drawdowns (100%) were below. It is in effect telling you the highest drawdown number in the sample and can be looked at as the worst case scenario. Murphy's law tells us, what can go wrong will go wrong, so knowing what the worst case scenario is in definitely in your best interest.

 

The above table represents possible future losses at different levels of probability. Computed probabilities are hypothetical in nature. Please see the important disclaimer regarding hypothetical results at the bottom of this newsletter.

You will quickly see that the worst case scenario doesn't look too appetizing until equity levels well above the recommended $75,000 initial capital. At $125,000 - the worst case scenario is 64%, or approximately $80,000. This would surely be a shock to the system and anyone who remained trading the systems through such a drawdown would deserve a medal of some sort, but that knowing that $80 K is as bad as it can get puts an investor in the right frame of mind when drawdowns start to occur. A good rule of thumb is to trade a system with at least as much money as the DD100 calculates.

The actual Helix SP drawdown since March of 2004 has been $37,774 when including $50 in commission. The table above shows that the average drawdown at the 99th percentile level across all simulations was $35,601. What COULD happen, DID happen. Do you think it's coincidence?

So for all those who have ever been surprised by a new max drawdown, pay heed to a Monte Carlo simulations, and get a feel for what may really be in store for you in the future. Attain Capital is happy to run Monte Carlo simulations for you on any historical data, just email montecarlo@attaincapital.com.

- Jeff Malec