#009: MY LITTLE SECRET: APPLICATION OF MONTE CARLO

Even though I have been living for years just a few hours’ drive from Monte Carlo, I've visited it just recently? (Yes, I traveled to over 60 countries but I almost don’t know my own neighborhood!). Yet, I’m in contact with Monte Carlo every single day. In fact, I’m in love with Monte Carlo! :-)

What I’m really talking about here, is a Monte Carlo Analysis (often abbreviated to MC or MCA), of course, not about the country of luxury yachts and super rich people. Monte Carlo Analysis (MCA) has been one of my favorite tools since the very beginning, perfectly fitting my rather conservative trading style.

So, what is it about? It is a very simple tool that can help you manage your risk in a better way, prepare you for realistic trading scenarios (I wrote about this in another important article) and give you a realistic estimation of how big your trading account should be. Remember, the only thing you can really control in your trading is a risk. Therefore, you should be damn sure you do it really well! I was very fortunate to come across MCA in a very early stage of my trading career. I have already been using MCA in my past; when I had been using a quite simple discretional day trading system (more than 10 years ago). Since then, I’ve developed very important habits to use MCA for every new system, my overall portfolio, and for making important risk-related decisions.

How exactly does MCA work and how do I use it?

The MCA principle is very simple: Its goal is to take all the trades from your backtest (backtesting is the very first and highly important step in a successful trading. I’ve always been backtesting extensively, even when trading discretionarily and using only Excel spreadsheet, putting all the trades into it manually) and randomly shuffle the order of the backtested trades many, many times (even up to 10.000 times) to see different outcomes of my trading results and trading equities when the order of the trades is different from backtest results. Why? Simply because the future order of your trades will very probably be highly independent of the past order! In other words, get ready for your future trading equity to look much different than the backtested equity – because the order of your trades will be different as well! And although your trades will be similar in its nature, the different order of wins and losses will produce significantly different characteristics than the “static” backtest – especially characteristics like Maximum Drawdown (among others). Many beginners are surprised when their live trading equity looks different than the backtested one and they often think that their system might be broken, but it often looks this way just because they haven’t performed the MCA and aren’t ready to face the reality!

So, let’s be more practical here and see some examples. In general, you can perform an MCA in an Excel Spreadsheet (I’m sure there is MCA in Excel on the internet), or use some more advanced, commercial tools, like Market System Analyzer, which I often use.

In its essence, it usually works like this:

You take all your backtest results, the more, the better. If you have just your P/L values of all your trades, that is sufficient.
You randomly change the order of all your backtest trades (you “shuffle” your results). With the trade order changed, there will be a different worst case drawdown than the one you have from your backtest results. You’ll note down the value of the new maximum drawdown obtained from the randomization of the trades order.
You repeat this process many times. The required minimum is 500 times. However, my heavy testing of MC concepts shows that you should use many more iterations – preferably 10,000.
Now you’ll have 10,000 different variations of the worst drawdown (each iteration will produce a different worst max drawdown value). What you need to do, is getting a so-called “95% confidence level”.
It simply means that you’ll sort all those 10,000 different values of the worst possible drawdown from the smallest to the biggest. Now you’ll find the line number 9.500 and that drawdown value you find on this line is the one that represents the 95% confidence level.
And this is “your number”. This is the real worst possible maximum drawdown, which you’ll probably experience in the future (in live trading). This is the number you need to be prepared for and to use for your capitalization. When this maximum drawdown is exceeded by even a bigger one in real-time trading, you should seriously start questioning your strategy – its lifetime might be at its very end.

An example

As I already said, MCA is an absolutely essential and crucial concept for my trading. I use it, in many ways (new and creative) every day. It’s the most important part of a workflow for any serious trader. It’s the best (and perhaps the only) way to build a bulletproof defense for your trading.

Therefore, I’ll close this article with an example, which should make the MCA concept really clear for anyone.

For the purpose of this example, I took my own ATS called Tom's BOSS. I took one of my current parameter sets and upload the data into MSA software. This is how the equity on emini Russell 2000 market looks like:

The important part is the maximum drawdown, which is, as you can see, in this case, 3,300 USD.

Now, let's “shuffle” the equity several times – simply randomize the order of the trades. This is the same system; nothing has been changed except for the order of trades (which is, btw., one of the many possibilities of the future trades order):

As you can see, the maximum drawdown has now popped up to 7,030 USD! And all it takes is to use a different order of your trades.

So, let's perform a full MCA. Let's shuffle our trades 10,000 times and see the maximum drawdown at the 95% confidence level. This is the setup I’ve used:

And here you can see the results:

As you can see, the worst possible drawdown is 7,530 USD. This is a highly probable drawdown that you can get any time in the future – in your live trading!

So, this is the number you need to work with, to get ready for and to capitalize on properly. This is what the future might look like (and from my experience, it often does), no matter what your original backtesting maximum drawdowns was. This number is the only serious one you should always consider. Don’t fight this concept. It’s one of the most important concepts in trading. I’ve been extremely lucky to use it since almost the beginning of my trading career.

Happy Trading!

Tomas

P.S. I was in Monte Carlo just a few weeks ago. For the very first time. In general, Monaco is a great place to visit! It is the 61st country I visited. My systems on the road just rock!