Application

Monte Carlo analysis is based off of the casino concept of Martingale betting. In Martingale betting, a gambler doubles his bet until he wins. When he finally wins, he'll make up his preceding losses plus an additional unit. Martingale betting assumes you will win before you run out of cash. However, this is not always probable.

The usefulness of this concept can be successfully applied towards investments. Let's say you developed a system that you are more than happy with the performance and are ready to begin trading it real time. You already considered that real world results are not as great as the hypothetical backtested results but you still have trust in your system. However, even by testing on both in-sample and out-of- sample quotes, you are not necessarily testing for worst case scenarios. Thereby making that smooth equity curve in your backtested results deceiving. It is possible that all your negative drawdowns were spaced out perfectly between successive gains. This would give you the impression that your system has less significant drawdowns than would be reality if trading real time. What would happen if these negative drawdowns happened to be spaced closer together? Would your account be large enough to withstand the drawdowns during this time so you can continue trading when the tides reverse? Or would you be wiped out and not be able to catch the next wave of trends?

SO HOW DOES IT WORK ?

The user can run a test on a subset of the total number of positions in their portfolio, or the "Positions Per Trial" text box. By doing this, a random sample of the specified positions are taken from the total number of positions in the trade list. The # of trials run should be a great enough number so you get a good idea of what the average will be. Higher # of trials results in longer testing time but usually gives a better picture of performance expectations. The option to cut the best and worst outliers is in place to make sure a few positions do not skew the results. Lastly, the Fixed Fraction determines how much capital you want to devote to each trade position. A value of 10, with an Initial Investment of $100,000, will allocate $10,000 to each position. With these values, if a stock was bought at $10 and jumped to $15, a 50% profit would be realized. Since $10,000 was allocated to each trade, a $5000 gain would be realized and the equity curve for that one position would increase $5000.

CHART TABS

Now that we went over the usefulness of running such simulations and how to apply them to trading strategy development, let’s take a look at the charts that PortfolioTK generates.

EQUITY CURVE TAB

The equity curve view shows you the results after X number of trades have occurred. For example, if you set the Positions Per Trial box to 50, each individual equity curve is composed of 50 trades. The ending equity represents what you can expect your account value to be at after 50 trades have been closed. Since the order of trades that make up each equity curve is randomly chosen, it allows you to see what-if scenarios. Some equity curves will have an exaggerated affect because the random trade order happened to put many positive trades in a successive row. Others curves will show worst case scenarios if many negative trades happen to occur in a successive row. Using these equity curves, you can get an idea as to what the average outcome will be in real time trading along with the possible best and worst case scenarios based on your trade list.

% RETURN SCATTER TAB

Each point in the scatter represents the outcome of one equity curve that was generated. The point shows what the profit % return was for that equity curve and how big the maximum drawdown % was. The more precise the grouping in points allows you to see the average. The points present outside this grouping represent extreme cases that are not as likely to occur but still possible.

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