Examples of Frequency Distributions from TradeSim Enterprise Edition

The frequency distribution is a very important tool as a way of characterizing the potential performance of a trading system. It only has relevance when trading a system using a portfolio of securities. This is because trading with a portfolio of securities no longer gives a unique outcome as it did when only trading or back testing with one security. When trading a system using a portfolio of securities the outcome of the trading system can now be considered to be a random event characterized by a discrete probability distribution function. This characteristic of a trading system is always overlooked using conventional charting packages because the system testers built into most charting packages are limited to testing a single security at the one time. Therefore the most important information useful for deducing and characterizing the performance of a trading system is lost and so the true performance of a particular trading system is never fully understood. Because TradeSim mimics the way a trading system is traded in real life the results from each simulation can be used to build up a statistical profile of a trading system. By repeatedly simulating a trading system using a random selection of securities that meet the entry date and position sizing requirements we can build up a statistical profile of a trading system based on the portfolio used. The following Profit Distribution was obtained by running a Monte Carlo simulation on a trading system based on a simple MACD crossover system with the following trading parameters.

A profit frequency distribution chart for this trading system was produced by running 5000 simulations on the trading system with each simulation generating a unique and random selection of trades that met the entry date and position sizing requirements. You will note how the distribution chart resembles the classic bell shaped Normal probability distribution function. Thus for the first time we can completely characterize a trading systems performance by attempting to exhaustively test every possible trading combination and then analyzing and correlating the resulting data. This is something that is impossible to do with standard charting and spreadsheet packages.

Note that for this example more than half of the trade simulations produced a loss implying that this system has less than a 50 percent chance of being profitable and one that would not be recommended for trading. An even worse aspect is the fact that we have not included any trade transaction costs, which would only serve to reduce bottom line profitability and shift the profit distribution curve to the left. With all other things being equal the outcome of a trading system when trading a portfolio of securities depends on the chance selection of securities, which is why one trader will obtain different results compared to another trader trading an identical trading system under the same conditions for the same period of time.

We have chosen a mediocre performing trading system to highlight the fact that simulating a trading system once using a portfolio of securities does not provide enough information to draw any valid statistical hypothesis, this is because there is no longer a unique outcome when trading a portfolio of securities as compared to trading a single security. The profit distribution curve allows one to estimate the probabilities of the outcome of a trading system with the ultimate aim of finding a trading system where the profit distribution lies exclusively on the right side of the 0 percent profit axis thus being a historically unconditionally profitable trading system and one that at the very least has got a high probability of being profitable in the future provided that the trader has the psychological discipline needed to trade it.

Shown below are the Percentage Winning and Percentage Losing Trades distribution charts for the MACD crossover system. Like the profit distribution charts both the Percentage Winning trades and Percentage Losing trades distribution charts approximate the classic bell shaped Normal probability distribution function. Again this is a fairly mediocre system with a much higher proportion of losing trades compared to winning trades. The TradeSim user manual outlines a simple strategy of dramatically improving the performance of this trading system by a very simple modification to the trading system. The effects of these modifications would never show up on a single security system tester.