This is a great article written by John Ehlers on the topic of evaluating trading system performance.
RISK OF RUIN By John Ehlers
INTRODUCTION– The concept of the Risk of Ruin arises from gambling theory. There are several formulations available, but they all generally try to answer the question of how many losing bets can you afford before you go broke. The Risk of Ruin equations don’t quite fit investing because all the losing bets are the same size (or modified by a strategy), whereas trading losses are seldom the same from trade to trade.
A better way to examine Risk of Ruin for a trader is done using probability theory. We can do this several ways. First, we can use our history of the probability of winning trades to compute an equivalent number of consecutive losing trades. Secondly, we can use our actual trade history to perform a Monte Carlo Analysis. Monte Carlo analysis is superior because it provides a wide range of trading performance expectations.
–CONSECUTIVE LOSING TRADES Let the probability of a winning trade be denoted by the symbol %. Then the probability of the first losing trade is (1-%). The probability of the second losing trade is also (1-%), but when compounded, the probability of getting two losing trades in a row is (1-%)^2. Generalizing, the probability of getting N losing trades in a row is (1-%)^N. The threshold of pain is the number of consecutive losing trades rather than drawdown because consecutive losers tend to make the trader think the trading system is broken. The probability of consecutive trades is shown in Figure 1.
Figure 1 can be used as follows: Assume that your system trades 30 times per year, and that you can stand only one sequence of 4 losing trades in a row in that year. Then, the maximum probability of consecutive losing trades you can stand is 0.033. With reference to Figure 1, you should use a trading system that has a probability of winning trades as .56 or better. If your threshold is 3 consecutive losing trades your system should have a probability of wins greater than .68.
Figure 1. Probability of Winning Trades must be High to Reduce the Probability of Consecutive Losing Trades.
It is unlikely that the maximum drawdown will result solely from consecutive losing trades. The more likely case is produced by a string of losing trades, then a small winning trade followed by another string of losing trades. We therefore need to think in terms of an equivalent number of consecutive losing trades. If we assume a Normal Probability Distribution of these losing trades and further assuming the maximum number of losing trades occurs at the 3 Sigma point of the probability distribution, the remaining area under the Normal curve is just 0.0027. Thus we can find the equivalent number of consecutive losing trades as:
Since the area under the normal curve is directly related to the probability of losing trades, and since exponential is the inverse of a logarithm, the number of consecutive losers increases EXPONENTIALLY as the probability of losing increases. This is not a good thing. In one sense it is the inverse of compound interest. Therefore, you always want to select a trading system that has a high percentage of winners.
Figure 2 shows the relationship between the percentage of profitable trades and the equivalent number of consecutive losing trades.
Figure 2. There is a substantial consecutive losing trades penalty for percentage wins less than 50%.
–MONTE CARLO ANALYSIS In my opinion, Monte Carlo Analysis is a superior method of estimating your probability of success, or conversely, your probability of failure with your trading method. The process is straightforward, and is based on your actual trading experience.
Here’s how Monte Carlo Analysis works: Take all of your trades for the last year, both winners and losers, and divide them into the average profit (or loss) per day for each day. Conceptually, write each of the daily profits on a slip of paper and drop them into a hat. Allowing for holidays, you should have 250 pieces of paper in the hat, one for each trading day during the year. Each run is accomplished by drawing a slip of paper from the hat, summing the profit from each draw, and replacing the slip of paper into the hat. You repeat the draw 250 times to simulate randomized trading for a year. It is possible to draw all winners in one year and all losers in another year. However, it is most likely you will draw some combination of winners and losers. You will make 10,000 statistical runs. When you have completed 10,000 draws you have simulated 10,000 years of randomized trading using your original real trading experience.
Due to the Central Limit Theorem, your 10,000 years of simulated trading will have a Normal Probability Distribution. From that Probability Distribution you can find your most likely annual profit as well as your probability of break even. You can even find the one Sigma point that gives you your expected profits with a 68% likelihood. Figure 3 is a screen capture from the performance page of http://www.stockspotter.com that shows the probable trading resulting from using the StockSpotter; five star rated signals.
Figure 3. StockSpotter Monte Carlo Performance SimulatorFigure 1.
–CONCLUSIONS In this paper you have seen two methods of evaluating trading system performance. The first technique computed the equivalent number of consecutive losing trades based on your historical probability of winning trades. The Monte Carlo analysis is more generalized and yields a wealth of information, including probability of break even, most likely annual profit, and your expectation of profit with a 68% likelihood. While these statistics don’t help you with trading decisions, they enable you to follow your trading strategy with confidence.