[Editor's note: StockSpotter.com is a system for trading stocks and commodity futures. John Ehlers is a well-known commodities trader, author, and the creator of MESA, a method of cycle analysis that he developed in the late 1970s. In the following interview, John discusses the difference between investing and gambling with TalkMarkets contributor, Ilene Carrie].

Ilene: John, in our last discussion about trading systems in general and yours in particular (Can trading be reduced to cycles, stresses and vibrations?) you mentioned Monte Carlo simulations and their use in measuring performance. Can you explain more about how you measure the performance of a trading system?

John: Let’s start with comparing trading with gambling. The two have several things in common.  In both cases you put money at risk in hopes of gaining rewards.  In both cases you can lose, but with trading you don’t necessarily lose what you bet. The probability of success in both cases ultimately depends on the combination of the payout (how much?) and the probability of winning (how often?).  Everyone knows that the odds favor the house in gaming, which accounts for the success of the casinos in Las Vegas.

In trading, the “Profit Factor” (ratio of gross winnings to gross losses) is synonymous with “Payout.”  A good trading system might have a Profit Factor of 1.5 or more and might have 65% winning trades. Using such a system heavily favors the traders. So why are not most traders blindingly rich?  I will examine that question from a statistical perspective.

The most common way to assess the performance of a trading system is to look at its equity growth curve.  Each trade profit (or loss) is added to the sum and plotted along a time line.  We can artificially create a statistical track record by assigning the Profit Factor to a winning trade and -1 to a losing trade.  That way, profits are normalized to the losses.  As we sum the trades we randomly assign winner or loser according to the probability of winning.

Ilene: Is it correct to say that the Payout or Profit Factor does not include the probability of winning, it’s simply the average amount of winning?

John: Yes.  The Payout is the amount you win if you win.  In trading, Profit Factor is analogous to Payout — but under the condition that a loss is valued at -1; i.e., the theoretical Payout of trading is normalized to the “average” loss.*

Ilene: How are the Monte Carlo simulations helpful?

John: The interesting fact from recomputing the spreadsheet several times is that you can get a lousy track record from a good trading system.  Worse yet, you can sometimes get a good track record from a lousy trading system.  This shows that a track record is not a particularly good method of judging the quality of a trading system. 

Even with good trading systems there are times when the equity curve stays under water for 50 or more trades.  Most traders abandon a good system when this happens, only to repeat the process with another system if they don’t stop trading altogether.  This is the difference between a trader and a casino.  Casinos stick with the system even when faced with a run of bad luck because they know the statistics are in their favor.

So the problem for a trader is to identify a good trading system and to gain the confidence to stick with it through a bad run.  Rather than pressing F9 on the spreadsheet a number of times to get a feeling for the average statistics, the trader could compute the bell-shaped probability curve as shown on the “One Symbol Bell Curve” tab of the spreadsheet.  This curve gives a feeling of relative probability of success, but on a normalized basis.

StockSpotter.com uses a unique Monte Carlo Simulation process to establish the bell curve estimation of success.  The Monte Carlo Simulation places all the trades in their database over the last three years, about 10,000 trades, and places them in the proverbial hat.  Trades are randomly pulled from the hat until a year’s worth of trading is achieved.  The profit for that year is recorded.  Then, the drawing process is repeated 5000 times to simulate 5000 years of trading.  The result is the bell curve of profitability shown below.

This probability curve clearly shows the most likely annual profit resulting from randomly selected trade signals provided by StockSpotter.com.  It also clearly shows the probability of annual break-even or better, and the probability of making even better than average profits.  Monte Carlo simulation is an excellent way to judge the quality of a trading strategy and to set expectations so the trader can stick with the strategy.

One interesting fact from statistics is that if you double the members of the ensemble, you cut the standard deviation of the bell curve by the square root of two.  If you trade randomly selected StockSpotter.com signals so that you are 100% in the market with four stocks, you will cut the standard deviation of the bell curve in half.  Since the Sharpe Ratio is basically the average profit divided by the standard deviation, you would double the Sharpe Ratio by trading that portfolio of randomly selected stocks.  StockSpotter.com also performs a Monte Carlo simulation of a portfolio of four randomly selected stocks, proving portfolio theory and demonstrating the power of statistics.  The probability bell curve for the portfolio is shown below.  The Sharpe Ratio of the portfolio is almost double the Sharpe Ratio of trading a single randomly selected stock.

Both gaming and trading involve losses, and having an expectation regarding losses is more important than a profit expectation because a realistic expectation of losses enables the trader to stay in the game.  StockSpotter.com addresses this issue by also computing a Monte Carlo simulation of drawdowns.  A drawdown is the dollar difference between the highest peak of the equity growth curve and the next subsequent lowest trough in the equity growth curve.  The probability curve for drawdown is different from the probability curve of profits because drawdowns cannot have a negative value.  The drawdown probability is somewhat like the probability of an arrow striking a target.  There is zero probability of hitting an exact bull’s-eye.  The probability rises with increasing radius from the center, and then decreases at larger radii because a very large miss is unlikely.  This is called a Rayleigh probability distribution.  The following chart is the Monte Carlo simulation of drawdowns for trades made using the trading signals.

Again, it is very easy to assess the extent and probability of a drawdown over a year’s worth of trading.

Another interesting figure describing a trading system is the Gain-to-Pain ratio, which is the ratio of the average profit to the average drawdown.  The Gain-to-Pain ratio can be determined almost at a glance by taking the ratio of the most likely profit to the most likely drawdown of the Monte Carlo simulations.

Ilene: Are you proving with numbers that a track record is far more limited than a Monte Carlo simulation in evaluating a trading system?

John: You got it. Monte Carlo simulations show how a system performs over thousands of trades — they are much more robust than a selected out track record. An annual track record is just one instance of what is basically a random variable.  Our Monte Carlo simulation simulates 5,000 years of randomized trading using the data base trades from the last three years. This large number of instances enables the bell curve to be computed. Since StockSpotter.com gives more trade signals than any trader can use, the randomized selection gives a statistically accurate measure of the annualized profit a trader can expect, regardless of the particular stock selections he makes.

Ilene: To bring our discussion full-circle, what is the difference between gambling and trading using the mathematical terms you just illustrated?

John: Both trading and gambling involve risk.  In the mathematics of it, you cannot lose more than you bet.  If you are trading Futures it is possible to lose a lot more than your margin, but in trading stocks you think in terms of losing a percentage of your capital outlay.  These differences complicate issue, however the principles are analogous.  Most casinos make a lot of money, and most gamblers lose money. In contrast, with a good trading system, the odds can be tipped significantly in the trader’s favor, but many traders lose money anyway.  This seems strange.

The difference is that the casinos have confidence in their system and therefore stick with it through runs of bad luck.  On the other hand, traders tend to quit when adversity strikes.  The lesson is to adapt a system in which you have confidence and then stick with it.

Picture via Pixabay. 

*For the more technically oriented: This excel spreadsheet is an example of creating an equity growth curve, using randomized selection of Profit Factor and Percent Winners on the randomized parameter tab.  You can create new equity growth curves by pressing F9, which recomputes the spreadsheet using new random variables.  You can also test different combinations of Profit Factor and Percent Winners by inserting different percent winners in cell B1 and different Profit Factors in cell B2. The red line on the spreadsheet is a plot of “Expectation” (the average profit per trade) times the number of trades.

For equation purposes: the notation PF = Profit Factor, % = Percent Wins (Probability of Winning), and q = (1-%) Percent Losers (i.e. the probability of losing is 1 minus the probability of winning), E = Expectation (average expected profit per trade).  If you have a random string of trades, then your Expectation would be something like: E = PF + PF – 1 + PF -1 – +PF………….and so on. The closed form of that infinite series is E=PF*% – 1*q = PF*% – (1-%). So, if PF = 1.5 and % = 0.65, your Expectation of Winning is E=1.5*0.65 – 1*0.35 = 0.975 – 0.35 = 0.625.  Expectation times the number of trades produces the Average Profit. This is Expectation: E=PF*% – (1 – %).  Again, this is normalized to the average losing trade being -1.