Trading System Expectancy

Expectancy along with position sizing are probably the two most important factors in trading/investing success. Sadly most people have never even heard of the concept.  In simple terms, expectancy is the average amount you can expect to win (or lose) per dollar at risk. Here’s the formula for expectancy:

Expectancy = (Probability of Win * Average Win) – (Probability of Loss * Average Loss)

As an example let’s say that a trader has a system that produces winning trades 30% of the time. That trader’s average winning trade nets 10% while losing trades lose 3%. So if he were trading $10,000 positions his expectancy would be:

(0.3 * $1,000) – (0.7 * $300) = $90

So even though that system produces losing trades 70% of the time the expectancy is still positive and thus the trader can make money over time. You can also see how you could have a system that produces winning trades the majority of the time but would have a negative expectancy if the average loss was larger than the average win:

(0.6 * $400) – (0.4 * $650) = -$20

In fact, you could come up with any number of scenarios that would give you a positive, or negative, expectancy. The interesting thing is that most of us would feel better with a system that produced more winning trades than losers. The vast majority of people would have a lot of trouble with the first system above because of our natural tendency to want to be right all of the time. Yet we can see just by those two examples that the percentage of winning trades is not the most important factor in building a system. As Dr. Van K. Tharp points out:

… your trading system should have a positive expectancy and you should understand what that means. The natural bias that most people have is to go for high probability systems with high reliability. We all are given this bias that you need to be right. We’re taught at school that 94 percent or better is an A and 70 or below is failure. Nothing below 70 is acceptable. Everyone is looking for high reliability entry systems, but its expectancy that is the key. And the real key to expectancy is how you get out of the markets not how you get in. How you take profits and how you get out of a bad position to protect your assets. The expectancy is really the amount you’ll make on the average per dollar risked. If you have a methodology that makes you 50 cents or better per dollar risked, that’s superb. Most people don’t. That means if you risk $1,000 that you’ll make on the average $500 for every trade – that’s averaging winners and losers together.

In ‘Trade Your Way to Financial Freedom‘ Dr. Tharp defines the following four components of expectancy (In the same section of the book Dr. Tharp also discusses how the size of you investing capital and your position-sizing model must be considered along with expectancy. 

1. Reliability, or what percentage of time you make money.
2. The relative size of your profits compared with your losses.
3. Your cost of making a trade. (commission & slippage)
4. How often you get the opportunity to trade.

The fourth item in that list is a very important and often overlooked aspect of trading. If you had two systems that both had the same positive expectancy, let’s say $100, the system that produced more trades would make more money over time. For example, system A produces 3 trades per week while system B produces 10 trades per week. After just one week B would have made $1,000 while A would only have made $300. 

Expectancy, position-sizing and other aspects of money management are far more important than discovering the holy grail entry system or indicator(s). Unfortunately entry techniques are where the vast majority of books and talking heads focus their attention. You could have the greatest stock picking system in the world but unless you take these money management issue into consideration you may not have any money left to trade the system. Having a system that gives you a positive expectancy should be in the forefront of your mind when putting together a trading plan.