Expectancy Versus Accuracy
Initial Considerations
In nearly every activity where there is a measurable difference between doing well and doing poorly, there is a natural human tendency to want the majority of attempts to result in success. In most cases, this is entirely appropriate. For a basketball player who attempts five free throws, the ideal outcome is five successful shots. Intuitively, people think that same way about trading. If a trader takes several positions, the more winning positions, the better. Is this really the best way to measure a trader's effectiveness?
Applications to Trading
In our own system metrics, we use the term "directional accuracy" to refer to the number of winning trades divided by the total number of trades. For example, if we place 100 trades and make money on 40 of them, our directional accuracy is 40%. Instinctively, most people will discount the possibility that such a series of trades could be profitable. After all, we are losing more often than we win. What this fails to account for is the size of the typical win and the size of the typical loss.
Suppose that each trade that goes in our favor, we make $1500 and every time a trade goes against us, we lose $500. In this case, a 40% win rate is more than sufficient to bring in impressive profits. The typical profit per trade can be expressed according to the formula for expectancy:
Expectancy = (Probability of Win * Average Win) + (Probability of Loss * Average Loss)
Expectancy = (0.4 * $1500) + (0.6 * -$500)
Expectancy = $600 - $300 = $300
Counterintuitive as it may be, most trades are losers, but the average trade results in a profit of $300. This isn't just a mathematical curiosity. This is how real world trading works and it's why most traders wind up leaving the market with less than they go in with. Most traders want to be right more than they want to be profitable.
Closing Thoughts
Which would be more profitable for the trader, a system like the one just mentioned, or one in which 75% of trades make money, but the average win is $100 and the average loss is $400? Which would be psychologically easier to trade, a system which makes money but requires the discipline to deal with numerous tiny losses, or a system which looses money but always has another winning trade just around the corner? Our system is certainly not easy to trade from a psychological point of view, but we believe our overall profit performance speaks for itself.
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