Expectancy

How can one describe a trading system and its potential to make money? Most folks use expectancy as a key metric. Expectancy is the amount of money you expect to make for each dollar risked on each trade. If you trade $1000 on a system with an expectancy of 0.05, then you would expect to make $50 per trade. You expect to make 5 cents per dollar risked and you are risking $1000 on the trade, so you expect to make $50.

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

In the case of a trade size of $1000, it might look like this:

Expectancy = (0.4 * 200) – (0.6 * 50) = $50

That is, you win on average 40% of the time, and your average win is $200. The probability of winning and losing have to add up to 1, so you lose on average 60% of the time with an average loss of $50. In this scenario, you expect to make $50 per trade with an expectancy of 0.05.

All of this assumes the word “average” is relevant, and that implies many, many trades, or, in the language of statistics, trials. Over many trials averages become relevant. Over very few trials, averages can be very misleading.

So is a trading system with an expectancy of 0.3 better than a system with an expectancy of 0.05? Who knows? You see, expectancy is a very important metric, but it isn’t sufficient to know a system’s potential. You also need to know how frequently the system trades. Let’s suppose that in a one month period you’ll have 40 trades with the 0.05 system and only 4 trades with the 0.4 system. Using a $1000 dollar trade size:

30 * (1000 * 0.05) = $1500
4 * (1000 * 0.3) = $1200

The system with lower expectancy comes out on top in terms of the revenue potential in month’s time! So expectancy isn’t sufficient in and of itself to describe a trading system, you need the trading frequency as well. But if the expectancy is below zero, no matter what the frequency, you aren’t going to make money.

One other perhaps less obvious point is worth mentioning. Many people focus on trades that last for a long time. There is a serious downside to this approach if you are building a trading system (versus a more ad hoc, discretionary trading methodology): it takes a long time to have sufficient trials to even know what the averages are, or to validate the averages you calculated in backtesting the system. In some cases, you never get there, as the markets tend to morph a bit over time and you’ll need to modify the specifics of your trading system along with them, making it very difficult to achieve any sort of valid average in a steady state. In statistics, the results obtained from lots of trials is almost always more valid than the results from a few trials.