Expectations About Expectancy.

Anybody who is serious about becoming a profitable trader will probably know what Expectancy is, if they've been around long enough. But, just in case, here's a quick overview.

Expectancy can be calculated using the following formula:

Expectancy= (Average Win * Win Rate)-(Average Loss * Loss Rate)

This needs to be calculated using a "statistically significant data set"- for a swing trader that might mean testing over years or even decades of data. Intra-day traders will probably need a month or two of data. The time over which your data is collected matters because you are inevitably going to test over various market conditions but the number (N) of trades is crucial. The larger the number, the more reliable the expectancy.

So, let's say you forward/back test a trade idea, taking 100 trades. Your WR is 40% (0.4) and your Avg Win is twice your Avg Loss then...

E= (2 * 0.4)-(1*0.6)=0.2... This means, on average, you make 20% (0.2) of whatever your risk (R) is per trade for every trade you make. Positive Expectancy! Yay!

But that's only half the story.

Here are the six charts from the "Readers' Poll" post. The last results I saw (before they magically disappeared from the poll! EDIT: They are back..for now. 5/11/12) had the winner as 3,4 & 6, which is the right answer.

What do they have in common? They each contain 10 random equity curve outcomes by trading a system/method with a Avg Win 3X larger than the Avg Loss with a WR of 30%. This equates to E=0.199.

The other three charts show 10 random equity curve outcomes with the same Expectancy except the combination of R:R (Reward to Risk ratio) and WR is different- Avg Win 1X Avg Loss with WR 60%.

The few people who voted were able to agree with a majority vote that the charts which belonged to a given group looked different to the charts that didn't. The difference is Variance.

A trading system with a lower WR and higher R:R (such as charts 3,4 & 6) will have a higher variance from the mean, an imaginary straight line that transects the wobbly move upwards (assuming positive expectancy). Likewise, a trading system with a higher WR and lower R:R will have a smoother, straighter equity curve that is closer to being like the mean of the data set.

The comparatively very different outcomes possible between the curves, as well as within the curves themselves, within a high variance approach makes sticking it out with a method as difficult as holding on to a trade that whips it's way to a target.

It's not just where the strategy ends up (Expectancy) but how it gets there (a function of WR and RR) that counts.