A common question among traders, new and experienced, is "how do you know if you have a good system?". Well one obvious answer is whether or not you're making money. But is there a more quantitative measure we can apply? Absolutely, it's called the expectation value of your trading system and it's crucial that you know it for a number of reasons. The first reason is that it tells you if it's possible to make money trading the system or not. The second reason is that it can help you evaluate your money management strategies.
If the expectation of your system is negative it will be impossible for you to make money. If on the other hand your system's expectation value is positive you can make money. Your expectation value will tell you the average amount you can expect to make on a trade over the long haul. But the interesting part is that once you have a positive expectation system it is money management that will be the biggest factor in how fast and how large your bankroll grows. If you have a high positive expectation but your account doesn't seem to be growing very fast then it might be a sign of poor money management. Having said that, it turns out, that even a system with a mediocre positive expectation can be turned into a money machine with the right money management techniques.
So how do we calculate expectation?
Here's the equation
Expectation = [1 + (W/L)] *P - 1
Where W = average size of a win, L = average size of a loss and P = probability of a winning trade.
So for example, if we've been tracking our trades for the past 100 trades (you do track the details of your trades don't you?) and we found the following
Average win W = $454
Average Loss L = $458
Probability Win = 63% (in other words 63 of the last 100 trades were winners)
Our expectation would be
Expectation = [1 + (454/458)]*0.63 - 1
Expectation = [1 + 0.99]*0.63 - 1
Expectation = 1.99*0.63 - 1
Expectation = 1.2537 - 1
Expectation = 0.2537
What this expectation is telling us is that with the system we used to get the results used in the example above, for every $1 we risk on the trade we can expect to be rewarded with a profit of $0.2537.
It's important to understand that this is not a predictive value, but a measure of past performance only. It tells us how our system has performed historically, not how it will do in the future. Also note that the calculation didn't have anything to do with how the trades were chosen. The only thing that matters is that the same system was used for all the trades involved in the above calculation. If at some point during our past trading we changed our system then we would need to begin new calculation using data from our new system.
So if it's not predictive what good is it? We'll nothing is "predictive" in the markets since we don't know the future, but having an expectation based on past performance can still give us an idea of the probability that our system will perform for us in the future. So obviously the more historical trades we have the more comfortable we can be that our system will perform with a "similar" expectation in the future.
Knowing the expectation of our system allows us to do a few things. We can determine if it's possible to make money or not. If it's positive we know we can make money (assuming it's positive enough to overcome commissions and slippage), if it's negative it will never make us money in the long run.
Also, knowing the expectation value of the past X number of trades we can now go back and experiment with different money management techniques to see how it would have affected our overall account balance. Even with a positive expectation, different position sizing choices can produce very significant differences in account balances over time due to the effects of draw downs and the compounding of our returns. The expectation value along with the probability of a winning trade can be used to go back and perform money management experiments to help us understand the effects of money management on our bankroll given the system we're trading. You can learn more about this in the Trader's Guide To Money Management at the end of this article.
Lastly, knowing the expectation value of more than one system allows us to make a quantitative comparison of historical performance between systems. This can help us decide when it's time to change systems or troubleshoot our existing one.
So what's the next step? Find or develop a trading system with a positive expectation and then focus on money management. Of course developing a system with a positive expectation isn't exactly trivial so if you can find one that's already been developed then by all means use it. In the end, the expectation of the system you trade is indifferent to who created it. If it's positive and you apply good money management techniques then you're on your way to some serious money.
As a trader I believe it's important to focus on your strengths and delegate your weaknesses. By using the Doubling Stocks newsletter to provide me with stock picks that have shown a high positive expectation I can focus on money management where I can make the biggest difference to my bankroll.
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