A common question among traders, new and experienced, “is how do you know if you have a good trading system?“.
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 Expectancy of your trading system and it’s crucial that you know it for a number of reasons.
Once you have a positive expectancy 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 expectancy, but your account doesn’t seem to be growing very fast then it might be a sign of poor money management.
It turns out that even a trading system with a positive, but still only mediocre, expectancy can be turned into a money machine with the right money management techniques. With proper money management it’s possible to parlay even a small edge into significant profits.
Avg_Win = $28
Avg_Loss = $180
% Win = 90% (90 of the last 100 trades were winners)
% Win = 10% (10 of the last 100 trades were losers)
Our expectancy would be:
Expectancy = [0.90 X $28] - [0.10 X $180]
Expectancy = $25.20 - $18.00
Expectancy = $7.20
What this expectancy is telling us is that even with a system that has much bigger losing trades (6X bigger in this example) than winning trades, we can still expect to make $7.20 for every $1 we risk over the long run.
The expectancy measure of a trading system is a statistical measure that becomes more accurate as the number of trades included in the calculation increases. As a rule of thumb, the expectancy value should contain about 100 trades or more to be accurate, although you can start to get a picture after about 30 or so trades.
Furthermore, expectancy is a measure of what you can expect to profit for every $1 risked over the long run. This “over the long run” part is important because it means that you cannot have any meaningful evaluation of a trading system over only a hand full of trades. You need to have enough trades so that the number averages out and converge on the expectancy value.
For instance, I know that a coin flip is 50/50 heads or tails. But that doesn’t mean that if I flip the coin twice I will produce 1 head and 1 tail. I could very easily get 2 heads which is 100% heads. We’re much less likely to get 5 heads in a row though. So as we increase the number of flips the percentage of heads to tails will gradually get closer and closer to the 50/50 ratio we expect.
This is called the law of large numbers and is a central concept in probability and statistics theory.
It essentially tells us that statistical measures are meaningless with only a small sample of trades (or coin flips) and that it takes a large number of samples to become accurate. It therefore makes no rational sense to judge any trading system on only a handful of trades. You need at least 30 trades before you even consider judging the trading system and 100 or more for really good accuracy.
It’s also 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.
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’ expectancy in the future.
Knowing the expectancy of our system allows us to do a few things
Even with a positive expectancy, different position sizing choices for your trades can produce very significant differences in account balances over time due to the effects of draw downs and the compounding of our returns.
Imagine every time we flip a coin we win $5 for a heads and we lose $2 for a tails. Over the long run the expectancy of this game is:
Expectancy = [% Win X Avg_Win] - [% Loss X Avg_Loss]
Expectancy = [0.50 X $10] - [0.50 X $2]
Expectancy = $5.00 - $1.00
Expectancy = $4.00
So with every $1 risked I’ll expect to make $4 in the long run. However, if we don’t exercise good position sizing then we could very well lose anyway because we could go bust early and not be around for the long run.
Imagine that I’m not too bright and I decide I want to risk %100 of my money on every trade in the above game. I have a 50% chance of losing all my money on my first coin flip. Even if I get lucky and win, I then have a 50% chance of losing all my money on the next coin flip if I continue to risk 100%. Clearly this is a doomed scenario because eventually I’m going to hit tails and lose all my money.
This was obviously an extreme example, but the point is that if you risk too much money on a single trade then even a trading system with a positive expectancy will be a losing system for you because the size of your losing trades will cause you to lose too much money and you will not be able to stay in the game for the long run in order for the expectancy of the system to be realized.
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 Expectancy of your trading system and it’s crucial that you know it for a number of reasons.
- it tells you if it’s possible to make money with the trading system or not
- it can help you evaluate the effect your tweaks and changes are having on the performance of your trading system
- it helps you work out the most effective money management strategies for overall results
Once you have a positive expectancy 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 expectancy, but your account doesn’t seem to be growing very fast then it might be a sign of poor money management.
It turns out that even a trading system with a positive, but still only mediocre, expectancy can be turned into a money machine with the right money management techniques. With proper money management it’s possible to parlay even a small edge into significant profits.
Calculating the Expectancy of Your Trading System
The expectancy formula below is a standard formula used by traders to calculate the expectancy of their trading systemExpectancy = (% Win X Avg_Win) - (% Loss X Avg_Loss)
Where:For example, let’s say we’ve tracked our last 100 trades and we found that we won 90% of our trades (90 trades) and lost 10% (10 trades), and that the average size of our winning trades was $28 while the average size of our losing trades was $180.
% Win = percentage of trades that are winners
% Loss = percentage of trades that are losers
Avg_Win = average size of a win
Avg_ Loss = average size of a loss
Avg_Win = $28
Avg_Loss = $180
% Win = 90% (90 of the last 100 trades were winners)
% Win = 10% (10 of the last 100 trades were losers)
Our expectancy would be:
Expectancy = [0.90 X $28] - [0.10 X $180]
Expectancy = $25.20 - $18.00
Expectancy = $7.20
What this expectancy is telling us is that even with a system that has much bigger losing trades (6X bigger in this example) than winning trades, we can still expect to make $7.20 for every $1 we risk over the long run.
Understanding Expectancy and its Limitations
The expectancy of a trading system is calculated from actual trading results. The numbers used are not theoretical but come directly from your past trade history. Also important to recognize is that since these are actual trades we are using the wins and losses already include such factors as slippage and commissions (since in FOREX your commission is generally your spread). This means that these wins and losses are true representations of the actual costs of the trades.The expectancy measure of a trading system is a statistical measure that becomes more accurate as the number of trades included in the calculation increases. As a rule of thumb, the expectancy value should contain about 100 trades or more to be accurate, although you can start to get a picture after about 30 or so trades.
Furthermore, expectancy is a measure of what you can expect to profit for every $1 risked over the long run. This “over the long run” part is important because it means that you cannot have any meaningful evaluation of a trading system over only a hand full of trades. You need to have enough trades so that the number averages out and converge on the expectancy value.
For instance, I know that a coin flip is 50/50 heads or tails. But that doesn’t mean that if I flip the coin twice I will produce 1 head and 1 tail. I could very easily get 2 heads which is 100% heads. We’re much less likely to get 5 heads in a row though. So as we increase the number of flips the percentage of heads to tails will gradually get closer and closer to the 50/50 ratio we expect.
This is called the law of large numbers and is a central concept in probability and statistics theory.
It essentially tells us that statistical measures are meaningless with only a small sample of trades (or coin flips) and that it takes a large number of samples to become accurate. It therefore makes no rational sense to judge any trading system on only a handful of trades. You need at least 30 trades before you even consider judging the trading system and 100 or more for really good accuracy.
It’s also 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.
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’ expectancy in the future.
Knowing the expectancy of our system allows us to do a few things
- we can determine if it’s possible to make money or not. If expectancy is positive we know we can make money, if it’s negative it will never make us money in the long run.
- Knowing the expectancy of more than one trading system allows you to make a quantitative comparison of historical performance between systems. Likewise, you can use expectancy as a way to compare the performance of different settings configurations within one trading system. In fact, this is the primary way to measure and tweak a system for better performance.
Positive Expectancy + Money Management = Long Term Success
A positive expectancy is a minimum requirement for long term success. The other required component is good money management. And money management is all about deciding how much to spend on each trade (how many lots?) and is what’s referred to as your position size.Even with a positive expectancy, different position sizing choices for your trades can produce very significant differences in account balances over time due to the effects of draw downs and the compounding of our returns.
Imagine every time we flip a coin we win $5 for a heads and we lose $2 for a tails. Over the long run the expectancy of this game is:
Expectancy = [% Win X Avg_Win] - [% Loss X Avg_Loss]
Expectancy = [0.50 X $10] - [0.50 X $2]
Expectancy = $5.00 - $1.00
Expectancy = $4.00
So with every $1 risked I’ll expect to make $4 in the long run. However, if we don’t exercise good position sizing then we could very well lose anyway because we could go bust early and not be around for the long run.
Imagine that I’m not too bright and I decide I want to risk %100 of my money on every trade in the above game. I have a 50% chance of losing all my money on my first coin flip. Even if I get lucky and win, I then have a 50% chance of losing all my money on the next coin flip if I continue to risk 100%. Clearly this is a doomed scenario because eventually I’m going to hit tails and lose all my money.
This was obviously an extreme example, but the point is that if you risk too much money on a single trade then even a trading system with a positive expectancy will be a losing system for you because the size of your losing trades will cause you to lose too much money and you will not be able to stay in the game for the long run in order for the expectancy of the system to be realized.
