| Projecting Forex Profits with Expectancy |
by John Jagerson We discussed why it's important to know what profits to expect. Now we discuss how to determine the profits your trading could bring.
What is expectancy? Expectancy is what it sounds like. It helps you understand how winners, losers, gains and losses relate to each other over the long term. This process helps you understand what your trading system profits should be, and helps validate your backtesting. In this lesson, we will develop expectancy in three steps. First, you will calculate your win- and loss-ratios. Second, you will calculate your reward-to-risk ratio. Finally, you will combine the two numbers into an expectancy ratio. That information will help to understand what you can expect in the future.
Steps for developing expectancy
1. Calculate your win and loss ratio 2. Calculate your reward to risk ratio 3. Combine those two ratios into an expectancy ratio  Win and loss ratios This is a simple number to calculate. First, from your back-testing period, sum the total number of trades that would have been taken. Next, total the number of winning trades from that set. Finally, divide the number of winning trades by the total number of trades. This gives you your win ratio. In the example system we have been building we have a win ratio of 28%. That means the system results in a profitable trade 28% of the time and losers 72% of the time. The win and loss ratios are calculated like this: (42 Total winners) / (150 Total trades) = 28% win ratio 100% - (28% win ratio) = 72% loss ratio
This may seem very low, but as we continue we see that doesn’t mean the system isn’t profitable.
Reward to risk ratio This is also a relatively simple number to calculate. As you know from the trading system exits lesson in this course, a losing trade will always exit on the stop loss, which is 100 pips below the entry. You also know that this system will exit a profitable trade with a gain of 600 pips. The risk to reward ratio therefore, is simply the size of a profitable trade divided by the size of a losing trade. This system has a Reward to risk ratio of 6, which is calculated like this:
(600 Winner size) / (100 Loser size) = 6
Expectancy ratio At this point we can combine these two numbers to create an expectancy ratio. This is a simple process of multiplying the reward to risk ratio (6) by the percentage of winning trades (28%), and subtracting the percentage of losing trades (72%), which is calculated like this:
(Reward to Risk ratio x win ratio) - Loss ratio = Expectancy Ratio (6*28%) – (72%) = .96
Superficially, this means that on average you expect this system’s trades to return .96 times the size of your losers or 96 pips on average. This is important for two reasons: First, it may seem obvious, but you know right away that you have a positive return. Second, you now have a number you can compare to other candidate systems to make decisions about which ones you employ. Typically, we look for a system with an expectancy of 1.0 or greater to give us a higher level of confidence that it can be traded successfully in the future. As we move forward through this course we will look at this and a modification of the system to see which is really better. It is important to remember that any system with an expectancy greater than 0 is profitable using past data. The key is finding one that will be profitable in the future.
You can also use this number to evaluate the effectiveness of modifications to this system. For example, let’s assume that you increased your stop loss by 50 pips to 150 and your profit target to 650 pips, and retested to see how your performance changed. Using this sample system above, your win/loss ratio increased to 31% because you were stopped out fewer times and had a couple larger winners. This sounds great, right? In this case, yes, it is better. We know this because its expectancy ratio is 1.17. Here is how that is calculated.
(1.86*.31%) – (69%) = 1.17
I like this example because it illustrates a general tendency for system performance to improve with larger stops. This is something that has been noted by technicians for years, but is one of the things that new traders struggle with a lot. Of course, that efficiency drops off after a certain point, but suffice it to say, expectancy can greatly help you understand how different stop losses and profit targets compare to each other and affect the system’s performance.
In case you are curious, expectancy with this system drops into the negative with a stop loss of 50 pips.
Other Factors Expectancy is an important factor but there are three fundamental considerations that are important to note when developing it:
1. Trading costs There is a simple method to help better understand the affects of trading costs on your system. Reduce the gains in your winners by the amount of trading costs, and increase your losers similarly. As I mentioned in a previous section, it is also good to assume a certain amount of slippage during entry. In other words, if you assume that your spread is 2 pips, and the market will move against you 10 pips before you have had a chance to enter your trades, you will need to either take 12 pips away from your winners and add 2 pips to your losers or build that into your profit target and risk by assuming that the market must move 612 pips to trigger an exit.
In the example above, I have already forced the backtesting module that to assume a 600 pip gain the market must move at least 612 pips. Likewise, two pips are added to each loss. In your system, this is an important step to remember; otherwise a seemingly good system may not actually be profitable.
2. Position Sizing From here you need to begin working on understanding how expectancy works with position sizing. An expectancy ratio may look good, but without proper and consistent position sizing (use of leverage, margin and lot size), your actual performance could still be poor. We will talk about position sizing again in the next section on backtesting procedures and software.
3. Historical versus Future Results It is important to point out that when you are building and testing a system initially, you rely on very fallible data. Past data is certainly useful, and it is the best alternative when you are developing an idea. However, the past is NOT an indication of what WILL happen in the future. You will not likely see results perfectly consistent with what you saw in the past over your testing period. It just doesn’t happen.
Rather than invalidating your expectancy analysis, however, I think this makes it even more important. If I don’t have an expectancy ratio larger than 1.0, you should be extremely skeptical of the system’s probability of success in the future. Our sample system qualifies well over the 1.0 expectancy bench-mark. By requiring more “cushion” from a system, you can be more confident in its chances for success in the future.
Summary Expectancy is a great way to compare and analyze systems and system modifications. It is a solid double-check on the viability of the system itself. If your expectancy ratio is negative you should not trade the system.
Expectancy also serves an important planning purpose. I always compare developing an expectancy ratio to the pre-flight checklist that a pilot uses before take off. If you are able to answer all the questions required for an expectancy ratio then you have done some good planning. If one of your trading factors is blank, or only an estimate, you need to solidify it before executing on your system. Next: Timing Your Forex Trades Keep up with us:
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3.25 Copyright (C) 2007 Alain Georgette / Copyright (C) 2006 Frantisek Hliva. All rights reserved." |
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