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About Positive Expectation


Traders sometimes refer to the expectation of a system.

You will hear it said that “a system must have a positive expectation to have any chance of success”.

This is true but we will go into the subject more deeply and try to explain what is really meant by this.

System rules are used for entering and leaving the market, in other words to decide where trades will be started and ended.

If your tests show that particular rules produce profitable results, then you can say that the rules have a positive expectation. If the results are not profitable, a negative expectation is indicated.

So what’s the big deal? All of this is obvious.

Yes, this is obvious and that is one of the reasons why expectation does not feature in the MODUS Method.

However, ‘expectation’ should not be dismissed as a useless concept. There are times when you may find it useful to know how to compare the expectations of two sets of system rules.

For example, when you are trying to devise a rule for entering or leaving the market as part of a system creation exercise, you may want a quick way of deciding whether certain ideas appear to be worth pursuing i.e. whether they merit a thorough evaluation using the MODUS Method.

At this stage, you just want to do some quick tests to see if this or that idea for a rule produces a ‘profitable expectation’.

You can do this on a single commodity basis, where only a few trades arise and then it will be easy to study them to see how your rule is working and what you might be able to improve.

While you are trying to generate new ideas and variations, you don’t want to be confused with hundreds of trades of varying position sizes - you just want to see if your rules idea might be any good. That is why you may have decided to look at single commodities and single contracts.

OK, so how is this done?

You run your tests with the proposed rules and come up with a few trades. You will expect more losers than winners but you will expect the winners to be significantly larger than the losers. This is because your rules will have been aimed at ‘running’ the winners and ‘cutting’ the losers.

Once you have your list of trades, showing single contract results, it is a simple matter to calculate the percentage of trades that made a profit (however large or small) and the average size of a winning trade and of a losing trade. That’s all you need to put a figure on the ‘expectation’ which we call the ‘E’ number.

You can use the E number to make comparisons between different alternative rules to determine which ones appear to be the most promising. Later, you will put your short-listed selections through a full evaluation in order to assess their potential.


The following example uses Microsoft Excel to do the calculating work, therefore the trade results are pasted into a spreadsheet:-

Trade $ Result Winning Losing
Number (1 contract) Trades Trades
1 190 190  
2 -20   -20
3 -64   -64
4 112 112  
5 -60   -60
6 -140   -140
7 -70   -70
8 -30   -30
9 90 90  
10 120 120  
128 512 -384

Average Size of Winning Trade
Average Size of Losing Trade -$64.00
Win/Loss Ratio 2
Percentage of Winning Trades 40%
"E" Number (Expectation) 0.2




What does the E number mean?

The E number is a convenient way of making a comparison between two different sets of system rules or variations of rules. The higher the E number the higher the ‘expectation’.

A literal interpretation of the number is as follows:

In the example above, for every $1 risked, there is a 40% win probability and a 60% probability of loss i.e. 60 cents loss. At the win/loss ratio of 2:1 the remaining 40 cents result in a win of 80 cents. That amounts to a net win of 80 minus 60 cents = 20 cents. Therefore E = 0.20 in the example above.

The E number should not be taken too seriously except as a quick method of comparing different rules. The results were obtained by historical test and give no indication of future expectation. They are only a measure of how this system might have traded in the past.

Lastly, it should be noted that money management, risk management and portfolio management are of much greater importance than ‘selection by E number.’ This is because provided they are of good quality, the three managers will always apply sound principles to the trading system, whereas the E number was only used to judge if a set of rules was likely to produce positive results. Important though this is, it cannot be predicted with any level of certainty, only by historical inference.


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