# Positive Expectancy



## James Austin (14 June 2008)

Hello All, 

I’ve been looking at the concept of Positive Expectancy, its calculation, and what is/isn’t a robust benchmark for positive expectancy.

A hypothetical day trading system produces the following results:

81% are winners
19% are losers
av. win is $492
av. loss is $416

I’ve come across two formulas to calculate expectancy. Both generate the same end result. But the proponents of each formula conflict in terms of what is/isn’t a desirable expectancy benchmark.

Formula one:

[probability of win x av. win] – [prob. of loss x av. loss] = expectancy 

using the above hypothetical:

[0.81 x 492] – [0.19 x 416] = 319 rounded

319/416 = 77 

So our hypothetical trader with the above stats expects to make 77 cents for every dollar $1 risked.

My research shows that proponents of this formula argue that an expectancy of 60 cents or greater represents a “good” system. 

ie., an expectancy of 60 cents is the benchmark. 


Formula two:

[reward to risk ratio x win ratio] – loss ratio = expectancy ratio

[492/416 x 0.81] – 0.19 = 0.77 expectancy ratio 


Each formula obviously gives the same answer. But the proponents of this second formula state that an expectancy ratio >1.0 is the benchmark.

So formula one advocates would be happy with their 77 cents, but formula two advocates would not.

My question,

Have I missed something in my attempt to understand expectancy and formulate a benchmark? Is it 60 cents or $1.00??

Thanks for feedback.

James.


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## Temjin (14 June 2008)

There isn't really a "benchmark" for the expectancy ratio. (at least in my opinion)

When you evaluate a system, you need to fully take into account the opportunity that it was able to give and the probability of generating a negative expectancy over the period in which you arrived at that final expectancy value. 

For example, system A produces 100 trades with a calculated expectancy of 2R while system B produces 1000 trades with a calculated expectancy of 0.2R. Note that these trades are completed over the same period of time.

Which system would you prefer then? From your definition, you would have taken system A because it had a "higher" expectancy value. However, if you calculate the expectunity, which is expectancy x opportunity, System A would have produced 200R and System B would have produced 500R over the same period. 

Now one would obviously choose System B because it produces more "profit" than System A over a given of time. 

However, this is not always to be the case. If System B has a higher probability of producing a negative expectancy over that period of time, which could be true because its average loss is greater than average win, then one may not be able to use as aggressive "position size" to take advantage of the system's expectunity. (i.e. if an aggressive position size is used, the account balance might experience a sufficently large enough drawdown that would make it difficult for it to recoup its balance) 

An example would be System A can sustain a position size of around 2% per trade while System B can only sustain a position size of around 0.5% without suffering a large enough percentage drawdown that any investors might feel uncomfortable with. System A will now generate 2% x 200R = 400% return (assuming no compounding) while System B would only generate 0.5% x 500R = 250% return over the same period. 

Thus, System A is now more favourable again. 

I'm not fully sure if this is correct though so somenoe please correct me if my explanation is flawed. But this is how I understand it. 

Cheers


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## wayneL (14 June 2008)

Frequency of trades is a very important factor too.

You must factor this in.


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## julius (15 June 2008)

Hi James,

Was the system you mention built with range bars?


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## tech/a (15 June 2008)

Temijin puts it nicely and Wayne makes an important point.

In addition I'll add that the character of the system(Method) must suit the user.
While taking 50 trades a day may suit some (Not me),I'll sacrafice return for time.

As for benchmarks--a positive expectancy is positive then frequency is thrown in to cap off return over time.


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## James Austin (15 June 2008)

thanks for the feedback, food for thought.

julius,
the stats are just hypthetical.

thanks
james


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## Porper (15 June 2008)

James Austin said:


> the stats are just hypthetical.




Glad to hear it, with those stats I would never have to work again.

Just on what Wayne was saying, if you have a positive expectancy (tested over time), then the more you trade the larger profits would be.(A question more than a statement).


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## tech/a (15 June 2008)

Pete.

Yes if your method wins more often than it loses.
(Less positions traded much more often.)
If it wins more than it loses its more about deep pockets than frequency.(More positions held longer)
If you think about the two methods it will become clear.


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## Bin57again (23 June 2008)

Just to add to the debate, commissions are also a key factor in expectancy of a system. I have loads of systems with a positive expectancy but none that are profitable once I add commissions...I'm still looking...Oh, actually, as Van Tharp points out, commissions aren't such a key factor if your position size is say $10m per trade. Unfortunately, I'm a few decimal points behind him...

Just while we're discussing this, is there anyone in the Sydney area who'd like to work with me on developing a short term system? Please PM me if you are interested...


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