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Expectancy is defined as "How much money gained for every $1 risked".

What is the expectancy for this particular series of trades?

  • Risked €1, won €2
  • Risked €2, won €1
  • Risked €3, won €6
  • Risked €3, won €6
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This question, about a particular (simple) application of a common definition, is both not "expert" and too localized. – Tal Fishman Oct 4 '11 at 1:36
Odd - I'm not sure why this was closed. The answer supplied the theory behind expectancy quite nicely. Problem solved. – Gravitas Oct 4 '11 at 19:54
It fits the definition of "too localized": "This question is unlikely to ever help any future visitors." You are merely asking how to apply a simple principle. It is like posting a question on SO asking "how do I declare a variable in C?" If your question is about the theory behind expectancy, then change the question and perhaps it could be re-opened. – Tal Fishman Oct 4 '11 at 20:07

closed as too localized by Tal Fishman, Bob Jansen, TheBridge, Joshua Chance, Steve Oct 4 '11 at 16:23

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, see the FAQ.

2 Answers

up vote 1 down vote accepted

Van Tharp addresses expectancy in his book, Trade Your Way to Financial Freedom. Here is his definition of expectancy.

$\frac{winPct * winAmt - losePct * loseAmt}{trades}$

I would recast your trades as follows:

  • Won €1
  • Lost €1
  • Won €3
  • Won €3

Your winning percentage is 75%. Your losing percentage is 25%. Your winning amount is €7. Your losing amount is €1.

So your expectancy would be $\frac{.75* €7 - .25 * €1}{4}$

Your expectancy, by Tharp's reckoning, would be €1,25. Tharp does not directly use the amount at risk. Rather, his definition takes into account that the trader or quant may choose a larger bet size when the odds are in his favor.

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1  
Another way to recast the trades is in Van Tharp's concept of R multiples, e.g. 2R, 0.5R, 2R and 2R, the average of which is 1.625, i.e. on average you can expect to make 1.625 times your risk per trade. – babelproofreader Oct 4 '11 at 21:56
Good point, @babelproofreader. The R multiples are also taking into account the OP's desire to take the amount at risk into account. – rajah9 Oct 5 '11 at 15:05
up vote 0 down vote

Lets see if I have this right:

Expectancy = average win / average loss.

Thus:

  • Risked €1, won €2 means total wins are now €1 for 1 trade.
  • Risked €2, won €2 means total losses are now €1 in 1 trade.
  • Risked €3, won €6 means total wins now rise to €4 over 2 trades.
  • Risked €3, won €6 means total wins now rise to €7 over 3 trades.

Thus, average win = €7 / 2 = €3.50, average loss €1 / 1 = €1, so expectancy is 3.50 for this series of trades?

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