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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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  • $\begingroup$ This question, about a particular (simple) application of a common definition, is both not "expert" and too localized. $\endgroup$ – Tal Fishman Oct 4 '11 at 1:36
  • $\begingroup$ Odd - I'm not sure why this was closed. The answer supplied the theory behind expectancy quite nicely. Problem solved. $\endgroup$ – Contango Oct 4 '11 at 19:54
  • $\begingroup$ 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. $\endgroup$ – Tal Fishman Oct 4 '11 at 20:07
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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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    $\begingroup$ 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. $\endgroup$ – babelproofreader Oct 4 '11 at 21:56
  • $\begingroup$ Good point, @babelproofreader. The R multiples are also taking into account the OP's desire to take the amount at risk into account. $\endgroup$ – rajah9 Oct 5 '11 at 15:05
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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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