# Expectancy



## Artamon (7 December 2005)

G'day folks,

I've been going over old posts on positive expectancy and risk/reward ratios to get a deeper understanding of what, undoubtedly, is the most important criteria prior to begin trading any system.

However, throughout the posts I have seen 2 sets of calculations on how to determine expectancy. And they don't give the same result so, obviously, one is incorrect.

In wayneL's very information article (https://www.aussiestockforums.com/forums/showpost.php?p=4858&postcount=25)
he uses the following formula:

Expectancy = ((1 + reward/risk ratio) * win/loss ratio) - 1

In numerous other articles and posts I've read, the following is used:

Expectancy = (Win % * Average Win) - (Loss % * Average Loss)

So, which is it?

I would think that using actual $ figures about the returns of a system would be more inclined to give a better reflection on the state of that system.

Andrew.


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## wayneL (8 December 2005)

Andrew,

The calc I use, measures the profit one can expect per $1 placed at risk. Risk being the dollar amount between the entry price and the stop loss price. This result will be constant no matter what size of account.

Therefore it is understandable to any observer.

The other calc would only have relevance to the account being traded.

Both are correct.

All personal choice I guess.


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## kaveman (8 December 2005)

Expectancy = ((1 + reward/risk ratio) * win/loss ratio) - 1
this seems to compare your actual results with your before-trade guesses

Expectancy = (Win % * Average Win) - (Loss % * Average Loss)
this only uses actual trading performance


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## Victor H (8 December 2005)

If you multiply the 1st formula by "Average Loss" then you will arrive at the 2nd Formula.

Note: A little ambiguity exists in the formulae above.     

Win/Loss Ratio = % Winners = [ 1- % Losers ]


Regards 
Victor.


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## wayneL (8 December 2005)

kaveman said:
			
		

> Expectancy = ((1 + reward/risk ratio) * win/loss ratio) - 1
> this seems to compare your actual results with your before-trade guesses




There seems to be confusion with different terminology. This formula measures actual historical performance as well.

I think "Expectancy" is the wrong term for either equation, as it implies future permormance. 

Perhaps "Performance" would be a better term for both equations


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## Victor H (8 December 2005)

This should clear up any confusion between the 2 formulae.

Consider a system whereby the following parameters are measured.

% Winners 	= 0.40
% Losers 	= 0.60
Average Win 	= $500
Average Loss 	= $200

Formula 1.

Expectancy 	= (( 1 + reward/risk ratio ) * win/loss ratio ) - 1
	       	= (( 1 + 500/200) * 0.40 ) - 1
		= 0.40
	             = 40 cents / $ Risked

Formula 2.

Expectancy 	= ( Win % * Average Win ) - ( Loss % * Average Loss )
		= ( 0.40 * $500 ) - ( 0.60 * $200 )
		= $80		

Hence the Expected Return ( / $ Risked ) = $80 / $200 
				     = 0.40 
				     = 40 cents / $ Risked


Regards Victor.


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## Artamon (8 December 2005)

Victor H said:
			
		

> This should clear up any confusion between the 2 formulae.
> Consider a system whereby the following parameters are measured.
> % Winners 	= 0.40
> % Losers 	= 0.60
> ...



Ok, this last post has made things quite a bit clearer, but can somebody shed some light on the following:

A strategy I once backtested in AmiBroker gave me a reported RRR of 1.26. The Avg win was $215. The Avg Loss was $105. My query is that 215/105 does not equal 1.26, which was the reported RRR. Is there something I'm missing?? I don't want to be concentrating too much on reported figures in various software, but If I'm using software to do some backtesting and reporting the results, I'd like to *know* that what I'm looking at is correct.

Thanks,
Andrew.


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## wayneL (8 December 2005)

Artamon said:
			
		

> Ok, this last post has made things quite a bit clearer, but can somebody shed some light on the following:
> 
> A strategy I once backtested in AmiBroker gave me a reported RRR of 1.26. The Avg win was $215. The Avg Loss was $105. My query is that 215/105 does not equal 1.26, which was the reported RRR. Is there something I'm missing?? I don't want to be concentrating too much on reported figures in various software, but If I'm using software to do some backtesting and reporting the results, I'd like to *know* that what I'm looking at is correct.
> 
> ...




This is from the Amibroker help files regarding the RRR in the report. 



> Risk-Reward Ratio - Measure of the relation between the risk inherent in a trading the system compared to its potential gain. Higher is better. Calculated as slope of equity line (expected annual return) divided by its standard error.


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## tech/a (8 December 2005)

Artamon said:
			
		

> . Is there something I'm missing??
> Thanks,
> Andrew.





Yep.

Number of winners V number of losers.IE % wins to losses.
Multiply them out and youll get your 1.26.
You have only one side of the equation.


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## It's Snake Pliskin (8 December 2005)

Artamon,

Click on this link:  http://www.yourproductteam.com/vti/tutorials.htm

and Van Tharp will explain r/multiples and expectency. It's audio and visual and quite easy to follow. Scroll down to Trading and it's the first one.

Snake


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## RichKid (11 December 2005)

Snake Pliskin said:
			
		

> Artamon,
> 
> Click on this link:  http://www.yourproductteam.com/vti/tutorials.htm
> 
> ...




Some further discussion of Van Tharp in the following thread (and elsewhere on ASF): https://www.aussiestockforums.com/forums/showthread.php?t=846&highlight=van+tharp


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