[R-SIG-Finance] Mathematical Expectation for a trading system

[Patrick Burns]

You might get different answers, but
I think you are essentially asking
the impossible.  You might be able
to estimate P, but estimates will be
very noisy.  With any strategy sometimes
the market agrees with the strategy
and sometimes it doesn't.

A friend told me about hearing a talk
on a strategy that did very well over
the last 60 or 70 years.  My friend
raised his hand and pointed out that
the strategy lost money for about
40 years, so the speaker may not have
been in business any more to take
advantage of the big gains later.

What you care about is P in the immediate
future.  That's a hard problem.



Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of "The R Inferno" and "A Guide for the Unwilling S User")

Mark Breman wrote:
> Hello,
> In "The mathematics of money management" by Ralph Vince there is a formula
> for calculating the Mathematical Expectation of a game (in R pseudo code):
> 
> ME  =  for(i in 1:N) { Pi * Ai}
> 
> where
> P = Probability of winning or losing
> A = Amount won or lost
> N = Number of possible outcomes.
> 
> Or in text: "Mathematical expectation is the amount you expect to make or
> lose, on average, each bet".
> 
> Now suppose I want to know the Mathematical expectation of a trading system.
> 
> I have a series of trade returns:
> 
>> trades$PnL
>  [1]  -5.75  10.00  -1.25  96.00 -16.00 -35.00  29.00 -18.25  -2.25 -10.25
> -21.75  -5.50   8.50 -20.50  -6.00  14.25  18.00
> [18]   3.75  -4.25  24.00  17.75  -9.50  11.25 -33.75   6.25 -28.00   1.00
>  36.75  14.00 -30.75  -0.50   6.75  19.25   5.25
> [35] -10.00 -23.25   9.25  11.00 -33.00 -19.00 -17.50  -5.50  -5.75  -8.50
> -24.50 -24.00   2.25  -1.00   0.75  -1.75  -2.25
> [52]   9.25  15.00  -2.25  -6.75   5.25  -4.75 -10.00  -2.00  63.50 -18.00
> -18.00  58.00  -8.75   1.00 -36.75 -23.50 -64.00
> [69] -15.75 -10.00 -34.75  27.75 -57.00 204.75 -45.00 -71.00 133.75
> 
> So I have A = trades$PnL and N=77, but how do I calculate P?
> 
> -Mark-
> 
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> 
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