Hhmmm, this is all very strange.
The subject of "Mathematics of money management" is about optimizing trade
size under reinvestment of profits (optimizing the Growth function G(f),
i.e. finding the optimal f)
Ralph Vince warns the reader that the trade system to start with should have
a positive Mathematical expectation to start with, because the optimal f can
not turn a losing system into a winning system.

>From the reactions here I conclude that it's impossible to calculate a
reliable Mathematical expectation for the system to start with, so what's
the value of optimal f if you can never be confident that the system is
profitable to start with?

Some reactions on this thread referred to the validity of historical data to
future performance of the system.
I think it's clear that there are no guarantees for the future whatsoever if
we formulate expectations solely based on data from the past. I think
this uncertainty is part of trading. But is it not possible to calculate a
Mathematical expectation for a system based on historical results which only
says something about the validity/performance of the system in the past?

Would the following approach be sensible/possible:
Take the historical profits and loses from the system and look at the
distribution of these results. If the distribution looks like a normal
distribution (as expected for stock market returns, at least in theory), use
the normal distribution to calculate the P (probability of winning or
losing) and calculate the Mathematical expectation?

-Mark-

2009/10/14 Mark Knecht <markknecht@gmail.com>

> On Wed, Oct 14, 2009 at 1:39 AM, Mark Breman <breman.mark@gmail.com>
> 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-
>
> Hi Mark,
>   The simple answer would be:
>
> 1) Look at all the data you have today. How many trades won? How many
> trades total? P = Total wins/ total trades
>
> 2) Start trading. After some fixed number of trades - say 30 more
> trades - how did the win/loss ratio compare?
>
>   Don't think only of the probability, but also how much does the
> probability vary? I have systems that trade 4000 times in 6 months. I
> constantly track win/loss ratios as a rolling calculation just to
> watch how the system might be doing in a new market type. My system
> might have a probability of winning 82% of the time over 4000 trades
> but goes up and down by 5% when looking at any 100 consecutive trades.
> (So 77%-87% wins) I consider that 'normal'. If it gets outside of 5% I
> might stop trading it until it's back in the 'normal' range.
>
>   Note that I do this also for what you call 'A' since the product
> represents the potential for making money if everything works out
> 'normally'. ;-)
>
> HTH,
> Mark
>

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