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At 10:48 PM -0500 12/16/98, Carroll Slemaker wrote:
>Your problem is incompletely defined. As some have already indirectly
>suggested (by making assumptions about the unspecified factors), the
>result will depend upon both (a) the size of each individual win and loss,
>and (b) the sequence in which these occur. I think it can be shown that
>the result would differ significantly if you took the same set of wins and
>losses and simply rearranged their sequence.
>You might, of course, assume an average win & loss size and assume further
>that they occur in alternating sequence. But I suspect that if you
>simulated your problem using random wins and losses, with your randomizing
>function chosen to approximate the 50% win/loss split and the average win
>size, you would find a VERY wide spread of results over several different
>simulations.
Actually, if the wins/losses are a constant percentage of capital and if
Andy adjusts the trade size as his capital increases/decreases, the order
of winning and losing trades wouldn't matter. You can see this from the
equation in my previous post:
End = Start*((1-L)*(1+2*L))^(n/2)
Assume 10 trades for simplicity, this would become:
End/Start = ((1-L)*(1+2*L))^5
Expanding this:
End/Start = (1-L) * (1-L) * (1-L) * (1-L) * (1-L) *
(1+2*L) * (1+2*L) * (1+2*L) * (1+2*L) * (1+2*L)
So you can see that the end value does not depend upon the order of winners
and losers.
If the win/loss was a constant dollar amount (instead of a constant
percentage), the result is the same (so long as you don't run out of money
during a string of losses).
But both of these cases are pretty hard to maintain in practice because of
margin requirements, etc. In most practical cases Carroll Slemaker's
conclusion would be correct.
This example illustrates the importance of the money management assumptions
you use.
Bob Fulks
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