hi john:

I'm not clear on whether you want expected value of the max length or the
expected value
of the length. but, if you want the latter in closed form and you know , p,
the probability of sucess ( in your case , the probability of winning
trade), then the number of trials before you win ( so the length would be
the number of losses )  can be thought as having a geometric distribution.
this distribution has expected value of (1-p)/p. and no, I definitely had to
look that up because I didn't remember the formula.

I'm not sure how one would handle the expected value of the max length
analytically. maybe
simulation is the only way but you might be able to do it faster using the
analytical result above.


On Tue, May 3, 2011 at 8:05 PM, BBands <bbands@gmail.com> wrote:

> About 1,000 years ago I calculated the expected length of a losing
> streak by iterative simulation using rle
>
>    trades <- sample(c("W", "L"), 1000, replace = TRUE, prob =
> c("0.66", "0.33"))
>    trades.rle <- rle(trades)
>    tapply(trades.rle$lengths, trades.rle$values, max)
>
> There must be other, better ways today...
>
>    jab
> --
> John Bollinger, CFA, CMT
> www.BollingerBands.com
>
> If you advance far enough, you arrive at the beginning.
>
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