How much is the "grail" worth? - page 12
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Now, this is indeed a non-trivial problem:
The trading results of the system with n trades are given. The maximum drawdown is dd %. What is the probability that with additional N trades the maximum drawdown in the new area will not exceed DD %?
Sequence of trades of the system is Bernoulli scheme with known probability of success p and known ratio of average profitable trade to average losing trade alpha.
if Bernoulli, then the larger the series of trades, the closer to NR. And then the drawdown dd% extra condition is one realization of SP, depending on the number of trades on which this drawdown is obtained. In general, when you have calculated variance and mo in one trade, it is simple to calculate that at the moment of the N-th trade the drawdown DD is exceeded. A bit complicated by the fact that we need not at the moment of the N-th trade, but at the moment of any of 1...N. But still it is quite simple - product of probabilities that we will not exceed drawdown after x=1...N trades and subtract the obtained from 1
DD makes sense as a manifestation of dependence in a series of trades. More precisely even the dependence of losing trades. In the Bernoulli scheme (trade independence) the drawdown is a function of the number of trades, Mo and dispersion (or probability of profitable/loss-making trades) and does not depend on the previous drawdown of any series.