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Alex Matulich on 23/05/08 02:26, wrote:
Adam Hardy wrote:
I don't know what Monte Carlo simulations are based on,
programmatically, or what they /can/ be based on,
It's pretty simple. A Monte Carlo simulation is merely poking
random inputs into a black box and getting outputs. Repeat over and
over. Then you have a collection of outputs on which you can do
stuff, such as gather statistics.
That's all there is to it.
In the case of position sizing, your input is your sequence of
individual profits and losses for each trade. You randomly scramble
this sequence, then apply the position sizing strategy to generate
a max profit and drawdown for that scrambled sequence. Do this
a thousand of times and you get a distribution of max profit and
drawdown.
Even better, instead of scrambling the sequence so that each trade
is used only once, use your list of trades as a bucket of samples,
and randomly sample from it to generate statistically similar
sequences that are longer than your original sequence.
OK, I understand now. I had assumed that you were generating sequences of random
price history. It is in that context that I would desire some leptokurtosis in
the resulting distribution - although I never investigated this approach. I
assume it would be best to simulate the shape of distribution that real price
histories show.
I see your approach gives you a range of outcomes from which you can then pick
and choose the result you like best - and so you find the fractional multiplier
which gives you your bet size.
Presumably the distribution of max profit and drawdown that you see when you use
optimal f is outside your comfort zone, and presumably when the losses are all
stacked up at the beginning of the sequence, your fixed fraction quickly becomes
less than the minimum unit you can trade on the exchange.
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