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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 sizng, 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.
>but are you able to define the kurtosis of the distribution?
I suppose so, but I don't see the need. In distributions generated
by the Monte Carlo analysis, I pretty much just use standard
deviation as the measure of quality. If the distribution shape
isn't normal, it's often lognormal (or close enough to it) that
statistical variance can be calculated.
>I mean, a normal distribution would be less than ideal,
Why? I'm measuring distribution of max profits for thousands of
sequences, not the distribution of profits on individual trades.
>I'd definitely want something with fat tails.
No, not really. A distribution of sequence max profits or drawdowns
with fat tails would mean bigger uncertainty in the performance of
your strategy. What matters more to me is standard deviation. A
large standard deviation of profits and drawdowns indicates that the
future performance of my strategy is less certain than a strategy
showing low standard deviations.
--
,|___ Alex Matulich -- alex@xxxxxxxxxxxxxx
// +__> Director of Research and Development
// \ Unicorn Research Corporation -- http://unicorn.us.com
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