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Vitaly:
First, trading at one-half optimal f produces much less than one-half the
maximum profit, so it is not an easy comparison.
Diversification works, but not to the point of doubling profit. The
improved returns (or should I say reduced risks) diminish as you add more
stocks. The math is too complex for *me* to explain, but an optimal fixed
fraction "wager" with diversification of trading systems as well as stocks
is the way to go.
Regards.
----- Original Message -----
From: Vitaly Larichev <vitaly@xxxxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: July 11, 1999 09:22
Subject: Optimal f and diversification
> Hi everybody,
>
> I've been following the optimal f discussion with a great interest. Thanks
a lot to those ready to
> share the knowledge.
>
> Still, there is a thing I stumble over and over again regarding the
optimal f. I have few books on
> money/management, and those I could look through at a book store didn't
help either (though I might
> miss the answer).
>
> Let's take again the classical example of coin tossing. If the game has a
positive expectation,
> you'll profit, but the amount depends critically on the fraction of the
capital you are willing to
> risk on each trade. OK, fair enough. To be specific, let's assume my
system does, say, 30 trades a
> year, and with optimal f the profit is highest. If f is less than optimal,
assume it's two times
> less, then it would take, roughly speaking (I understand, there is not a
direct proportionality
> here), 60 trades or 2 years to achieve the same gain. Now, being a wise
guy <g>, I know a thing
> about diversification. So, I figure, instead of buying each time the same
stock (market), why not to
> buy two stocks with half money I would allocate otherwise. It would make f
two times less optimal
> for each stock, but if they are "uncorrelated" and, one more assumption to
make my case, have the
> same statistics with the respect to my trading system, it will look like
trading the same stock 60
> times a year with half f optimal that would deliver the same annual profit
as a single stock with 30
> trades and f optimal. But the risk of loosing money including drawdowns
size is much less here. Then
> one would be encouraged to go further and diversify even more where
payments per trade (commissions,
> slippage) may become a critical factor. So Kelly formula for finding f
optimal which applies to a
> single stock case, seems a bit too irrelevant to any practical
implications?
>
> Do I miss something here?
>
> Thanks.
>
> Cheers, Vitaly
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