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Vitaly:
It's touched on in Chapter 1 of "The Mathematics of Money Management", and
delved into thoroughly in Chapter 6 (the one I call the "Huh?" chapter).
Regards.
----- Original Message -----
From: Vitaly Larichev <vitaly@xxxxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: July 13, 1999 05:40
Subject: Re: Optimal f and diversification
> Glen,
>
> For the theory advanced so far, I suspected the diversification issue
> should be tackled anyway, but couldn't find a relevant reference. Could
> you, please, guide me?
>
> Thanks for the response.
>
> Cheers, Vitaly
>
>
> Glen Wallace wrote:
>
> > 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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