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Rudolph and all:
Ed Winters' description of optimal f was right on the money (pun intended).
I would like to add to his comments, not because I'm pushing optimal f, but
because I think money management is such a critical component of a
trading/investment plan. Maybe if I reiterate some of Ed's points, a few
more people might be persuaded to investigate what is available and maybe
one or two of those will avoid suffering a catastrophic loss.
Rudolph, your first impression is a good one. Optimal f is a method to
calculate the optimal number of shares or futures contracts to trade based
on either historical results *or* a mathematical distribution of results
(ie. a mix of what has happened as well as what is expected to happen in the
future).
Optimal f is a fixed fractional method; that is, a certain proportion of
your equity is invested whether your equity increases or decreases. Some
other alternatives might be a constant number of contracts, a martingale or
anti-martingale system, or an experience-based system. The key, whatever
method you choose, is to be able to quantify your risks and potential
rewards as much as possible.
You asked, "What is ... the criterion to select an optimal re-investment
factor?" Optimal f looks at your average returns and your biggest loss --
or biggest possible loss within a selected number of standard deviations --
to find the number of shares or contracts that will yield the highest
geometric average return without wiping out your account when you suffer the
maximum loss. Specifically, all you need to prove is that your trading
system produces a positive mathematical expectation. How you exploit that
positive mathematical expectation (ie. with money management) will determine
whether you are successful or you blow out your account in 3 months time. A
good example is Ralph Vince's coin toss scenario. In a game where you bet a
fixed fraction of your stake to maximize your profit and where you have a
50% chance of winning $2 and a 50% chance of losing $1, it is possible to
lose your entire stake if you bet too aggressively (your bets are much
greater than the optimal bet). It is also possible to achieve a mediocre
profit (by betting less or slightly more than the optimal). Optimal f will
tell you that if you bet 25% of your stake each time in this case, you will
achieve the highest return possible - 955% profit in this
example after 20 coin tosses.
Here is a quote from "The Mathematics of Money Management" that brought all
this stuff home to me. "In other words, it doesn't matter how profitable
your trading system is on a 1 contract basis, so long as it is profitable,
even if marginally so. If you have a system that makes $10 per contract per
trade ..., you can use money management to make it far more profitable than
a system that shows a $1,000 average trade .... What matters, then, is not
how profitable your system has been, but rather how certain is it that the
system will show at least a marginal profit in the future. Therefore, the
most important preparation a trader can do is to make certain as possible
that he has a positive mathematical expectation in the future."
You also expressed concern about the use of historical data to compute
details for future trades. I agree with your concern. Unless your
historical data takes into account the rare, extremely large losses (and,
arguably, wins too), your optimal f calculation will only be a rough
approximation and the odds are that you will suffer a devastating loss,
particularly if you're in the futures markets. Ralph Vince describes
several other, more accurate (but far less practical, in my opinion) methods
for calculating optimal f based on a variety of returns distributions -
Normal distribution, skewed distributions, platykurtic and leptokurtic
distributions, and many others. You should recognize that historical data
is used just to approximate (and in some cases, a poor approximation of) the
actual distribution of returns.
This has rambled on a lot longer than I expected. My goal here, though, was
not to sell people on optimal f (because it is just one of several methods),
but rather on money management as a whole. It just took Ralph Vince's work
to make *me* realize that at best, I have been achieving mediocre returns
and at worst, playing a foolishly risky game.
Hope this helps.
----- Original Message -----
From: rudolf stricker <rst@xxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: July 3, 1999 04:02
Subject: Re: Formula for Optimal f needed
> On Thu, 1 Jul 1999 17:57:32 -0400, you wrote:
>
> >Spreadsheet for optimalf from Futures Mangazine attached.
>
> Ed, thank you very much for posting the Excel sheets on Optimal f
> calculation from Futures Magazine!
>
> Even if I have to look more into the details of the procedure to get
> the idea behind the sheets: Can you (or someone else) give some hints
> about the general outline of the Optimal f method?
>
> My first impression is:
> Based on a test set of "historical" data, a probability distribution
> for wins & losses is constructed, which reflects the capabilities of
> the trading system and the characteristics of the market under
> consideration. From this, the result for new investments is estimated,
> but how is this done? - What is (in simple words) the criterion to
> select an optimal re-investment factor?
>
> Some general remarks on the Optimal f method:
> Seemingly, it follows the approach, that there is no other information
> about risk than "historical" trades. Imo, this is not true in
> general, especially when it comes to well-known side effects e.g. from
> political events, etc.
> Additionally, rapid market changes cannot be condensed easily in
> "historical" data. So this "historical" approach has some general
> drawbacks, imo.
> Finally, the trading system (like mine) often gives a basic estimate
> for something like "risk" for every upcoming trade, and I would like
> to combine this "known risk" with the "statistical risk" (like used in
> the Optimal f method) for my money management. - Any pointer in this
> direction?
>
> mfg rudolf stricker
> | Disclaimer: The views of this user are strictly his own.
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