Ralph Vince - Portfolio Mathematics

(Brent) #1

Optimalf 147


(or lose) 50% before a quantity adjustment is necessary. Contrast this to a
$500,000 account, where there would be a contract adjustment for every 1%
change in equity. Clearly, the larger account can take advantage of the bene-
fits provided by optimalfbetter than a smaller account can. Theoretically,
optimalfassumes you can trade in infinitely divisible quantities, which is
not the case in real life, where the smallest quantity you can trade in is a
single contract. In the asymptotic sense this does not matter. In the real-life
integer-bet scenario, a good case could be presented for trading a market
system that requires as small a percentage of the account equity as possi-
ble, especially for smaller accounts. But there is a trade-off here as well.
Since we are striving to trade in markets that would require us to trade in
greater multiples, we will be paying greater commissions, execution costs,
and slippage. Bear in mind that the amount required per contract in real
life is the greater of the initial margin requirement or the dollar amount per
contract dictated by the optimalf.
As the charts bear out, you pay a substantial penalty for deviating from
the optimal fixed dollar fraction.Being at the right value forfis more
important than how good your trading system is(provided of course that
the system is profitable on a single-contract basis)! Therefore, the finer you
can cut it (i.e., the more frequently you adjust the size of the positions you
are trading, so as to align yourself with what the optimalfdictates), the
better off you are. Most accounts, therefore, would be better off trading
the smaller markets. Corn may not seem like a very exciting market to you
compared to the S&Ps. Yet, for most people, the corn market can get awfully
exciting if they have a few hundred contracts on.
Throughout the text, we refigure the amount of contracts you should
have on for the next trade based on the dictates of the optimal f for a
given market system. However, the finer you can cut it, the better. If you
refigure how many contracts you should have on every day as opposed to
simply every week, you will be that much better off. If you refigure how many
contracts you should have on every hour as opposed to every day, you will be
even better off. However, there is the old trade-off of commissions, slippage,
and fees, not to mention the cost of mistakes, which will be more likely the
more frequently you realign yourself with the dictates of the optimalf. Bear
in mind that realigning yourself on every trade is not the only way to do it,
and the finer (more frequently) you can cut it—the more often you realign
yourself with the dictates of the optimalf—the more the benefits of the
optimalfwill work for you. Ideally, you will realign yourself with optimal
fon as close to a continuous basis as possible with respect to the trade-offs
of commissions, fees, slippage, and the costs of human error.
It is doubtful whether anyone in the history of the markets has been
able to religiously stick to trading on a constant contract basis. If someone
quadrupled their money, would they still stick to trading in the same exact

Free download pdf