Ralph Vince - Portfolio Mathematics

176 THE HANDBOOK OF PORTFOLIO MATHEMATICS

trade. Although we cannot expect the worst-case drawdown in the future
not to exceed the worst-case drawdown historically, it is rather unlikely
that we will start trading right at the beginning of a new historic drawdown.
A trader utilizing this idea will then subtract the amount in Equation
(5.01) from his or her equity each day. With the remainder, he or she will
then divide by (Biggest Loss/−f). The answer obtained will be rounded
down to the integer, and 1 will be added. The result is how many contracts
to trade.
An example may help clarify. Suppose we have a system where the op-
timalfis .4, the biggest historical loss is−$3,000, the maximum drawdown
was−$6,000, and the margin is $2,500. Employing Equation (5.01) then:

A=MAX{(−$3, 000/−.4), ($2, 500+ABS(−$6, 000))}

=MAX{($7, 500), ($2, 500+$6, 000)}

=MAX{$7, 500, $8, 500)}

=$8, 500

We would thus allocate $8,500 for the first contract. Now suppose we
are dealing with $22,500 in account equity. We therefore subtract this first
contract allocation from the equity:

$22, 500−$8, 500=$14, 000

We then divide this amount by the optimalfin dollars:

$14, 000/$7, 500= 1. 867

Then we take this result down to the integer:

INT(1.867)= 1

and add 1 to the result (the one contract represented by the $8,500 we have
subtracted from our equity):

1 + 1 = 2

We therefore would trade two contracts. If we were just trading at the
optimalflevel of one contract for every $7,500 in account equity, we would
have traded three contracts ($22,500/$7,500). As you can see, this technique
can be utilized no matter how large an account’s equity is (yet the larger the
equity, the closer the two answers will be). Further, the larger the equity,
the less likely it is that we will eventually experience a drawdown that will
have us eventually trading only one contract. For smaller accounts, or for
accounts just starting out, this is a good idea to employ.