332 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 10.1 Percent growth per period for constant contract, static, and dy-
namicf
its static counterpart. At an initial active equity allocation of 100% (1.0),
the dynamic never overtakes the static fractionalf (rather, they grow at
the same rate). Also affecting the rate at which the dynamic fractionalf
overtakes its static counterpart is the geometric mean of the portfolio itself.
The higher the geometric mean, the sooner the dynamic will overtake its
static counterpart. At a geometric mean of 1.0, the dynamic never overtakes
its static counterpart.
The more time that elapses, the greater the difference between the
static fractionalfand the dynamic fractional fstrategy. Asymptotically,
the dynamic fractionalfstrategy has infinitely greater wealth than its static
counterpart.
One last important point about Figure 10.1. The constant contract line
crosses the other two lines before they cross over each other.
In the long run, you are better off to practice asset allocation with a
dynamic fractionalftechnique. That is, you determine an initial level—a
percentage—to allocate as active equity. The remainder is inactive equity.
The day-to-day equity changes are reflected in the active portion only. The
inactive dollar amount remains constant. Therefore, each day you subtract
the constant inactive dollar amount from your total account equity. This
difference is the active portion, and it is on this active portion that you will
figure your quantities to trade in, based on the optimalflevels.
Now, when the margin requirement is calculated for the positions, it
will not be exactly the same as your active equity. It can be more or less;
it doesn’t matter. Thus, unless your margin requirement is for 100% of the