The Geometry of Leverage Space Portfolios 343
Thisfshift is doubtless a problem to all traders. Oftentimes, if thefshift is
toward zero for many axes—that is, as the scenario spectrums weaken—it
can cause what would otherwise be a winning method on a constant unit
basis to be a losing program because the trader is beyond the peak of thef
curve (to the right of the peak) to an extent that he is in a losing position.
fshift exists in all markets and approaches. It frequently occurs to the
point at which many scenario spectrums get allocations in one period in
an optimal portfolio construction, then no allocations in the period imme-
diately following. This tells us that the performance, out of sample, tends
to greatly diminish. The reverse is also true. Markets that appear as poor
candidates in one period where an optimal portfolio is determined, then
come on strong in the period immediately following, since the scenarios do
not measure up.
When constructing scenarios and scenario sets, you should pay partic-
ular attention to this characteristic: Markets that have been performing well
will tend to underperform in the next period and vice versa. Bearing this in
mind when constructing your scenarios and scenario spectrums will help
you to develop more robust portfolios, and help alleviatefshift.
Tailoring a Trading Program through Reallocation
THROUGH REALLOCATION
Often, money managers may opt for the dynamicf, as opposed to the static,
even when the number of holding periods is less than that specified by Equa-
tion (10.05) simply because the dynamic provides a better implementation
of portfolio insurance.
In such cases, it is important that the money manager not reallocate
until Equation (10.05) is satisfied—that is, until enough holding periods
elapse that the dynamic can begin to outperform the static counterpart.
A real key to tailoring trading programs to fit the money manager’s goals
in these instances is by reallocating on the upside. That is, at some upside
point in active equity, you should reallocate to achieve a certain goal, yet
that point is beyond some minimum point in time (i.e., number of elapsed
holding periods).
Returning to Figure 10.1, Equation (10.05) gives usT, or where the
crossing of the staticfline by the dynamicfline occurs with respect to
the horizontal coordinate. That is the point, in terms of number of elapsed
holding periods, at which we obtain more benefit from trading the dynamic
frather than the staticf. However, once we knowTfrom Equation (10.05),
we can figure theY, or vertical, axis where the points cross as:
Y=FRAC∗Geometric MeanT−FRAC (10.09)