298 THE HANDBOOK OF PORTFOLIO MATHEMATICS
So, we see thatleverageis a term that refers to either the degree to which
we borrow money to take a position in an asset, or thescheduleupon which
we take further positions in assets (whether we borrow to do this or not).
That said, since the focus of the new framework is onleverage,wecan
easily see that it applies to speculative vehicles in the sense that leverage
refers to the level of borrowing to take a position in a (speculative) asset.
However, the new framework, in focusing on leverage, applies to all assets,
including the most conservative, in the sense that leverage also refers to the
progression, the schedule upon which we take (or remove) further positions
in an asset. Ultimately, leverage in both senses is every bit as important as
market timing. That is, the progression of asset accumulation and removal
in even a very conservative bond fund is every bit as important as the bond
market timing or the bond selection process.
Thus, the entire notion ofoptimal fnot only applies to futures and
option traders as well, but to any asset allocation scheme, and not just
allocating among investment vehicles.
The trading world is vastly different today than just a few decades ago as
a result of the proliferation of derivatives trading. Most frequently, a major
characteristic with many derivatives is the leverage they bring to bear on an
account. The old framework, the old two-dimensional E-V framework, was
ill-equipped to handle problems of this sort. The modern environmentde-
mandsa new asset allocation framework focused on the effects of leverage.
The framework presented herein addresses exactly this.
This focus on leverage, more than any other explanation, is the main
reason why the new framework is superior to its predecessors. Like the
old framework, the new framework tells us optimal relative allocations
among assets. But the new framework does far more. The new framework is
dynamic—it tells us the immense consequences and payoffs of our schedule
of taking (and removing) assets through time, giving us aframework, a map,
of what consequences and rewards we can expect by following such-and-
such a schedule. Certain points on the map may be more appealing than
others to different individuals with different needs and desires. What may
be optimal to one person may not be optimal to another. Yet thismap
allows us to see what we get and give up by progressing according to a
certain schedule—something the earlier frameworks did not. This feature,
this map of leverage space (and remember, leverage has two meanings here),
distinguishes the new framework from its predecessors in many ways, and
it alone makes the new framework superior.
Lastly, the new framework is superior to the old in that the user of the
new framework can more readily see the consequences of his or her actions.
Under the old framework, “So what if I have a little more V for a given E?”
Under the new framework, you can see exactly what altitude that puts you at
on the landscape, that is, exactly what multiple you make on your starting