The Geometry of Leverage Space Portfolios 363
In the real world of trading, you must insulate yourself from the undulations
in the landscape. Thus, drawdown minimization under the new framework
lends itself very well to implementing continuous dominance.
So we have now gone full circle, from discerning the landscape of lever-
age space and finding the growth optimal point on it to retreating away from
that point to approach the real-world primary constraint of drawdown min-
imization and capital preservation. By simply increasing the exponent, by
whatever means available to us, we achieve growth. We can possibly achieve
equivalent growth if we can get a high enoughT, a high enough exponent.
Since the exponent is the number of holding periods in a given span of time,
we want to get as many holding periods in a given span of time as possible.
This does not necessarily mean, however, to trade as many components as
possible. All correlations revert to one. Further, we must always assume
that worst-case scenarios will manifest simultaneously for all components
traded. We must consider that the compositef, the sum of thefvalues for
all components being simultaneously traded, is a drawdown that we will,
therefore, experience. This suggests that, in seeking to approach drawdown
optimality, yet still striving for equivalent growth as at the growth optimal
point, we trade as few components as possible, with as small anffor each
component as possible, while managing to get as many holding periods in
a given span of time as possible.
The growth optimal point is a dangerous place to be. However, if we hit
it just right, that is, if we are at the place where the peak will be, we can see
tremendous growth. Even so, we will endure severe drawdowns. However,
the leverage space framework allows us to formulate a plan, a place to be
on the map of leverage space, to achieve drawdown minimization. It further
allows us an alternate avenue to achieve growth, by increasingT, the expo-
nent, by whatever means necessary. This strategy is not so mathematically
obvious when viewed under the earlier frameworks.
This is but one means, and a very crude one at that, for mitigating
drawdowns in the Leverage Space Model. In Chapter 12, we will see how the
terrain of leverage space is “pock-marked,” by “holes,” where the probability
of a given drawdown is too high for an investor’s utility preference.
When viewed in the sense to be presented in Chapter 12, the drawdown
mitigation technique just mentioned, virtually insures the investor will not
be within a pock-marked-out area of the terrain. However, he pays a steep
price here for being way to the left of the peak of all curves in leverage
space. In Chapter 12, we will see that, although the 0,...0 edge point in
leverage space is never pock-marked out, we can determine other, far more
favorable areas in the terrain.