The Leverage Space Model 303
mathematically optimal answer with respect to leverage (including how I
progress my stake as I go on), would be .5 of .46 of the account. But the old
mean variance models do not tell me that. They are not attuned to the use of
leverage (with both of its meanings). The answers tell me nothing of where
Iaminthen+1 dimensional landscape. Also, there are important points
within then+1 dimensional landscape other than the peak. For instance,
as we will see in the next chapter, the points of inflection in the landscape
are also very important. The old E-V models tell us nothing about any of
this.
In fact, the old models simply tell us that allocating one-half of our
stake to each of these games will beoptimalin that you will get the greatest
return for a given level of variance, or the lowest variance for a given level
of return. How much you want to lever it is a matter of your utility—your
personal preference.
In reality, though, there is an optimal point of leverage, an optimal
place in then+1 dimensional landscape. There are also other important
points in this landscape. When you trade, you automatically reside some-
where in this landscape (again, just because you do not acknowledge it does
not mean it does not apply to you). The old models were oblivious to this.
This new framework addresses this problem and has the users aware of the
use/misuse of leverage within an optimal portfolio in a foremost sense. In
short, the new framework simply yields more and more useful information
than its predecessors.
Again, if a trader is utilizing two market systems simultaneously, then
where he resides on the three-dimensional landscape is everything. Where
he resides on it is every bit as important as his market systems, his timing,
or his trading ability.
Mathematical Optimization
Mathematical optimization is an exercise in finding a maximum or mini-
mum value of an objective function for a given parameter(s). The objective
function is, thus, something that can be solved only through an iterative
procedure.
For example, the process of finding the optimalffor a single market
system, or a single scenario spectrum, is an exercise in mathematical opti-
mization. Here, the mathematical optimization technique can be something
quite brutish like trying allfvalues from 0 to 1.0 by .01. The objective func-
tion can be one of the functions presented in Chapter 4 for finding the
geometric mean HPR for a given value offunder different conditions. The
parameter is that value forfbeing tried between 0 and 1.