346 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 10.3 Points where one method overtakes another can be viewed with
respect to time or return
run sense, but ensures that it will be at the highest equity at any
point in time, however near or far into the future that is! No longer
must someone adhering to optimal f (or, in a broader sense, this new
framework) reconcile themselves with the notion that it will be domi-
nant in the long run. Rather, the techniques about to be illustrated seek
dominance at all points in time!
Everyone is at an fvalue whether they acknowledge it or not. Since
nearly everyone is diluting what their optimalfvalues are—either intention-
ally or unintentionally through ignorance—these techniques always maxi-
mize the profitability of an account in cases of dilutedfvalues, not just, as
has always been the case with geometric mean maximization, in the very
long run.
Again, we must turn our attention to growth functions and rates. Look
at Figure 10.3 where growth (the growth functions) is represented as a
percentage of our starting stake. Now consider Figure 10.4, which shows
the growth rate as a percentage of our stake.
Again, these charts show a 20% initial active equity, traded on both
a static and a dynamic basis. Since they both start out trading the same
number of units, that very same number of units is shown being traded
straight through as a constant contract. The geometric mean HPR (at fullf)
used in this chart was 1.01933; therefore, the geometric mean at the .2 static
fractionalfwas 1.005, and the arithmetic average HPR at fullfwas 1.0265.
Notice that by always trading that technique which has the highest
gradient at the moment, we ensure the probability of the account being
at its greatest equity at any point in time. Thus, we start out trading on a