Characteristics of Optimalf 201
FIGURE 5.2 Pythagorean Theorem in money management
The exponent of the estimated TWR,T, will take care of itself. That is
to say that increasingTis not a problem, as we can increase the number
of markets we are following, trading more short-term types of systems, and
so on.
We can rewrite Equation [3.04] to appear as:
A^2 =G^2 +S^2This brings us to the point where we can envision exactly what the
relationships are. Notice that this equation is the familiar Pythagorean The-
orem: The hypotenuse of a right-angle triangle squared equals the sum of
the squares of its sides (Figure 5.2). But here, the hypotenuse isA, and we
want to maximize one of the legs,G.
In maximizingG, any increase inSwill require an increase inAto offset.
WhenSequals zero, thenAequalsG, thus conforming to the misconstrued
growth function TWR=(1+R)T.
So, in terms of their relative effect onG, we can state that an increase
inAis equal to a decrease of the same amount inS, and vice versa. Thus,
any amount by which the dispersion in trades is reduced (in terms of re-
ducing the standard deviation) is equivalent to an increase in the arithmetic
average HPR. This is true regardless of whether or not you are trading at
optimalf!
If a trader is trading on a fixed fractional basis, then he wants to maxi-
mizeG, not necessarilyA.In maximizingG, the trader should realize that
the standard deviation,S, affectsGin directly the same proportion as does
A, per the Pythagorean Theorem! Thus, when the trader reduces the stan-
dard deviation (S) of his trades, it is equivalent to an equal increase in the
arithmetic average HPR (A), and vice versa!