The Geometry of Leverage Space Portfolios 347
FIGURE 10.4 Growth rate as a percentage of stake
constant contract basis, with the number of units being determined as that
number which would be traded initially if we were trading a fractionalf.
Next, the static f gradient dominates, at which point in time (or on
the upside in equity) we switch to trading the staticfFinally, the dynamic
gradient dominates, at which point we switch to trading on a dynamic f
basis, Notice that by always trading that technique which has the highest
gradient at that moment means you will be on the highest of the three lines
in Figure 10.3.
The growth function,Y, for the constant contract technique is now given
as:
∗
Y= 1 +(AHPR−1)∗FRAC∗T (10.11)
∗Just as Equation (10.05) gave us that point where the dynamic overtakes the static
with respect to the horizontal axisT, we can determine from Equations (10.11) and
(10.12) where the static overtakes a constant contract as that value ofTwhere
Equation (10.12) equals Equation (10.11).
1 +(AHPR−1)∗FRAC∗T=>FGHPRT
Likewise, this can be expressed in terms of theYcoordinate, to tell us at what
percentage of profit, on the total equity in the account, we should switch from a
constant contract to staticftrading:
Y=FGHPRT− 1
The value forTused in the preceding equation is derived from the one above it.