The Geometry of Leverage Space Portfolios 351
On the seventeenth play, we can see that the dynamicfgradient over-
takes the others, so we must now switch over to trading on a dynamicf
basis. Here is how. When we started, we decided that we were going to
trade a 20% active equity, in effect (because we decided to trade at one-fifth
the full optimalf). Since our starting stake was $200, then it means we
would have started out, going into play 1, with $40 active equity. We would
therefore have $160 inactive equity.
So, going into play 17, where we want to switch over to dynamic, we
subtract $160 from whatever is our equity. The difference we then divide
by $4, the optimalf$, and that is how many bets we make on play 17. We
proceed by doing this before each play, ad infinitum.
Therefore, let’s assume our stake stood at $292 after the sixteenth play.
We subtract $160 from this, leaving us with $132, which we then divide by
the optimalf$, which is $4, for a result of 33. We would thus make 33 bets
on the seventeenth play (i.e., bet $33).
If you prefer, you can also figure these continuous dominance break-
points as an upside percentage gain which must be made before switching
to the next level. This is the preferred way. Just as Equation (10.09) gives us
the vertical, orY, coordinate corresponding to Equation (10.05)’s horizon-
tal coordinate, we can determine the vertical coordinates corresponding to
Equations (10.14) through (10.16). Since you move from a constant contract
to staticfat that value ofTwhereby Equation (10.15) is greater than Equa-
tion (10.14), you can then plug thatTinto Equation (10.12) and subtract 1
from the answer. This is the percentage gain on your starting equity required
to switch from a constant contract to staticf.
Since you move to dynamicffrom staticfat that value ofTwhereby
Equation (10.16) is greater than Equation (10.15), you can then plug that
value forTinto Equation (10.13), subtract 1 from the answer, and that is the
percentage profit from your starting equity to move to trading on a dynamic
fbasis.
Important Points to the Left of the Peak in then+
IN THEn+1-DIMENSIONAL LANDSCAPE
We continue this discussion that is directed towards most money managers,
who will trade a dilutedfset (whether they know it or not), that is, they will
trade at less aggressive levels than optimal for the different scenario spec-
trums or market systems they are employing. We refer to this as being to the
left, a term which comes from the idea that, if we were looking at trading one
scenario spectrum, we would have one curve drawn out in two-dimensional
space, where being to the left of the peak corresponds to having less units
on a trade than is optimal. If we are trading two scenario spectrurms, we
have a topographical map in three-dimensional space, where such money