The Geometry of Leverage Space Portfolios 361
FIGURE 10.11 Drawdown optimality is approached at a different point on the
landscape than the growth optimal point
However, as was mentioned earlier in this text, in the real world of
trading, the markets do not conform so neatly to the theoretical ideal. The
problem is that, unlike the two-to-one coin-toss games shown, the distri-
bution of returns changes through time as market conditions change. The
landscape is polymorphic, moving around as market conditions change. The
closer you are to where the peak is, the more dramatic the negative effects
will be on you when it moves, simply because the landscape is the steepest
in the areas nearest the peak. If we were to draw a landscape map, such
as the one in Figure 10.11, but only incorporating data over a period when
both systems were losing, the landscape (the altitude or TWR) would be at
1.0 at thefcoordinates 0,0, and then it would slide off, parabolically, from
there.
We approach drawdown optimality by hunkering down in thosefvalues
near zero for all components. In Figure 10.11 we would want to be tucked
down in the upper-left corner, near zero for allfvalues. The reason for this
is that, as the landscape undulates, as the peak moves around, the negative
effects on those in that corner are very minimal. In other words, as market
conditionschange, the effect on a trader down in this corner is minimized.
The seeming problem, then, is that growth is sacrificed and this sacrifice
in growth occurs with an exponential difference. However, the solution to