The Geometry of Leverage Space Portfolios 333
equity in the account, you will have some unused cash in the account on any
given holding period. Thus, you are almost always inadvertently allocating
something to cash (or cash equivalents). So you can see that there isn’t any
need for a scenario spectrum for cash or cash equivalents—they already
get their proper allocation when you do the active and inactive equity split.
Reallocation
Notice in Figure 10.1 that, trading at a dynamic fractionalf, eventually the
active portion of your equity will dwarf the inactive portion, and you will be
faced with a portfolio that is far too aggressive for your blood—the same
situation you faced in the beginning when you looked at trading the portfolio
at the full optimalfamount. Thus, at some point in time in the future, you
will want toreallocateback to some level of initial active equity.
For instance, you start out at a 10% initial active equity on a $100,000
account. You, therefore, have $10,000 active equity—equity that you are
trading full out at the optimalflevel. Each day, you will subtract $90,000
from the equity on the account. The difference is the active equity, and it is
on the active equity that you trade at the full optimalflevels.
Now, assume that this account got up to $1 million equity. Thus, sub-
tracting the constant dollar inactive amount of $90,000 leaves you at an
active equity of $910,000, which means you are now at 91% active equity.
Thus, you face those gigantic drawdowns that you sought to avoid initially,
when you dilutedfand started trading at a 10% initial active equity.
Consider the case of reallocating after every trade or every day. Such
is the case with static fractionalftrading. Recall again Equation (10.08a),
the time required to reach a specific goal.
Let’s return to our system that we are trading with a .2 active portion
and a geometric mean of 1.01933. We will compare this to trading at the
static fractional .2f, where the resultant geometric mean is 1.005. Now, if
we are starting out with a $100,000 account, and we want to reallocate at
$110,000 total equity, the number of days (since our geometric means here
are on a per-day basis) required by the static fractional .2fis:
ln(1.1)
ln(1.005)= 19. 10956
This compares to using $20,000 of the $100,000 total equity at the full f
amount, and trying to get the total account up to $110,000. This would
represent a goal of 1.5 times the $20,000:
ln(1.5)
ln(1.01933)