324 THE HANDBOOK OF PORTFOLIO MATHEMATICS
all positions can be assigned anf value as detailed in earlier chapters.
Often, people practice asset allocation is by splitting their equity into two
subaccounts, an active subaccount and an inactive subaccount. These are
not two separate accounts; rather, in theory, they are a way of splitting a
single account.
The technique works as follows. First, you must decide upon an initial
fractional level. Let’s suppose that, initially, you want to emulate an account
at the halfflevel. Therefore, your initial fractional level is .5 (the initial frac-
tional level must be greater than 0 and less than 1). This means you will split
your account, with .5 of the equity in your account going into the inactive
subaccount and .5 going into the active subaccount. Let’s assume we are
starting out with a $100,000 account. Therefore, $50,000 is initially in the
inactive subaccount and $50,000 is in the active subaccount. It is the equity
in the active subaccount that you use to determine how many units to trade.
These subaccounts are not real; they are a hypothetical construct you are
creating in order to manage your money more effectively. You always use the
full optimalfs with this technique. Any equity changes are reflected in the
active portion of the account. Therefore, each day, you must look at the ac-
count’s total equity (closed equity plus open equity, marking open positions
to the market) and subtract the inactive amount (which will remain con-
stant from day to day). The difference is your active equity, and it is on this
difference that you will calculate how many units to trade at the fullflevels.
Let’s suppose that the optimalffor market system A is to trade one
contract for every $2,500 in account equity. You come into the first day with
$50,000 in active equity and, therefore, you will look to trade 20 units. If
you were using the straight halffstrategy, you would end up with the same
number of units on day one. At halff, you would trade one contract for every
$5,000 in account equity ($2,500/.5) and you would use the full $100,000
account equity to figure how many units to trade. Therefore, under the half
fstrategy, you would trade 20 units on this day as well.
However, as soon as the equity in the account changes, the number of
units you will trade changes as well. Let’s assume that you make $5,000 this
next day, thus pushing the total equity in the account up to $105,000. Under
the halffstrategy, you will now be trading 21 units. However, under the
split equity technique, you must subtract the now-constant inactive amount
of $50,000 from your total equity of $105,000. This leaves an active equity
portion of $55,000, from which you will figure your contract size at the
optimalflevel of one contract for every $2,500 in equity. Therefore, under
the split equity technique, you will now look to trade 22 units.
The procedure works the same on the downside of the equity curve as
well, with the split equity technique peeling off units at a faster rate than
the fractionalfstrategy. Suppose we lost $5,000 on the first day of trading,
putting the total account equity at $95,000. Under the fractionalfstrategy,