334 THE HANDBOOK OF PORTFOLIO MATHEMATICS
At lower goals, the static fractional f strategy grows faster than its
corresponding dynamic fractionalfcounterpart. As time elapses, the dy-
namic overtakes the static until, eventually, the dynamic is infinitely further
ahead. Figure 10.1 graphically displays this relationship between the static
and dynamic fractionalf’s.
If you reallocate too frequently, you are only shooting yourself in the
foot, as the technique would be inferior to its static fractionalfcounterpart.
Therefore, since you are better off, in the long run, to use the dynamic frac-
tionalfapproach to asset allocation, you are also better off to reallocate
funds between the active and inactive subaccounts as infrequently as pos-
sible. Ideally, you will only make this division between active and inactive
equity once, at the outset of the program.
It is not beneficial to reallocate too frequently. Ideally, you will never
reallocate. Ideally, you will let the fraction of optimalfyou are using keep
approaching 1 as your account equity grows. In reality, however, you most
likely will reallocate at some point in time. Hopefully, you will not reallocate
so frequently that it becomes a problem.
Reallocation seems to do just the opposite of what we want to do,
in that reallocation trims back after a run up in equity, or adds more eq-
uity to the active portion after a period in which the equity has been run
down.
Reallocation is a compromise. It is a compromise between the theoret-
ical ideal and the real-life implementation. The techniques discussed allow
us to make the most of this compromise. Ideally, you would never reallo-
cate. Your humble little $10,000 account, when it grew to $10 million, would
never go through reallocation. Ideally, you would sit through the drawdown
which took your account down to $50,000 from the $10 million mark be-
fore it shot up to $20 million. Ideally, if your active equity were depleted
down to one dollar, you would still be able to trade a fractional contract (a
microcontract?). In an ideal world, all of these things would be possible.
In real life, you are going to reallocate at some point on the upside or the
downside. Given that you are going to do this, you might as well do it in a
systematic, beneficial way.
In reallocating—compromising—youresetthings back to a state where
you would be if you were starting the program all over again, only at a dif-
ferent equity level. Then, you let the outcome of the trading dictate where
the fraction offfloats to by using a dynamic fractionalfin between re-
allocations. Things can get levered up awfully fast, even when starting out
with an active equity allocation of only 5%. Remember, you are using the
full optimalfon this 5%, and if your program does modestly well, you’ll be
trading in substantial quantities relative to the total equity in the account in
short order.