Characteristics of Optimalf 193
geometric mean at thefvalue employed. The variability en route to that
goal is also a function of thefvalue employed.
Yet these considerations, the degree of the geometric mean and thef
employed, aresecondaryto the fact that you must have a positive math-
ematical expectation, although they are useful in comparing two systems
or techniques that have positive mathematical expectations and an equal
confidence of their working in the future.
TOO MUCH SENSITIVITY
Too Much Sensitivity to the Biggest Loss
A recurring criticism with the entire approach of optimalfis that it is too
dependent on the biggest losing trade. This seems to be rather disturbing
to many traders. They argue that the amount of contracts you put on today
should not be so much a function of a single bad trade in the past.
Numerous different algorithms have been worked up by people to al-
leviate this apparent oversensitivity to the largest loss. Many of these al-
gorithms work by adjusting the largest loss upward or downward to make
the largest loss be a function of the current volatility in the market. The
relationship seems to be a quadratic one. That is, the absolute value of the
largest loss seems to get bigger at a faster rate than the volatility. (Volatility
is usually defined by these practitioners as the average daily range of the last
few weeks, or average absolute value of the daily net change of the last few
weeks, or any of the other conventional measures of volatility.) However,
this is not a deterministic relationship. That is, just because the volatility is
X today does not mean that our largest losswillbe XY. It simply means that
it usually issomewhere nearXY.
If we could determine in advance what the largest possible loss would
be going into today, we could then have a much better handle on our money
management.^2 Here again is a case where we must consider the worst-case
(^2) This is where using options in a trading strategy is so useful. Either buying a put or
call outright in opposition to the underlying position to limit the loss to the strike
price of the options, or simply buying options outright in lieu of the underlying,
gives you a floor, an absolute maximum loss. Knowing this is extremely handy from a
money-management, particularly an optimalf, standpoint. Futher, if you know what
your maximum possible loss is in advance (e.g., a day trade), then you can always
determine what thefis in dollars perfectly for any trade by the relation dollars at
risk per unit/optimalf. For example, suppose a day trader knew his optimalfwas
.4. His stop today, on a one-unit basis, is going to be $900. He will therefore optimally
trade one unit for every $2,250 ($900/.4) in account equity.