the defective units as quickly as possible, but also not letting the high-value units
stay on the line for too long.
In short, you’re trying hard to maximize your payoff by making all of the
units deviate as little as possible from each other or from the average unit (to keep
a low standard deviation). Obviously, you would like the assembly line to run as
fast as possible, but only after you have examined one unit can the next unit be
placed on the line. Thus, the longer the time spent examining a single unit, the
lower your payoff will be.
Along comes an obviously defective unit that is bound to lower your results.
Without wasting any time, you toss it in the garbage, freeing up the line for anoth-
er unit. The next unit looks pretty average, but to be sure, you examine it for a
while longer than you did the previous one before you take it off the line. In fact,
without knowing it, with this average unit, you spent an average amount of time.
But the third unit that comes along is much trickier. This one shows all the
right features for being a real money maker, and while you’re watching it, these
features grow even bigger, promising to make this unit at least three times as valu-
able as the average unit. What to do? Should you let it grow even bigger, or should
you free up the line for more units? But then, all of a sudden it breaks. You freeze
in panic, and more time passes before you come to your senses and throw it in the
garbage. In the end, the time you spent processing this too-good-to-be-true unit
could have been used processing three average units.
What happened here? By trying to increase your profits from an individual
unit, you put yourself in unfamiliar territory, which made you act in panic, thus
increasing the standard deviation of the outcome and lowering the number of units
produced. In the end, this resulted in less overall profits.
But wait a minute, you say. What about the big winners? Doesn’t the old
adage say that I should let my profits run? Yes, it does, but there is a price to pay
in doing so. The price is that you will lose track of what is average. The really big
winners are usually few and far between; the rest are just a bunch of lookalikes that
confuse you. By staying away from all of them, you are freeing both your time and
money to produce several average units, which in the end should prove both more
profitable and less risky. At the very least, you need to keep track of what is aver-
age and what is not.
This is where descriptive statistics and terms such as standard deviation,
kurtosis, and skewcome in. A system’s standard deviation of returns tells you how
much an individual trade is likely to deviate from the average trade, or rather, the
likelihood that it will stay within certain boundaries, as indicated by the standard
deviation interval.
For this to be true, we need to assume that all trades are normally distributed
around their mean and that the outcome of one trade is independent of the outcome
of the others. This isn’t necessarily always the case, but we have to assume it is,
because it will most likely cost us more to not do so, in the form of either largerCHAPTER 2 Calculating Profit 23