the value of the average trade, or so that the ratio between the average trade and the
standard deviation increases and becomes as large as possible. This is called the
risk-adjusted return. The system with the highest risk-adjusted return is the safest
one to trade, given its estimated and desired average profit per trade.
For example, a system with an average profit of $500 and a standard devia-
tion of $700 has the same risk-adjusted return as a system with an average profit
of $5,000 and a standard deviation of $7,000 (500 / 700 5,000 / 7,000 0.71).
Consequently, both give you the same bang for your buck, and neither can be con-
sidered any better than the other, with only this information at hand. A system with
an average profit of $300 and a standard deviation of $400, on the other hand, has
a risk-adjusted return of 0.75 (300 / 400), which is higher than either of the other
systems, and therefore makes it the safest one to trade. To increase the profits from
a system with a low average profit but a high risk-adjusted return, simply utilize
it on as many markets as possible to increase the number of trades and, in the end,
the net profit.DISTRIBUTION OF TRADES
So far, when we have used several of our statistical measurements, such as the aver-
age profit and the standard deviation of the outcomes, we have assumed that all our
variables, such as the percentage profit per trade, have been normally distributed
and statistically independent, continuous random variables. The beauty of these
assumptions is that the familiar bell-shaped curve of the normal distribution is easy
to understand, and it lends itself to approximate other close to normally distributed
variables as well. Figure 2.4 shows what such a distribution can look like.
Note, however, that for a variable to be random, it does not have to be nor-
mally distributed, as Figure 2.5 shows. This chart is simply created with the help of
the random function in Excel. Figure 2.4, in turn, is created by taking a 10-period
average of the random variable in Figure 2.5. Many times, a random variable that
is an average of another random variable is distributed approximately as a normal
random variable, regardless of the distribution of the original variable. This is also
called the central limit theorem. Therefore, it is likely that the average profit per
trade from several individual markets will be normally distributed, no matter the
distribution of trades within any of the individual markets, or that the profit over
several similar time periods (say a month) will be normally distributed, although the
distribution of the trades might not.
However, a normal distribution can very well be both higher and narrower,
or lower and fatter, than that in Figure 2.4. The main thing is that it has a single
mode (one value that appears more frequently than others) and is symmetrical,
with equally as many observations on both sides of the mean. For a normally dis-
tributed variable the mean, median(the middle value, if all values are sorted from
the smallest to the largest), and modeshould be the same.CHAPTER 2 Calculating Profit 25