For the longest time, the normal distribution has been the statistical distribu-
tion most analysts used to calculate market returns, although it has long been evi-
dent that the market does not follow a normal distribution. This can be seen in
Figure 2.6, which shows the daily percentage returns for the S&P 500 index over
the period April 1982 to October 1999. As you can see, this curve is not entirely
symmetrical, and it has much fatter tails than the normal distribution curve in
Figure 2.4.
If a distribution has a relatively peaked and narrow body and fatter tails than
a normal distribution, it is said to be leptokurtic. If the opposite holds true, it is
said to be platykurtic. To calculate the kurtosis of a variable, you can use the kurt
function in Excel. In the case of the daily distributions of returns for the S&P 500
index, the kurtosis equals 56. A positive value means that the distribution is lep-
tokurtic, whereas a negative value means that it is platykurtic. When building a
trading system, we prefer the distribution of returns be platykurtic, so that we
make sure that the system does not stand or fall with any large outlier trades.
However, this is a double-edged sword: A positive value for the kurtosis (the
distribution is leptokurtic with a narrow body) also might indicate that we are
doing a good job in keeping most of our trades as similar as possible to the aver-26 PART 1 How to Evaluate a System
FIGURE 2.4
Normal distribution curve.Occurrences