Chapter 38: The Distribution of Stock Prices 795 
Figure 38-3 perhaps shows even more starkly how the bull market has affected 
things over the last six-plus years. There are over 1,600 data points for IBM (i.e., daily 
readings) in Figure 38-3, yet the whole distribution is skewed to the right. It appar­
ently was able to move up quite easily throughout this time period. In fact, the worst 
move that occurred was one move of -2.5 standard deviations, while there were 
about ten moves of +4.0 standard deviations or more. 
For a longer-term look at how IBM behaves, consider the longer-term distribu­
tion of IBM prices, going back to March 1987, as shown in Figure 38-4. 
From Figure 38-4, it's clear that this longer-term distribution conforms more 
closely to the normal distribution in that it has a sort of symmetrical look, as opposed 
to Figure 38-3, which is clearly biased to the right (upside). 
These two graphs have implications for the big picture study shown in Figure 
38-1. The database used for this study had data for most stocks only going back to 
1993 (IBM is one of the exceptions); but if the broad study of all stocks were run 
using data all the way back to 1987, it is certain that the "actual" price distribution 
would be more evenly centered, as opposed to its justification to the right (upside). 
That's because there would be more bearish periods in the longer study (1987, 1989, 
and 1990 all had some rather nasty periods). Still, this doesn't detract from the basic 
premise that stocks can move farther than the normal distribution would indicate. 
WHAT THIS MEANS FOR OPTION TRADERS 
The most obvious thing that an option trader can learn from these distributions and 
studies is that buying options is probably a lot more feasible than conventional wisdom 
would have you believe. The old thinking that selling an option is "best" because it 
wastes away every day is false. In reality, when you have sold an option, you are exposed 
to adverse price movements and adverse movements in implied volatility all during the 
life of the option. The likelihood of those occurring is great, and they generally have 
more influence on the price of the aption in the short run than does time decay. 
You might ask, "But doesn't all the volatility in 1999 and 2000 just distort the 
figures, making the big moves more likely than they ever were, and possibly ever will 
be again?" The answer to that is a resounding, "Nol" The reason is that the current 
20-day historical volatility was used on each day of the study in order to determine 
how many standard deviations each stock moved. So, in 1999 and 2000, that histori­
cal volatility was a high number and it therefore means that the stock would have had 
to move a very long way to move four standard deviations. In 1993, however, when 
the market was in the doldrums, historical volatility was low, and so a much smaller