796 Part VI: Measuring and Trading Volatility 
move was needed to register a 4-standard deviation move. To see a specific example 
of how this works in actual practice, look carefully at the chart of IBM in Figure 38-
4, the one that encompasses the crash of '87. Don't you think it's a little strange that 
the chart doesn't show any moves of greater than minus 4.0 standard deviations? The 
reason is that IBM's historical volatility had already increased so much in the days 
preceding the crash day itself, that when IBM fell on the day of the crash, its move 
was less than minus 4.0 standard deviations. (Actually, its one-day move was greater 
than -4 standard deviations, but the 30-day move - which is what the graphs in Figure 
38-3 and 38-4 depict - was not.) 
STOCK PRICE DISTRIBUTION SUMMARY 
One can say with a great deal of certainty that stocks do not conform to the normal 
distribution. Actually, the normal distribution is a decent approximation of stock 
price movement rrwst of the time, but it's these "outlying" results that can hurt any­
one using it as a basis for a nonvolatility strategy. 
Scientists working on chaos theo:ry have been trying to get a better handle on 
this. An article in Scientific American magazine ("A Fractal Walk Down Wall Street," 
Februa:ry 1999 issue) met some criticism from followers of Elliot Wave theo:ry, in that 
they claim the article's author is purporting to have "invented" things that R. N. 
Elliott discovered years ago. I don't know about that, but I do know that the article 
addresses these same points in more detail. In the article, the author points out that 
chaos theo:ry was applied to the prediction of earthquakes. Essentially, it concluded 
that earthquakes can't be predicted. Is this therefore a useless analysis? No, says the 
author. It means that humans should concentrate on building stronger buildings that 
can withstand the earthquakes, for no one can predict when they may occur. Relating 
this to the option market, this means that one should concentrate on building strate­
gies that can withstand the chaotic movements that occasionally occur, since chaotic 
stock price behavior can't be predicted either. 
It is important that option traders, above all people, understand the risks of 
making too conservative an estimate of stock price movement. These risks are espe­
cially great for the writer of an option (and that includes covered writers and spread­
ers, who may be giving away too much upside by writing a call against long stock or 
long calls). By quantifying past stock price movements, as has been done in this chap­
ter, my aim is to convince you that "conventional" assumptions are not good enough 
for your analyses. This doesn't mean that it's okay to buy overpriced options just 
because stocks can make large moves with a greater frequency than most option