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+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