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training_data/relevant/text/0a0a0ebd89a067e0dc3876d08d74880d311891dc3582a4cbe401772494cb699e.txt

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+Chapter 38: The Distribution of Stock Prices 
+TABLE 38-5. 
+Index price movements. 
+Total Indices: 135 
+Upside Moves: 
+Downside Moves: 
+TABLE 38-6. 
+3cr 
+32 
+None 
+4cr 
+15 
+Scr 
+3 
+Index price movements, least volatile period. 
+Total Indices: 66 
+Upside Moves: 
+Downside Moves: 
+3cr 
+l 
+3 
+4cr 
+l 
+0 
+Scr 
+0 
+0 
+789 
+Dates: 10/22/99-12/7/99 
+>6cr 
+0 
+Total 
+50 
+Dates: 7/1/93-8/17/93 
+>6cr 
+0 
+0 
+Total 
+2 
+3 
+Total number of indices moving >=3cr: 5 (8% of the indices studied) 
+indices made oversized moves - probably a bias because of the strong Internet stock 
+market during that time period. The low-volatility period showed a more reasonable, 
+but still somewhat eye-opening, 8% making moves of greater than three standard 
+deviations. So, even selling index options isn't as safe as it's cracked up to be, when 
+they can make moves of this size, defying the "normal" probabilities. 
+Since that period in 1999 was rather volatile, and all on the upside, the same 
+study was conducted, once again using the least volatile period of July 1993. 
+In Table 38-6, the numbers are lower than they are for stocks, but still much 
+greater than one might expect according to the lognormal distribution. 
+These examples of stock price movement are interesting, but are not rigorous­
+ly complete enough to be able to substantiate the broad conclusion that stock prices 
+don't behave lognormally. Thus, a more complete study was conducted. The follow­
+ing section presents the results of this research. 
+THE DISTRIBUTION OF STOCK PRICES 
+The earlier examples pointed out that, at least in those specific instances, stock price 
+movements don't conform to the lognormal distribution, which is the distribution 
+used in many mathematical models that are intended to describe the behavior of 
+stock and option prices. This isn't new information to mathematicians; papers dating 
+back to the mid-1960s have pointed out that the lognormal distribution is flawed. 
+However, it isn't a terrible description of the way that stock prices behave, so many 
+applications have continued to use the lognormal distribution.