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