27 lines
2.0 KiB
Plaintext
27 lines
2.0 KiB
Plaintext
The Distribution of
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Stock Prices
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Much of the work that has been done in statistics and related areas regarding the
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stock market has made the assumption that stock prices are distributed normally, or
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more specifically, lognonnally. In actual practice, this is usually an incorrect assump
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tion. For the option strategist, this means that some of the things one might believe
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about certain option strategies having an advantage over certain other option strate
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gies might be incorrect. In this chapter, a number of facts concerning stock price dis
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tribution will be brought to light, including how it might affect the option strategist.
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MISCONCEPTIONS ABOUT VOLATILITY
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Statistics are used to estimate stock price movement (and futures and indices as well)
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in many areas of financial analysis. Many authors have written extensively about the
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use of probabilities to aid in choosing viable option strategies. Stock mutual fund
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managers often use volatility estimates to help them determine how risky their port
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folios are. The uses are myriad. Unfortunately, almost all of these applications are
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wrong! Perhaps wrong is too strong a word, but almost all estimates of stock price
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movement are overly conservative. This can be very dangerous if one is using such
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estimates for the purposes of, say, writing naked options or engaging in some other
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such strategy in which volatile stock price movement is undesirable.
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As a review for those not familiar with mathematical distributions, the lognor
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mal distribution is what's commonly used to describe stock prices because its shape
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is intuitively similar to the way stocks behave - they can't go below zero, they can rise
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to infinity, and most of the time they don't go much of anywhere. On top of that, the
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distribution's shape is based on the historical volatility of the underlying instrument.
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In a lognormal distribution (and normal distribution, too), stocks remain within 3
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standard deviations of their current price 99. 7 4% of the time. A standard deviation
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