38 lines
2.8 KiB
Plaintext
38 lines
2.8 KiB
Plaintext
Chapter 38: The Distribution of Stock Prices 809
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a deeply out-of-the-money put credit spread usually destroys most or all of its prof
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itability, so an accurate initial assessment of the probabilities of having to make such
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an adjustment is important.
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Option buyers, too, would benefit from the use of a more accurate probability
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estimate. This is especially true for neutral strategies, such as straddle or strangle
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buying, when the trader is interested in the chances of the stock being able to move
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far enough to hit one or the other of the straddle's break-even points at some time
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during the life of the straddle.
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The Monte Carlo probability calculation can be expanded to include other sorts
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of distributions. In the world of statistics, there are many distributions that define ran
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dom patterns. The lognormal distribution is but one of them (although it is the one
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that most closely follows stock prices movements in general). Also, there is a school of
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thought that says that each stock's individual price distribution patterns should be ana
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lyzed when looking at strategies on that stock, as opposed to using a general stock
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price distribution accumulated over the entire market. There is much debate about
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that, because an individual stock's trading pattern can change abruptly just consider
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any of the Internet stocks in the late 1990s and early 2000s. Thus, a probability esti
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mate based on a single stock's behavior, even if that behavior extends back several
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years, might be too unreliable a statistic upon which to base a probability estimate.
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In summary, then, one should use a probability calculator before taking an
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option position, even an outright option buy. Perhaps straight stock traders should
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use a probability calcutor as well. In doing so, though, one should be aware of the
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limitations of the estimate: It is heavily biased by the volatility estimate that is input
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and by the assumption of what distribution the underlying instrument will adhere to
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during the life of the position. While neither of those limitations can be overcome
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completely, one can mitigate the problems by using a conservative volatility estimate.
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Also, he can look at the results of the probability calculation under several distribu
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tions (perhaps lognormal, fat tail, and the distribution using only the past price
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behavior of the underlying instrument in question) and see how they differ. In that
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case, he would at least have a feeling for what could happen during the life of the
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option position.
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EXPECTED RETURN
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The concept of expected return was described in the chapter on mathematical appli
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cations. In short, expected return is a position's expected profit divided by its invest
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ment ( or expected investment if the investment varies with stock price, as in a naked
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option position or a futures position). The crucial component, though, is expected
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profit. |