33 lines
2.1 KiB
Plaintext
33 lines
2.1 KiB
Plaintext
Chapter 28: Mathematical Applications 471
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Thus, once the low starting point is chosen and the probability of being below that
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price is determined, one can compute the probability of being at prices that are suc
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cessively higher merely by iterating with the preceding formula. In reality, one is
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using this information to integrate the distribution curve. Any method of approxi
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mating the integral that is used in basic calculus, such as the Trapezoidal Rule or
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Simpson's Rule, would be applicable here for more accurate results, if they are
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desired.
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A partial example of an expected return calculation follows.
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Example: XYZ is currently at 33 and has an annual volatility of 25%. The previous
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bull spread is being established- buy the February 30 and sell the February 35 for a
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2-point debit - and these are 6-month options. Table 28-7 gives the necessary com
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ponents for computing the expected return. Column (A), the probability of being
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below price q, is computed according to the previously given formula, where p = 33
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and vt = .177 (t = .25-V ½). The first stock price that needs to be looked at is 30, since
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all results for the bull spread are equal below that price - a 100% loss on the spread.
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The calculations would be performed for each eighth (or tenth) of a point up through
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a price of 35. The expected return is compute<l by multiplying the two right-hand
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columns, (B) and (C), and summing the results. Note that column (B) is determined
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by subtracting successive numbers in column (A). It would not be particularly
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enlightening to carry this example to completion, since the rest of the computations
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are similar and there is a large number of them.
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In theory, if one had the data and the computer power, he could evaluate a wide
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range of strategies every day and come up with the best positions on an expected
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return basis. He would probably get a few option buys (puts or calls), some bull
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TABLE 28-7.
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Calculation of expected returns.
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Price at Expiration (A) (B) (()
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(q) P (below q) P (of being at q) Profit on Spread
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30 .295 .295 -$200
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30 1/s .301 .006 - 187.50
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30 1/4 .308 .007 - 175
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303/s .316 .008 - 162.50 |