44 lines
2.2 KiB
Plaintext
44 lines
2.2 KiB
Plaintext
Chapter 28: Mathematical Applications
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TABLE 28-5.
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Calculation of expected returns.
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Price of XYZ in 6 Months
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Below 30
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31
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32
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33
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34
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Above 35
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467
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Chance of XYZ Being at That Price ·
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20%
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10%
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10%
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10%
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10%
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40%
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100%
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Since the percentages total 100%, all the outcomes have theoretically been
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allowed for. Now suppose a February 30 call is trading at 4 and a February 35 call is
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trading at 2 points. A bull spread could be established by buying the February 30 and
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selling the February 35. This position would cost 2 points - that is, it is a 2-point
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debit. The spreader could make 3 points if XYZ were above 35 at expiration for a
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return of 150%, or he could lose 100% if XYZ were below 30 at expiration. The
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expected return for this spread can be computed by multiplying the outcome at expi
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ration for each price by the probability of being at that price, and then summing the
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results. For example, if XYZ is below 30 at expiration, the spreader loses $200. It was
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assumed that there is a 20% chance of XYZ being below 30 at expiration, so the
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expected loss is 20% times $200, or $40. Table 28-6 shows the computation of the
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expected results at all the prices. The total expected profit is $100. This means that
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the expected return (profit divided by investment) is 50% ($100/$200). This appears
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to be an attractive spread, because the spreader could "expect" to make 50% of his
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money, less commissions.
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What has really been calculated in this example is merely the return that one
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would expect to make in the long run if he invested in the same position many times
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throughout history. Saying that a particular position has an expected return of 8 or
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9% is no different from saying that common stocks return 8 or 9% in the long run.
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Of course, in bull markets stock would do much better, and in bear markets much
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worse. In a similar manner, this example bull spread with an expected return of 50%
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may do as well as the maximum profit or as poorly as losing 100% in any one case. It
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is the total return on many cases that has the expected return of 50%. Mathematical
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theory holds that, if one constantly invests in positions with positive expected returns,
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he should have a better chance of making rrwney. |