36 lines
2.6 KiB
Plaintext
36 lines
2.6 KiB
Plaintext
Chapter 28: Mathematical Applications 487
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Finally, the computer can compute the expected return of a position already in
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place. This would give a more dynamic picture of the position, and this expected
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return is usually for a relatively short time period. That time period might be 30 days,
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or the time remaining until expiration, whichever is less. The expected return is cal
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culated in much the same manner as the expected return computation described ear
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lier in this chapter. First, one uses the stock's volatility to construct a range of prices
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over which to examine the position. Second, one uses the Black-Scholes model to
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calculate the values of the various options in the position at that future time and at
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the various stock prices. Some of the results should be displayed in table form by the
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computer program. The expected profit is computed, as described earlier, by sum
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ming the multiples of the probabilities of the stock being at each price by the result
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of the position at that price. The expected return is then computed by dividing the
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expected profit by the expected investment. Since margin computations can require
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involved computer programs, it is sufficient to omit this last step and merely observe
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the expected profit. The following example shows how a sample position might look
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as the computer displays the position itself, the ESP, the profit at expiration, and the
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expected profit in 30 days. A complex position is assumed, in order that the value of
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these analyses can be demonstrated.
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Example: The following position exists when XYZ is at 31 ¾. It is essentially a back
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spread combined with a reverse ratio write. It resembles a long straddle in that there
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is increased profit potential in either direction if the stock moves far enough by expi
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ration. Initially, the computer should display the position and the ESP.
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Position Delta ESP
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Short 4,500 XYZ 1.00 Short 4,500 shares
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Short 100 XYZ April 25 calls 0.89 Short 8, 900 shares
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Long 50 XYZ April 30 calls 0.76 Long 3,800 shares
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Long 139 XYZ July 30 calls 0.74 Long 10,286 shares
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Total ESP Long 686 shares
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Total money in position: $163,500 credit
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The advantage of using the ESP is that this fairly complex position is reduced to a sin
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gle number. The entire position is equivalent to being long 686 shares of the com
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mon stock. Essentially, this is close to delta-neutral for such a large position. The next
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item that the computer should display is the total credit or debit in the position to
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date. With this information, an expiration picture can be drawn if it is applicable. In
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this position, since there is a mixture of April and July options, a strict expiration pie- |