28 lines
1.7 KiB
Plaintext
28 lines
1.7 KiB
Plaintext
What Susie will want to know is why she made $800. Why not more?
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Why not less, for that matter? When trading delta neutral, especially with
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more complex trades involving multiple legs, a manual computation of each
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leg of the spread can be tedious. And to be sure, just looking at the profit or
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loss on each leg doesn’t provide an explanation.
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Susie can see where her profits or losses came from by considering the
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profit or loss for each influence contributing to the option’s value. Exhibit
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12.6 shows the breakdown.
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EXHIBIT 12.6 Profit breakdown by greek.
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Delta
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Susie started out long 0.20 deltas. A $2 rise in the stock price yielded a $40
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profit attributable to that initial delta.
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Gamma
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As the stock rose, the negative delta of the position increased as a result of
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negative gamma. The delta of the stock remained the same, but the negative
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delta of the 50 call grew by the amount of the gamma. Deriving an exact
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P&(L) attributable to gamma is difficult because gamma is a dynamic
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metric: as the stock price changes, so can the gamma. This calculation
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assumes that gamma remains constant. Therefore, the gamma calculation
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here provides only an estimate.
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The initial position gamma of −1.6 means the delta decreases by 3.2 with
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a $2 rise in the stock (–1.60 times the $2 rise in the stock price). Susie, then,
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would multiply −3.2 by $2 to find the loss on −3.2 deltas over a $2 rise. But
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she wasn’t short 3.2 deltas for the whole $2. She started out with zero deltas
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attributable to gamma and ended up being 3.2 shorter from gamma over that
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$2 move. Therefore, if she assumes her negative delta from gamma grew
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steadily from 0 to −3.2, she can estimate her average delta loss over that
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move by dividing by 2. |