A stock price is currently $23 . A reverse (i.e short) butterfly spread is created from options with strike prices of $20, $25, and $30 . Which of the following is true?
A. The gain when the stock price is greater than $30 is less than the gain when the stock price is less than $20
B. The gain when the stock price is greater than $30 is greater than the gain when the stock price is less than $20
C. The gain when the stock price is greater than $30 is the same as the gain when the stock price is less than $20
D. It is incorrect to assume that there is always a gain when the stock price is greater than $30 or less than $20
C
The gain from a very high stock price or a very low stock price is the same. Suppose calls are used. In the case of a very low stock price none are exercised and the gain is c1+c3−2c2 from the option premium. In the case of a very high stock price all options are exercised. The net payoff is zero and the gain is the same.
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