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Answer: $S(0)/c(0)$
If the stock price doubles from \(S(0)\) to \(2S(0)\), then a call with strike \(K=S(0)\) has payoff: \[ \max(2S(0)-S(0),0)=S(0) \] If the entire amount \(X\) is invested: - Number of shares purchased = \(X/S(0)\) - Number of call options purchased = \(X/c(0)\) Future stock payoff: \[ \frac{X}{S(0)} \times S(0) = X \] Future option payoff: \[ \frac{X}{c(0)} \times S(0) \] Therefore, the payoff leverage ratio is: \[ \frac{X/c(0) \times S(0)}{X} = \frac{S(0)}{c(0)} \] **Correct answer: C. $S(0)/c(0)$**
Author: Manit Arora
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Question 138.3: Assume you have dollars to invest in a stock with a current stock price of . You decide to invest the full in one of two strategies: either you purchase shares at , or you buy FMV call options with strike equal to that have a premium cost of . If the stock doubles to $2 \cdot S(0)$, and we define the “payoff leverage ratio” as the ratio of the future option payoff to the purchased stock payoff, what is the payoff leverage ratio implied by the option payoff?
A
Zero
B
2.0
C
D
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