Answer-first summary for fast verification
Answer: zero
If the stock falls to \(0.5S(0)\), then a call option with strike \(K = S(0)\) is **out of the money** and expires worthless. So: - **Option payoff = 0** - Therefore the ratio of option payoff to stock payoff is **0** Hence, the payoff leverage ratio is **zero**.
Author: Manit Arora
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Q-138.4 Assume the same as above: you have (X) dollars to invest entirely in either stock at a price of S(0) or call options with K = S(0) that have a premium cost of c(0). The payoff leverage ratio is the ratio of future option payoff divided by the future stock payoff. If the stock drops 50% to one-half the value of S(0), what is the payoff leverage ratio?
A
zero
B
2.0
C
S(0)/c(0)
D
c(0)/S(0)
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