Answer-first summary for fast verification
Answer: 7.0: 1.0
**Correct answer: C** Compute the profit from each strategy when the stock rises from **$20** to **$40**. ### 1) Buy the stock With $10,000 and a stock price of $20, Peter buys: \[ 10{,}000 / 20 = 500 \text{ shares} \] If the stock rises to $40, the profit is: \[ (40 - 20) \times 500 = 10{,}000 \] ### 2) Buy call options Each call costs $2.50, so Peter buys: \[ 10{,}000 / 2.50 = 4{,}000 \text{ options} \] At expiration, each option has intrinsic value: \[ 40 - 20 = 20 \] Total payoff: \[ 20 \times 4{,}000 = 80{,}000 \] Profit on the options position: \[ 80{,}000 - 10{,}000 = 70{,}000 \] ### Ratio of profits Stock profit : option profit = \[ 10{,}000 : 70{,}000 = 1 : 7 \] So the ratio is equivalently **7.0 : 1.0** in favor of the option strategy, which matches **C**.
Author: Manit Arora
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Question 707.2. Peter has $10,000.00 to invest (speculate) in an exciting technology company whose stock price currently trades at $20.00 per share. At-the-money call options are priced at $2.50 per option. He wants to compare the difference between buying the stock and buying the call options; in either of the two scenarios, he will invest his entire $10,000. If the stock doubles (from $20.00 to $40.00), what is the ratio of profits between the two alternatives? Please note that option profit equals payoff minus initial cost, and we are unconcerned with the time value of money here.
A
1.0: 1.0; i.e., no leverage
B
2.5: 1.0
C
7.0: 1.0
D
20.0: 1.0
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