Answer-first summary for fast verification
Answer: $13.17 or $30.92
The answer is **C**. At the time of purchase, the stock price is $25.00, so the options are ATM with strike prices of **25**. - Cost of two calls = 2 × 3.40 = **6.80** - Cost of one put = **2.30** - Total initial cost = **9.10** An ROI of 30% means profit must equal: - 0.30 × 9.10 = **2.73** So the total payoff must be: - 9.10 + 2.73 = **11.83** Now solve by region: - If $S \ge 25$: - Put expires worthless - Payoff = 2(S - 25) - 2(S - 25) = 11.83 - S = **30.915** ≈ **30.92** - If $S \le 25$: - Calls expire worthless - Payoff = 25 - S - 25 - S = 11.83 - S = **13.17** Therefore, the ROI equals 30.0% at **$13.17 or $30.92**.
Author: Manit Arora
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Question 606.3
While the stock price is $25.00, a trader buys three at-the-money (ATM) options: two calls and one put. The calls cost $3.40 and the put costs $2.30. The trader defines return on investment (ROI) as profit divided by initial cost without regard to the time value of money. The trader is aiming for an ROI of 30.0%. At what stock price(s) is the trade's ROI equal to 30.0%?
A
$38.00
B
$19.23 or $36.51
C
$13.17 or $30.92
D
This trade cannot achieve an ROI of 30.0%
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