
Explanation:
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.
An ROI of 30% means profit must equal:
So the total payoff must be:
Now solve by region:
If :
If :
Therefore, the ROI equals 30.0% at $13.17 or $30.92.
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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%