Practice Question
Suppose that the price of a share of stock in ADT Co. is currently trading at $30/share. Consider building a portfolio with the following option positions:
• Buy a put option with a strike price of $40 for a $2.5 premium.
• Sell two put options each with a strike price of $24 for a $1 premium each.
Which of the following is correct?
A) The maximum profit of this portfolio is $16.00.
B) All statements are incorrect.
C) The maximum profit of this portfolio is 15.50.
D) The maximum loss of this portfolio is $0.
E) The maximum loss of this portfolio is unlimited.
Step 1: Define the Option Positions
- Buy 1 Put @ $40 for $2.5 (right to sell at $40)
- Sell 2 Puts @ $24 for $1 each (obligation to buy at $24)
Step 2: Net Premium Paid
Net premium = \( 2.5 - 2 = 0.5 \)
Step 3: Analyze Payoffs
Max profit happens when stock drops to or below $24:
- Buy put: \( 40 - 24 = 16 \)
- Sold puts: both exercised, but buy/sell at $24 → no further loss
- Net profit = \( 16 - 0.5 = 15.5 \)
| Stock Price (S) | Total Payoff |
|---|---|
| $20 | $15.5 |
| $24 | $15.5 |
| $30 | $5.5 |
| $40 | -0.5 |
| $45 | -0.5 |
Step 4: Conclusion
The strategy's maximum profit is $15.5, occurring when stock price ≤ $24. Maximum loss is limited to $0.5 when none of the options are exercised.