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.
What is the maximum profit?
Step 1: Analyze Each Option Position
- 📉 Buy 1 Put @ $40 for a $2.5 premium → Right to sell at $40
- 📈 Sell 2 Puts @ $24 for $1 premium each → Obligation to buy at $24
Step 2: Net Premium Paid
\( \text{Net premium} = 2.5 - 2 = 0.5 \)
Step 3: Determine Max Profit Scenario
If stock price ends at $24:
• Bought put: \( 40 - 24 = 16 \)
• Sold puts expire worthless
• Net profit = \( 16 - 0.5 = 15.5 \)
| Stock Price | Total Payoff |
|---|---|
| $20 | ~$8.5 (loss from sold puts dominates) |
| $24 | $15.5 (max profit) |
| $30 | $5.5 |
| $40 | −$0.5 |
Step 4: Conclusion
✅ The **maximum profit is $15.50**, achieved when the stock finishes at **$24** — just low enough to exercise the $40 put but not the sold $24 puts.