Practice Question
Suppose that the price of a share of stock in ABC Corporation is currently trading at $30/share. Consider building a portfolio with the following option positions:
• Buy a call option with a strike price of $25
• Sell two call options each with a strike price of $40
• Buy a call option with a strike price of $55
Draw a payoff diagram of this portfolio.
Step 1: Define the Payoff for Each Option
- Buy Call at $25: \( \max(S - 25, 0) \)
- Sell Two Calls at $40: \( -2 \times \max(S - 40, 0) \)
- Buy Call at $55: \( \max(S - 55, 0) \)
Step 2: Combine the Payoffs
Total payoff: \[ \max(S - 25, 0) - 2 \times \max(S - 40, 0) + \max(S - 55, 0) \]
Step 3: Calculate Total Payoff at Key Prices
| Stock Price (S) | Payoff |
|---|---|
| $20 | $0 |
| $30 | $5 |
| $40 | $15 |
| $45 | $10 |
| $55 | $0 |
| $60 | $0 |
Step 4: Conclusion
The payoff diagram forms a triangle peaking at $15 when \( S = 40 \). This is similar to a butterfly spread strategy.