Practice Question
Draw a payoff diagram of 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
Answer +
Correct Answer: Maximum payoff is $15 at a stock price of $40. Payoff is $0 at all other prices listed.
Explanation +
Step-by-step breakdown:
The payoff of this option strategy depends on the combination of three positions:
- Long Call @ $25: Payoff = max(0, S − 25)
- Short 2 Calls @ $40: Payoff = −2 × max(0, S − 40)
- Long Call @ $55: Payoff = max(0, S − 55)
Payoffs at key prices:
| Stock Price (S) | Call @ $25 | −2 × Call @ $40 | Call @ $55 | Total Payoff |
|---|---|---|---|---|
| $0 | $0 | $0 | $0 | $0 |
| $25 | $0 | $0 | $0 | $0 |
| $40 | $15 | $0 | $0 | $15 |
| $55 | $30 | −$30 | $0 | $0 |
| $80 | $55 | −$80 | $25 | $0 |
Conclusion:
The combined strategy resembles a butterfly spread that peaks at $40. The maximum profit of $15 is achieved at that price. Outside of this point, profits decrease and fall to $0.
Final Answer: Payoff peaks at $15 when the stock price is $40. Payoff is $0 at $0, $25, $55, and $80.