Practice Question
Suppose that the price of a share of stock XYZ Corporation is currently at $20 per share. Consider building the following options portfolio:
• Buy a call option with strike price $40
• Sell a call option with strike price $60
Both options share the same maturity and underlying stock.
A) Draw a payoff diagram of this portfolio and compute payoff.
B) If the stock price is $60, what is your profit?
C) If the stock price is $100, what is your profit?
Profit at $60: $20
Profit at $100: $20
Step 1: Structure of the Portfolio
- ✅ Long call at $40: payoff = \( \max(0, S - 40) \)
- ❌ Short call at $60: payoff = \( -\max(0, S - 60) \)
- Net payoff = \( \max(0, S - 40) - \max(0, S - 60) \)
Step 2: Payoff Table
| Stock Price (S) | Long Call | Short Call | Net Payoff |
|---|---|---|---|
| $20 | $0 | $0 | $0 |
| $40 | $0 | $0 | $0 |
| $50 | $10 | $0 | $10 |
| $60 | $20 | $0 | $20 |
| $100 | $60 | −$40 | $20 |
Step 3: Profit Explanation
• As long as the entry cost of the spread is $0 (break-even construction), profit equals payoff.
• Profit is capped at $20 when stock ≥ $60.
• Stock prices above $60 don’t increase payoff because the short call loses value at the same rate the long call gains it.