Question

Suppose we are long 5 call options struck at 40 costing $6 each, and short 3 call options struck at 35 costing $10 each. All options expire in 1 month and the 1 month interest rate is 10 basis points. Draw the payoff and profit graphs. Under what circumstances do we break even? What is our maximum loss and at what stock price does it occur? What is our maximum gain, and at what stock price? (Label your profit graph!)

Answer 1

1. Break Even Stock Price = Income from Long Call Options - Premium of Long Call Options - Income from Short Call Options + Premium of Short Call Options = 0

Break Even Stock Price = 5 * (Stock Price - $40) - $6 * 5 - 3 * (Stock Price - $35) + 3 * $10 = 0

5 * (Stock Price - $40) - $6 * 5 - 3 * (Stock Price - $35) + 3 * $10 = 0

Break Even Stock Price = $47.50

2. Maximum Loss Happens when the stock is priced at $40 which leads to a maximum loss of = Loss on Short Call Options + Premium on Long call Options - Premium on Short Call Options

3 * ($40 - $35) + 5 * $6 - 3 * $10

Maximum Loss = $15

3. Maximum gain will be unlimited which will increase with an increase in stock price