Question

You just bought one share of Microsoft for $110. You are convinced it will trade in a narrow range for the next year so sell one call option on Microsoft with an exercise price of $105 and three months to maturity. The option price is $15. The $15 proceeds from the option sale are deposited in a non-interest bearing margin account. On the expiration date of the option, what is the maximum profit of your combined position in the stock and the option? [Hint: construct a table of payoffs as a function of the future stock price.] a. $15 b. $5 c. unlimited d. $10

Answer 1

Spot Price of Share = $ 110 | Exercise Price of Option = $ 105 | Time to maturity = 3 months

Option Price = $ 15

We will build a payoff table using below example of a scenario.

Let's take a narrow range of 5 up and down. First let's look at the case when stock price increases by 5 to $ 115

Payoff from Spot trade = Current Stock Price - Price at share bought = 115 - 110 = $ 5

Payoff from Call Option = (Exercise Price - Stock Price) + Option Price = (105 - 115) + 15 = -10 + 15 = $ 5

Total Payoff from the combined position is $ 10.

Now let's take the other extreme where stock price has decreased by 5 to $ 105

Payoff from Spot trade = Current Stock Price - Price at share bought = 105 - 110 = $ - 5

Payoff from Call Option = (Exercise Price - Stock Price) + Option Price = (105 - 105) + 15 = $ 15

Total Payoff from the combined position is $ 10.

Similarly, we can create a payoff table and below is same for prices range increased to 10.

Hence, the maximum profit that the investor can make from the combined position is $ 10 which is Option D.