Question

Adam Smith just purchased 700 shares of AT&E at $54.05, and he has decided to write covered calls against these stocks. Accordingly, he sells 7 AT&E calls at their current market price of $5.02. The calls have 3 months to expiration and carry a strike price of $56.00. The stock pays a quarterly dividend of $0.49 a share the next dividend to be paid in about a month). a. Determine the total profit and holding period return Adam will generate if the stock rises to $56.00 a share by the expiration date on the calls. b. What happens to Adam's profit (and return) if the price of the stock rises to more than $56.00 a share? c. Does this covered call position offer any protection (or cushion) against a drop in the price of the stock? Explain. a. If the stock rises to $56.00 a share by the expiration date on the calls, the total profit is $ (Round to the nearest cent.) The total holding period return is %. (Round to two decimal places.) b. What happens to Adam's profit (and return) if the price of the stock rises to more than $56.00 a share? (Select the best answer below.) O A. For any price above $56.00, the loss on the call option will be offset exactly by the additional capital gains made on the long position in the stock, leaving the profit unchanged. The HPR also remains the same. OB. For any price above $56.00, the loss on the call option will exceed the additional capital gains made on the long position in the stock, leaving the profit unchanged. The HPR also remains the same. O C. For any price above $56.00, the loss on the call option will suppress the additional capital gains made on the long position in the stock, leaving zero profit. The HPR will also be zero. OD. For any price above $56.00, the gain on the call option will be offset exactly by the capital loss made on the long position in the stock, leaving the profit unchanged. The HPR also remains the same. c. Does this covered call position offer any protection (or cushion) against a drop in the price of the stock? Explain. (Select the best answer below.) O A. The covered call position offers no protection against a drop in stock price. The capital loss on the stock can not be protected by the option premium received. OB. The covered call position offers total protection against a drop in stock price. The capital loss on the stock will be fully protected. O C. The covered call position offers limited protection against an increase in stock price. The capital loss on the stock can be protected to the extent of the option premium received. OD. The covered call position offers limited protection against a drop in stock price. The capital loss on the stock can be protected to the extent of the option premium received

Answer 1

Write covered call means go short on call option

K: strike price = 56

Pay-off short call = -max(S - K,0) = -max(S - 56,0)

(a) if the stock rises to $56.00 a share by the expiration date on the calls

Profit per share = 56 - 54.05 = 1.95

dividend per share = 0.49

call premium per share = 5.02

Pay-off from short call = -max(56-56,0) = 0

Total profit = 1.95+0.49+5.02-0 = 7.46

Profit on 700 shares = 700*7.46 = $5222

Holding period return = 7.46/54.05 = 0.1380 = 13.82%

(b) What happens to Adam's profit (and return) if the price of the stock rises to more than $56.00

If stock rises to say S > 56

Profit per share = S - 54.05

dividend per share = 0.49

call premium per share = 5.02

Pay-off from short call = -max(S-56,0) = -(S - 56)

Total profit = (S - 54.05) + 0.49 + 5.02 - (S - 56) = 7.46

Profit will remain constant at 7.46 if stock price rises above 56

(c) Does this covered call position offer any protection (or cushion) against a drop in the price of the stock?

Let S be the stock price on expiry and S < 56

Profit per share = S - 54.05

dividend per share = 0.49

call premium per share = 5.02

Pay-off from short call = -max(S-56,0) = 0

Total profit = (S - 54.05) + 0.49 + 5.02 - 0 = S - 48.54

If total profit = 0

Then S = $48.54. Yes the short call provides protection till stock price fall to $48.54. Beyond that losses will happen