Question

Question 4

Suppose Joey holds a share of SCB common stock, currently valued at $48. She is concerned that over the next few months the value of her holding might decline and she would like to hedge that risk by supplementing her holding with one of the following two option positions, all of which expire at the same point in the future.

a. Complete a table similar to the following for each of the following positions:

i. A long position in a put option with an exercise price of $45 and a premium of $2.

ii. A short position in a call option with an exercise price of $45 and a premium of $4.

In calculating combined terminal position value, ignore the time differential between the initial option expense or receipt and the terminal payoff. Expiration date SCB stock price	Expiration date option payoff	Initial option premium	Combined terminal position value
25
30
35
40
45
50
55
60
65
70
75

b. Graph the combined terminal position value for each of the above hedged positions, using combined terminal position value on the vertical axis (Y) and SCB’s expiration date stock price on the horizontal axis (X).

c. Explain which of the two hedging strategies mentioned above is better if Joey’s objective is also to enjoy the upside gain of the stock.

Answer 1

a-i). Long put option with K = 45 and premium = 2

Option payoff = max(K-underying price at expiry, 0)

Option value at expiry = option payoff - 2 (since put option is bought, premium is paid by the buyer to the seller)

a-ii). Short call option with K = 45 and premium = 4

Option payoff = - max(underying price at expiry -K, 0) (the payoff for the seller will be the negative of the payoff for the buyer)

Option value at expiry = option payoff + 4 (since premium is paid to the seller)

a-iii). Combined terminal position value: This will the sum of the two positions taken above, so

terminal position option payoff = max(45-S,0) - max(S-45,0)

terminal position option value = terminal position option payoff - 2 + 4

b). Graph of the terminal position option value:

c). If a fall in stock price is anticipated then long put option is a better strategy as loss will be capped and if price falls then there will be a gain.