Assuming that the options are priced fairly, use the concept of put-call parity to calculate the… 1 answer below »

Suppose that an investor holds a share of Sophia common stock, currently valued at $50. 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 three different derivative positions, all of which expire at the same point in the future:

(1) A short position in a forward with a contract price of $50

(2) A long position in a put option with an exercise price of $50 and a front-end premium expense of $3.23

(3) A short position in a call option with an exercise price of $50 and a front-end premium receipt of $5.20

a. Using a table similar to the following, calculate the expiration date value of the investor’s combined (i.e., stock and derivative) position. In calculating net portfolio value, ignore the time differential between the initial derivative expense or receipt and the terminal payoff.

Expiration Date
Sophia Stock Price

Expiration Date
Derivative Payoff

Initial Derivative Premium

Combined
Terminal
Position Value

25

30

35

40

45

50

55

60

65

70

75

b. For each of the three hedge portfolios, graph the expiration date value of her combined position on the vertical axis, with potential expiration date share prices of Sophia stock on the horizontal axis.

c. Assuming that the options are priced fairly, use the concept of put-call parity to calculate the zerovalue contract price (i.e., F0,T) for a forward agreement on Sophia stock. Explain why this value differs from the $50 contract price used in Part a and Part b.