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 and 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 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 beteen the initial derivative expense of receipt and the terminal payoff.
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 zero-value
contract price (i.e., FO,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.
Expiration Date Expiration Date Initial Combined Terminal
Sophia Stock Price Derivative Payoff Derivative Premium Position Value