Suppose that the current price of UD Inc. is $60 a share. UD is an unusual company: in one year, its stock price can be only one of two values. If things go well for the company, the price will go up to $80, and if things go poorly, the price will fall to $40. The continuously compounded risk-free rate is 3% per year.

John is considering two investments:

Investment1: A seemingly bizarre portfolio that buys 0.5 shares of the stock and short-sells 0.2 units of a one-year risk-free zero-coupon bond with a face value of $100.

Investment2: An at-the-money (X=$60) call option with one year left to expiration.

a.How much will Investment 1 be worth in one year if the Up state of the world occurs? How much will it be worth if the Down state occurs?

b.How much will Investment 2 be worth in one year if the Up state of the world occurs? How much will it be worth if the Down state occurs?

c.Do the two investments have the same risk? Explain why or why not.

d.What does it cost today to buy Investment 1?

e.We know that to prevent arbitrage, two investments with identical future cash flows must have identical prices today. Based on this logic, what must be the price of Investment 2?

f.Using the information above and your answer in part e), what must be the price of a UD Inc. at-the-money put option with one year to expiration?