Reference no: EM132490636
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.
Question 1: 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?
Question 2: 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?
Question 3: Do the two investments have the same risk? Explain why or why not.
Question 4: What does it cost today to buy Investment 1?
Question 5: 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?
Question 6: Using the information above and your answer in part 5), what must be the price of a UD Inc. at-the-money put option with one year to expiration?
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