4. A put and a call are selling for $5 each on a share of stock currently worth $50. Both the put and call expire in one year and have exercise prices equal to $50. The market for stocks and options are perfectly efficient, with no-arbitrage pricing evident.
a. What is the riskless return rate in this economy?
b. How would your answer to part a of this question change if investors were strongly risk averse?
c. In this same economy, suppose that the spot price of gold is $1,800 per ounce. What is the futures price of an ounce of gold assuming that the Expectations Hypothesis for futures pricing holds? Ignore part d of this question to answer this part c.
d. Now, assume a single exception to perfect market efficiency, with the annual cost of storing gold being $2 per ounce. However, the riskless interest or return rate is still consistent with the correct answer for part a. Would this futures market for gold more likely be in contango, backwardation, both or neither?
5. In a discreet, two-period, perfectly efficient market, a stock is selling for $1 per share. In each of the two one-year periods in this economy, the stock’s price will either double or drop in price by 40%. All riskless bonds will yield 10% each year; that is, the yield curve is flat. You may assume that markets are efficient and allow for no-arbitrage pricing. What is the time-zero (now) no-arbitrage market value of a 2-year call in this economy if its exercise price equals 2?
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