CHAPTER 5 Determination of Forward and Futures Prices
Practice Questions
Problem 5.8. Is the futures price of a stock index greater than or less than the expected future value of the index? Explain your answer. The futures price of a stock index is always less than the expected future value of the index. This follows from Section 5.14 and the fact that the index has positive systematic risk. For an alternative argument, let µ be the expected return required by investors on the index so that E ( ST ) = S0 e ( µ − q )T . Because µ > r and F0 = S0 e( r − q )T , it follows that E (ST ) > F0 . Problem 5.9. A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of…show more content… When it is hedged using futures contracts, the daily settlement process does leave the company exposed to some risk. Explain the nature of this risk. In particular, consider whether the company is better off using a futures contract or a forward contract when a) The value of the foreign currency falls rapidly during the life of the contract b) The value of the foreign currency rises rapidly during the life of the contract c) The value of the foreign currency first rises and then falls back to its initial value
d) The value of the foreign currency first falls and then rises back to its initial value Assume that the forward price equals the futures price. In total the gain or loss under a futures contract is equal to the gain or loss under the corresponding forward contract. However the timing of the cash flows is different. When the time value of money is taken into account a futures contract may prove to be more valuable or less valuable than a forward contract. Of course the company does not know in advance which will work out better. The long forward contract provides a perfect hedge. The long futures contract provides a slightly imperfect hedge. a) In this case the forward contract would lead to a slightly better outcome. The company will make a loss on its hedge. If the hedge is with a forward contract the whole of the loss will be realized at the end. If it is with a futures contract the loss
