Question

Prices of bond futures can be used to access the markets expectations about future interest rates and therefore can be used as the basis for pricing other financial securities. A 10-year annual coupon bond with face value $1,000 is currently selling for $919. The futures price of this bond for delivery in 1 year is $888. The bond pays coupon of $88 annually. Assume that the coupon is paid before the delivery of the bond.

(a) What is the 1-year interest rate implied by the spot and futures prices of bonds? (Hint: Recall the PV formula of bond prices for a one-year horizon.)

(b) In the gold futures market, the spot price of gold is $1337 per ounce. There is no storage cost. What is the futures price per ounce of gold for delivery in one year? Suppose there is no uncertainty in interest rates.

(c) Suppose your friend Emily has also longed a forward contract on gold for delivery one year from now. But the contract was entered last year. The forward price she locked in was $1375. Clearly her contract is valuable now because the gold price has risen since last year, and no one is able to lock in such a low price now. What is the maximum amount you would pay now for having her contract? Does it violate the proposition that forward and futures contracts should have zero value at the time of initiation? Explain.

(d) A jewelry producer just received an order that is worth $1 million from a department store for gold necklaces to be delivered in 6 months. The producer will be paid in 6 months. He cant buy gold now because he cant afford the storage cost. Suppose the gold necklaces can be produced instantaneously. What is the risk of the producer? What hedging strategy would you recommend to him? Explain briefly why the strategy would work.

Answer 1

a: Price of bond today or PV =919

Coupon on bond = 88

Future price for delivery after 1 year =888

Coupon payment is given before delivery of bond

So total amount bond holder would get in 1 year = Coupon payment + Future price of bond = 88+888 = $976

Present value of bond = $919

So total amount made on holding bond for 1 year = $976-$919= $57

So implied interest rate = Profit for holding a bond*1 00/ present value of bond

= $57*1 00/$919

= 6.202%

So implied interest rate for holding bond for 1 year = 6.202%