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1、CHAPTER 14FORWARD AND FUTURES PRICESObjectives To explain the economic role of futures markets To show what information can and cannot be inferred from forward and futures prices.Outline14.1Distinctions Between Forward and Futures Contracts14.2The Economic Function of Futures Markets14.3The Role of
2、Speculators14.4Relation Between Commodity Spot and Futures Prices14.5Extracting Information from Commodity Futures Prices14.6Spot-Futures Price Parity for Gold14.7Financial Futures14.8The Implied Risk-Free Rate14.9The Forward Price Is Not a Forecast of the Spot Price14.10Forward-Spot Parity with Cas
3、h Payouts14.11Implied Dividends14.12The Foreign-Exchange Parity Relation14.13The Role of Expectations in Determining Exchange RatesSummary Futures contracts make it possible to separate the decision of whether to physically store a commodity from the decision to have financial exposure to its price
4、changes. Speculators in futures markets improve the informational content of futures prices and make futures markets more liquid than they would otherwise be. The futures price of wheat cannot exceed the spot price by more than the cost of carry: The forward-spot price parity relation for gold is th
5、at the forward price equals the spot price times the cost of carry:This relation is maintained by the force of arbitrage. One can infer the implied cost of carry and the implied storage costs from the observed spot and forward prices and the risk-free interest rate. The forward-spot parity relation
6、for stocks is that the forward price equals the spot price times 1 plus the risk-free rate less the expected cash dividend. This relation can therefore be used to infer the implied dividend from the observed spot and forward prices and the risk-free interest rate. The forward-spot price parity relat
7、ion for the dollar/yen exchange rate involves two interest rates: where F is the forward price of the yen, S is the current spot price, rY is the yen interest rate, and r$ is the dollar interest rate. If the forward dollar/yen exchange rate is an unbiased forecast of the future spot exchange rate, t
8、hen one can infer that forecast either from the forward rate or from the dollar-denominated and yen-denominated risk-free interest rates.Solutions to Problems at End of ChapterForward Contracts and Forward-Spot Parity.1. Suppose that you are planning a trip to England. The trip is a year from now, a
9、nd you have reserved a hotel room in London at a price of 50 per day. You do not have to pay for the room in advance. The exchange rate is currently $1.50 to the pound sterling.a. Explain several possible ways that you could completely hedge the exchange rate risk in this situation.b. Suppose that r
10、=.12 and r$=.08. Because S=$1.50, what must the forward price of the pound be?c. Show that if F is $0.10 higher than in your answer to part b, there would be an arbitrage opportunity. SOLUTION:a. Ways to hedge the exchange rate risk:Pay for the room in advanceBuy the pounds you will need in the forw
11、ard market.Invest the present value of the rental payments in a pound-denominated riskless asset.b. F = S (1+r$)/(1+r) = $1.50 x 1.08/1.12 = $1.4464 per poundc. If F is $1.55 then arbitrage profits can be made by borrowing dollars, investing in pounds and selling them forward at the inflated forward
12、 price. After paying off principle and interest on the dollars borrowed, you would have pure arbitrage profits left over. For example, Borrow $1.50,Convert it into 1 pound,Invest it in pound-denominated bonds to have 1.12 pounds a year from now,Sell 1.12 pounds forward at $1.55 per pound to have $1.
13、736 a year from now,After 1 year, pay off the principle and interest on the loan ($1.50x 1.08 = $1.62).This series of transactions leaves you with $.116 a year from now with no initial outlay of your money.Arbitrage PositionImmediate Cash FlowCash Flow 1 Year From Now Borrow $1.50$1.50 -$1.62Buy pou
14、nd-denominated bond -$1.50S1Sell 1.12 pounds forward at $1.55 per pound0$1.736-S1 Net Cash Flows0$1.736-$1.62 = $.116Forward-Spot Parity Relation with Known Cash Payouts2. Suppose that the Treasury yield curve is flat at an interest rate of 7% per year (compounded semiannually).a. What is the spot p
15、rice of a 30-year Treasury bond with an 8% coupon rate assuming coupons are paid semiannually?b. What is the forward price of the bond for delivery six months from now?c. Show that if the forward price is $1 lower than in your answer to part b, there should be an arbitrage opportunity.SOLUTION:a.The spot price of the 30-year Treasury is $1,124.724:niPVFVPMTResult603.5?100040PV =1124.724b.The forward price for delivery six months from now is $1,124.089:F = S(1+r) - C = $1,124.724 x 1.035 - 40 =$1,124.089c.If the forward price is only $1,123.089, then arbitrage profit
