1. 1 Chapter 14: Forward & Futures Prices Copyright © Prentice Hall Inc. 2000. Author: Nick Bagley, bdellaSoft, Inc. Objective How to price forward and futures Storage of commodities Cost of carry Understanding financial futures

2. 2 Chapter 14: Contents 1 Distinction Between Forward & Futures Contracts 2 The Economic Function of Futures Markets 3 The Role of Speculators 4 Relationship Between Commodity Spot & Futures Prices 5 Extracting Information from Commodity Futures Prices 6 Spot-Futures Price Parity for Gold 7 Financial Futures 8 The “Implied” Risk-Free Rate 9 The Forward Price is not a Forecast of the Spot Price 10 Forward-Spot Parity with Cash Payouts 11 “Implied” Dividends 12 The Foreign Exchange Parity Relation 13 The Role of Expectations in Determining Exchange Rates

3. 3 Terms –Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interest –Mark-to-market –Margin requirement –Margin call

4. 4 Characteristics of Futures Futures are:Futures are: –standard contracts –immune from the credit worthiness of buyer and seller because exchange stands between tradersexchange stands between traders contracts marked to market dailycontracts marked to market daily margin requirementsmargin requirements

5. 5 Spot-Futures Price Parity for Gold There are two ways to invest in goldThere are two ways to invest in gold buy an ounce of gold at S 0, store it for a year at a storage cost of $h/$S 0, and sell it for S 1buy an ounce of gold at S 0, store it for a year at a storage cost of $h/$S 0, and sell it for S 1 invest S 0 in a 1-year T-bill with return r f, and purchase a 1-ounce of gold forward, F, for delivery in 1-yearinvest S 0 in a 1-year T-bill with return r f, and purchase a 1-ounce of gold forward, F, for delivery in 1-year

6. 6 Spot-Futures Price Parity for Gold A contract with life T:A contract with life T: This is not a causal relationship, but the forward and current spot jointly determine the marketThis is not a causal relationship, but the forward and current spot jointly determine the market If we know one, then the rule of one market determines that we know the otherIf we know one, then the rule of one market determines that we know the other

7. 7 Rule of One Price: No Arbitrage Profits Purchase Actual Au Sell T-Bill Sell Au Forward Sell Actual Au Settle T-Bill Settle Au Forward Au = Gold

8. 8 Implied Cost of Carry As a consequence of the forward-spot price parity relationship, you can’t extract information about the expected future spot price of gold (unlike one wheat case) from futures pricesAs a consequence of the forward-spot price parity relationship, you can’t extract information about the expected future spot price of gold (unlike one wheat case) from futures prices The implied cost of carry (per $spot) is h = (F - S 0 )/S 0 - r fThe implied cost of carry (per $spot) is h = (F - S 0 )/S 0 - r f

9. 9 Financial Futures With no storage cost, the relationship between the forward and the spot isWith no storage cost, the relationship between the forward and the spot is Any deviation from this will result in an arbitrage opportunityAny deviation from this will result in an arbitrage opportunity

10. 10 14.8 The “Implied” Risk-Free Rate Rearranging the formula, the implied interest rate on a forward given the spot isRearranging the formula, the implied interest rate on a forward given the spot is This is reminiscent of the formula for the interest rate on a discount bondThis is reminiscent of the formula for the interest rate on a discount bond

11. 11 14.9 The Forward Price is not a Forecast of the Spot Price Following the diagrams in Chapter 12 we might suppose that the expected price of a stock isFollowing the diagrams in Chapter 12 we might suppose that the expected price of a stock is If this is indeed correct, then the forward price is not an indicator of the expected spot price at the maturity of the forwardIf this is indeed correct, then the forward price is not an indicator of the expected spot price at the maturity of the forward

12. 12 Forward-Spot Parity with Cash Payouts The S 0 - F relationship becomesThe S 0 - F relationship becomes Note: (forward price > the spot price) if (D the spot price) if (D < r S) Because D is not known with certainty, this is a quasi-arbitrage situationBecause D is not known with certainty, this is a quasi-arbitrage situation

13. 13 14.11 “Implied” Dividends From the last slide, we may obtain the implied dividendFrom the last slide, we may obtain the implied dividend

14. Exchange Rate Example 15000 ¥ (Borrowed) 15450 ¥ (Repaid) £100 (Invested) £109 (Matures) Time 3% ¥/¥ (direct) 3% ¥/£/£/¥ 150 ¥/£ 9%£/£ Forward ¥/£ JapanU.K.

15. 15 The Foreign Exchange Parity Relation We used the diagram to show thatWe used the diagram to show that Recall there is a time structure of interest, and the appropriate risk free rate should be usedRecall there is a time structure of interest, and the appropriate risk free rate should be used