1. 1 Chapter 14: Future Prices Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley 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 14.1 Distinction Between Forward & Futures Contracts parties agree to exchange some item in the future at a delivery price specified nowparties agree to exchange some item in the future at a delivery price specified now the forward price is defined as the delivery price which makes the current market value of the contract zerothe forward price is defined as the delivery price which makes the current market value of the contract zero no money is paid in the present by either party to the otherno money is paid in the present by either party to the other –the face value of the contract is the quantity of the item specified in the contract multiplied by the forward price –the party who agrees to buy the specified takes the long position, and the party who agrees to sell the item takes the short position

4. 4 Terms –Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interest –Mark-to-market –Margin requirement –Margin call

5. 5 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

6. 6 14.2 The Economic Function of Futures Markets The futures markets facilitate the re- allocation of exposure to commodity price risk among market participantsThe futures markets facilitate the re- allocation of exposure to commodity price risk among market participants But:But:

7. 7 –by providing a means to hedge the price risk associated with storing a commodity, futures contracts make it possible to separate the decision of whether to physically store a commodity from the decision to have financial exposure to price changes

8. 8 The Economic Function of Futures Markets (Continued) A distributor, j, may hedge byA distributor, j, may hedge by –selling the commodity on the spot market now at a price S –selling short a futures contract at a price F and deliver the commodity at a specified time in the future there will be a carrying cost C j for distributor j, and she will store only if C j < F - Sthere will be a carrying cost C j for distributor j, and she will store only if C j < F - S

9. 9 The Economic Function of Futures Markets (Continued) The difference between the futures price and the spot price, F - S, is called the spread, and governs how much wheat will be stored, and by whomThe difference between the futures price and the spot price, F - S, is called the spread, and governs how much wheat will be stored, and by whom

10. 10 The Economic Function of Futures Markets (Continued) Suppose the commodity is wheat, and next year’s crop is expected to be much higher than average, then futures prices may be lower than the spot, (the spread may be negative,) nobody will store wheatSuppose the commodity is wheat, and next year’s crop is expected to be much higher than average, then futures prices may be lower than the spot, (the spread may be negative,) nobody will store wheat

11. 11 The Economic Function of Futures Markets (Continued) The existence of the futures market for wheat conveys information to all producers, distributors, and consumers; and this eliminates the necessity for market participants to gather and process information in order to forecast the future spot priceThe existence of the futures market for wheat conveys information to all producers, distributors, and consumers; and this eliminates the necessity for market participants to gather and process information in order to forecast the future spot price

12. 12 14.3 The Role of Speculators –Hedger anyone using a futures market to reduce riskanyone using a futures market to reduce risk –Speculator anyone who takes a position in the market (increasing his risk) in order to profit from his forecasts of future spot pricesanyone who takes a position in the market (increasing his risk) in order to profit from his forecasts of future spot prices –(A producer, distributor or consumer who chooses not to hedge her risk may be considered to be a speculator)

13. 13 The Role of Speculators: Example –Suppose that the current 1-month futures in wheat is $1.5/bushel, and a farming family with stored wheat believes that the price will rise to $2.00 –Not hedging the stored wheat results in the family being exposed to the vagrancies of the wheat market, and it becomes, in effect, a wheat speculator (just like their cobbler cousins who are long wheat futures)

14. 14 The Role of Speculators: Gamblers and Wasters Critic: “Speculators have no social value”Critic: “Speculators have no social value” Answer:Answer: –Successful speculators make the market more efficient as an information resourcemore efficient as an information resource provide liquidity when it is needed, which is when producers, distributors, and consumers can’t or won’t hedgeprovide liquidity when it is needed, which is when producers, distributors, and consumers can’t or won’t hedge more efficient by contributing towards recovering the fixed costs of providing a futures exchangemore efficient by contributing towards recovering the fixed costs of providing a futures exchange

15. 15 14.4 Relationship Between Commodity Spot and Futures Prices Arbitrageurs place an upper bound on futures prices by locking in a sure profit on futures prices if the spread between the futures price and spot price becomes greater than the cost of carry, F - S  CArbitrageurs place an upper bound on futures prices by locking in a sure profit on futures prices if the spread between the futures price and spot price becomes greater than the cost of carry, F - S  C –the cost of carry varies as a function of time and warehousing organization

16. 16 14.5 Extracting Information from Commodity Futures Prices Case 1 If (Futures Price < Current Spot)Case 1 If (Futures Price < Current Spot) –Then the futures price is an indicator of the expected future spot price The futures price is a biased estimate because there are risk premiums and discounts associated with holding the commodityThe futures price is a biased estimate because there are risk premiums and discounts associated with holding the commodity

17. 17 Extracting Information from Commodity Futures Prices Case 2 If (Futures Price > Current Spot)Case 2 If (Futures Price > Current Spot) –Then the futures price is not an indicator of the expected future spot price The spread cannot exceed the cost of carryThe spread cannot exceed the cost of carry

18. 18 14.6 Spot-Futures Price Parity for Gold In the case of gold futures, arbitrage establishes an upper- and lower-bound on the spread between the futures and spot prices, resulting in the spot- futures price-parity relationshipIn the case of gold futures, arbitrage establishes an upper- and lower-bound on the spread between the futures and spot prices, resulting in the spot- futures price-parity relationship

19. 19 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

20. 20 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

21. 21 Spot-Futures Price Parity for Gold The following diagram shows how to create synthetic gold, T-bills, or gold forward contract from the other twoThe following diagram shows how to create synthetic gold, T-bills, or gold forward contract from the other two All prices are predetermined,All prices are predetermined, –except the price of the one year of the forward and the price in one year of the gold, but the difference between them is equal to the known financing and storage costs

22. 22 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

23. 23 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

24. 24 14.7 Financial Futures We now focus on financial futuresWe now focus on financial futures –standardized contracts for future delivery of stocks, bonds, indices, and foreign currency –they have no intrinsic value, but represent claims on future cash flows –they have very low storage costs –settlement is usually in cash

25. 25 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

26. 26 Financial Futures: Example Consider shares in Bablonics, Inc, trading at $50 each, ($5,000 for a round lot); assume 6-month T-bills yield 6% (compounded semiannually)Consider shares in Bablonics, Inc, trading at $50 each, ($5,000 for a round lot); assume 6-month T-bills yield 6% (compounded semiannually)

27. 27 Bablonics, Inc (Continued) 1 Purchase one round lot of stock at spot1 Purchase one round lot of stock at spot –This results in a negative cash flow today of $5,000 (out), and will generate a cash flow of 100*Spot 6m (in) in six months

28. 28 Bablonics, Inc (Continued) 2 Cover today’s negative cash flow by selling short $5,000 worth of 6-month T- bills with a face value of 5000 (1+ 0.06/2)^0.5 = $5,1502 Cover today’s negative cash flow by selling short $5,000 worth of 6-month T- bills with a face value of 5000 (1+ 0.06/2)^0.5 = $5,150 The cash flow today is $5,000 (in), and the cash flow in six months time will be $5,150 (out)The cash flow today is $5,000 (in), and the cash flow in six months time will be $5,150 (out)

29. 29 Bablonics, Inc (Continued) 3 Cover the risk exposure by selling 100 shares forward at the equilibrium price of 5000*(1+0.06/2)^0.5 = $5,1503 Cover the risk exposure by selling 100 shares forward at the equilibrium price of 5000*(1+0.06/2)^0.5 = $5,150 –There is no cash flow today, but the value of this forward contract in six months time will be $(Spot 6m - 5,150)

30. 30 Bablonics, Inc (Continued) -$5,000 (long stock) + $5,000 (short bond) + $0 (short forward) = $0 -$5,000 (long stock) + $5,000 (short bond) + $0 (short forward) = $0

31. 31 Bablonics, Inc (Continued) Cash Flow in 6-MonthsCash Flow in 6-Months + $Spot 6m (settle long stock) - $5,150 (settle short bond) +($5,150 - $Spot 6m ) (settle forward) = $0

32. 32 Bablonics, Inc (Conclusion) If your net risk-free investment was zero,If your net risk-free investment was zero, –and you receive nothing that is what you should expectthat is what you should expect –and you expect to: received positive value with no risk, then the rule of one price has been violatedreceived positive value with no risk, then the rule of one price has been violated lose value with no risk, then reverse the direction of all transactions, and again you profit with no risklose value with no risk, then reverse the direction of all transactions, and again you profit with no risk

33. 33 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

34. 34 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

35. 35 The Forward Price is not a Forecast of the Spot Price The forward price is obtained without risk from the current spot and riskless bondThe forward price is obtained without risk from the current spot and riskless bond The spot value at a future date is obtained by investing in the security and accepting (market) risk, and this risk must be rewardedThe spot value at a future date is obtained by investing in the security and accepting (market) risk, and this risk must be rewarded

36. 36 14.10 Forward-Spot Parity with Cash Payouts So far we have assumed that there is no dividendSo far we have assumed that there is no dividend –Now suppose that everybody expects an uncertain dividend in 1 year of D –It is not possible to replicate D because of this uncertainty –We will treat D as if it were known with certainty, and only deal with 1-year forwards

37. 37 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

38. 38 14.11 “Implied” Dividends From the last slide, we may obtain the implied dividendFrom the last slide, we may obtain the implied dividend

39. 39 14.12 The Foreign Exchange Parity Relation Recall from Chapter 2 the following diagram:Recall from Chapter 2 the following diagram:

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

41. 41 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

42. 42 14.13 The Role of Expectations in Determining Exchange Rates –Consider a world in which there are two countries, Domestic & Foreign, and conditions are such in each country that the the yield curves are flat, with yields of 5% and 10% respectively –Further assume that the exchange rate is 1 today –The 1-year forward is 1*1.05/1.10=0.9545

43. 43 The Role of Expectations in Determining Exchange Rates –If the interest rate in Foreign is higher than in Domestic, one explanation may be that the rate of inflation is higher. –Assume no taxes, and the interest rate difference is the result inflation being 5% and 10% respectively –Then the price dynamics of both countries will result in an exchange rate of 0.9545 next year, which is also the forward rate

44. 44 The Role of Expectations in Determining Exchange Rates –In real life, things are not so simple, but several mechanisms may be postulated that support the expectations hypothesis –International investor confidence, and their forecasts of inflation, place price pressure on both spot and forward exchange rates through the international bond market