1. 14-1 Chapter 14 Futures Contracts

2. 14-2 Futures Contracts Points in time Delivery date Enter into contract Now 0 Short delivers commodity and receives payment. Long receives commodity and makes payment.

3. 14-3 Silver Futures Points in time Delivery date Enter into contract Now 0 Short delivers silver and receives $8.00. Long receives silver and pays $8.00.

4. 14-4 Offsetting a Short Futures Position Points in time Delivery date March 15March 16 0 Short at $8.00 per ounce September 15 Long at $8.05 per ounce

5. 14-5 Short at $8.00Offset (Long) at $8.05 +$8.00- $8.05 = -$0.05 Long at $8.00Offset (Short) at $8.05 - $8.00+ $8.05 = +$0.05 Zero Sum Game Price Rises: Long Gains + Short Loses

6. 14-6 Short at $8.00Offset (Long) at $7.70 +$8.00- $7.70 = +$0.30 Long at $8.00Offset (Short) at $7.70 - $8.00+ $7.70 = -$0.30 Price Falls: Long Loses & Short Gains

7. 14-7 Usually delivery is not made because it is cheaper to offset than to take delivery. Transport costs. There is a Clearinghouse which keeps track of the longs and shorts. The total number of longs = total number of shorts and is called the Open Interest.

8. 14-8 Longs Shorts Helen4Sherman3 Ellen1Herman2 Total Longs = Total Shorts. Suppose Helen offsets 1 contract. What happens to the Open Interest? Open Interest--Day 1

9. 14-9 The New Open Interest Depends upon Who Goes Long. Case 1:A new long enters the market. Melon goes long 1 contract. Longs Shorts Helen3Sherman3 Ellen1Herman2 Melon15 Open Interest is unchanged. Open Interest--Day 2

10. 14-10 Case 2:Helen offsets 1 and Sherman offsets 1. Longs Shorts Helen3Sherman2 Ellen1Herman24 Open Interest decreases if a long and a short offset. Open Interest would increase if there is an additional long contract and an additional short contract. Open Interest--Day 2

11. 14-11 Margin or Performance Bond uFutures markets require a percent of the value of the commodity to be put deposited as a performance guarantee. uOtherwise participants might be tempted to take a futures position, cashing in the profit if they gain and defaulting (not paying) if they lose.

12. 14-12 Margin Introduces Financial Leverage %  Equity =. %  Underlying asset %Put down Typically, futures contracts require that 5% be put down. Thus,

13. 14-13 ROR i Worse off with levered Better off with levered Unlevered Levered ROR underlying asset i i = Interest rate

14. 14-14 Marking-to-Market At the end of trading, the futures exchanges determine a Settlement Price, basically a closing price. Then, the collateral of the longs and shorts is changed by the change in settlement price from one day to the next. The collateral of the shorts is reduced by $0.10 and the collateral of the longs is increased by $0.10. Monday SettleTuesday Settle $8.00$8.10

15. 14-15 Daily Price Limits Most futures contracts specify the maximum price change from day to day. These result in price limits. Upper limit Lower limit Settle MondayTuesday

16. 14-16 Forward versus Futures Contracts ForwardFutures CollateralNoneYes Marking-to-MarketNoneDaily Compensating balancesUsuallyNone ResaleLimitedActive trading on organized exchanges Contract termsCustom madeStandardized DeliveryUsually deliveredUsually offset Market sizeSmall, private. Large, public, impersonal Participants know each other

17. 14-17 Determinants of Futures Price for Nonstorable Commodity 0 Delivery Date F = Expected Spot Price at Delivery Date.

18. 14-18 F = P + Interest + Storage until delivery. Futures =Spot Price + Interest + Storage until delivery. Determinants of Futures Price for Storable Commodity

19. 14-19 IfP = $400 = Spot Price. R = 10%.

20. 14-20 Creating a Forward Position from a Spot Position ActionsPoints in Time Cash flows 0Delivery Date Borrow+PRepay – [P + Interest + Storage] Buy commodity–P Net cash flows0–[P + Interest + Storage]

21. 14-21 Arbitrage Example If Futures Price Is above Equilibrium Level ActionsPoints in Time Cash flows 0Delivery Date Short futures+500 Borrow+400 Buy commodity–400 Repay loan + Interest–400(1.10) Deliver commodity in futures market Net cash flows0 500 – 400(1.10) = 60

22. 14-22 Arbitrage If Futures Price Is above Equilibrium Level ActionsPoints in Time Cash flows 0Delivery Date Short futures+F Borrow+P Buy commodity–P Repay loan + Interest–P(1 + R) Deliver commodity in futures market Net cash flows0F – P(1 + R)

23. 14-23 Arbitrage If Futures Price Is below Equilibrium Level ActionsPoints in Time Cash flows 0Delivery Date Long futures–F Short commodity+P Invest proceeds–P+P(1 + R) Take delivery on futures and close short position Net cash flows0–[F – P(1 + R)]

24. 14-24 Arbitrage Example If Futures Price Is below Equilibrium Level ActionsPoints in Time Cash flows 0Delivery Date Long futures–400 Short commodity+400 Invest proceeds–400+400(1.10) Take delivery on futures and close short position Net cash flows0 –[400 – 400(1.10)] = 40

25. 14-25 $ Delivery Date Futures Price for More Distant Delivery Dates 0 Now 123 P0P0 Theoretical Futures Prices F 0,1 = P 0 (1 + R 0,1 ) F 0,2 = P 0 (1 + R 0,2 ) 2 Interest F 0,3 = P 0 (1 + R 03 ) 3

26. 14-26 Delivery Date Futures Prices for More Distant Delivery Dates, Assuming 10% Interest Rate and P 0 = 400. 0 Now 123 Spot price 400 532.40 484 440 $

27. 14-27 The Impact of Convenience Yield $ Delivery date F theoretical F actual Spot price Short Long Arbitrage 012012   

28. 14-28 Futures price of light sweet crude oil observed on September 28, 1990 Delivery monthFutures price ($ per barrel) November 1990$39.51 December 1990 38.31 January 1991 36.72 February 1991 35.40 March 1991 34.15 April 1991 33.00 May 1991 31.95 June 1991 31.00 July 1991 30.20 August 1991 29.55 September 1991 29.05 October 1991 28.62 November 1991 28.27 December 1991 27.98 January 1992 27.71 February 1992 27.45 March 1992 27.20 April 1992 26.96

29. 14-29 Speculative Positions

30. 14-30

31. 14-31

32. 14-32 Short Hedge Net= [-P 0 + P 1 ] + [F 0 - F 1 ] = [  Spot] + [  F] = [-100 + 95] + [96 - 92] = [-5,000] + [4,000] = -1,000 = Net loss. 0 Close Time Sell Spot +P 1 Buy Spot -P 0 Short Futures +F 0 Delivery date Long Futures -F 1

33. 14-33 Spot and Futures Prices Spot Price Futures Price FF PP

34. 14-34 One-for-One Hedge # units of spot = # units of futures If, Partial Hedge. Optimal Hedge # units of futures = = LongShort

35. 14-35 Spot Price Futures Price $1.25 $1 Example of Optimal Hedge

36. 14-36 Optimal Hedge Rate = 1/1.25 = 0.80. For every unit long spot, go short 0.80 units of futures.  Net= (  Spot)(# Units) – (  F)(# Units) = ($1)(1) – (1.25)(0.80)  Net= 0.