1. FIN 413 – RISK MANAGEMENT Futures and Forward Markets

2. Topics to be covered Spot versus futures transactions Futures trading Cancelling a futures position Convergence of futures and spot prices Operation of margin Making/taking delivery Forward contracts

3. Suggested questions from Hull 6 th edition: #2.1,2.8, 2.11, 2.12, 2.21 5 th edition: #2.1,2.8, 2.11, 2.12, 2.21

4. Futures contract An agreement between two parties (a buyer and a seller) to exchange a specified quantity of an asset (the underlying asset) during a specified future period (the delivery period of the contract) at a specified place for a price (the futures price) agreed to in advance (when the contract is first entered into).

5. Spot versus futures transaction Spot transaction: Now Futures transaction: NowT Agreement is reached.Item is exchanged for $.Agreement is reached.Item is exchanged for $.

6. Futures trading Futures contract Buyer Long Seller Short Takes delivery.Makes delivery.

7. Futures trading Organized futures exchanges: CBOT: corn, soybeans, wheat, Treasury bonds, Treasury notes CME: pork bellies, live cattle, live hogs, S&P 500 stock index, foreign currencies, Eurodollars WCE: canola, flaxseed, oats, western barley ME: Canadian government bonds, S&P/TSX Canada 60 index Hull, pages 543: URLs of the major exchanges

8. History 17 th century futures market for rice, Japan 1971: Breakdown of Bretton Woods Accord 1848: CBOT 1904: WCE 1874: CME 1972: currency futures 1975: interest-rate futures 1982: stock-index futures

9. Example It is June. Vancouver food processor will require canola in September. Buys 20 metric tons in the futures market. –Instructs its broker to buy one futures contract (for the delivery of 20 metric tons of canola) with delivery in September. –Broker passes the instructions to the WCE. –Instructions are forwarded to a trader on the floor of the exchange.

10. Example (continued) The trader assesses the best price (the lowest price) available. The trader indicates a willingness to buy one September contract at that price. If another trader indicates a willingness to sell at that price, a deal is done. Otherwise, the first trader must signal a willingness to buy at a higher price. Eventually, an agreement will be reached, for example, $387 per metric ton or $7,740 in total.

11. Example (continued) The trader who agrees to sell canola at $387 per metric ton might represent an Alberta farmer. Both the food processor and the farmer have entered into a legally binding agreement. Futures prices are determined by the forces of demand and supply. Futures prices fluctuate over the life of each contract. At any time, a futures contract has zero value to a prospective buyer or seller. Apart from commissions and bid-ask spreads, a futures contract requires no initial payment or premium. The futures price simply represents the price at which the parties agree today to transact in the future. Futures exchanges offer electronic trading services.

12. Mechanics of futures trading A trader can buy/sell futures through: –A full-service futures broker. –A discount, online futures broker. Full-service broker: –Charges a commission. –Executes trades. –Provides advice and other services. –May provide online trading at reduced rates. Discount broker: –Charges a smaller commission. –Executes trades and provides fewer other services.

13. Futures markets Futures contracts trade on organized exchanges. Their terms are standardized with respect to: –The underlying asset: the required quality and quantity are specified. –Delivery location: where delivery can be made. –Delivery period: when delivery can be made. www.wce.ca

14. Futures markets Futures exchanges offer the short: –The quality option. –The delivery option. –The timing option. The price charged to the long is adjusted accordingly. If the short notifies the exchange of his/her intention to deliver, the short is matched with the buyer holding the oldest outstanding long position in the contract. The long is notified to take delivery.

15. The minimum tick The exchange does not want to keep track of price changes smaller than $0.10 per metric tonne (or $2 per contract). Transaction 1 $387 Vancouver food processor Alberta farmer Transaction 2 $387.03 $387 Some buyer Some seller

16. Life of Mar08 canola futures contract 1 st trading day t 1 Trader takes position in contract Delivery period Delivery month: March 2008 Life of contract: About 2.5 years Last trading day: March 14, 2008 F S F1F1 S1S1

17. Question & examples Question: Do farmers use futures contracts? Examples: #2.8, 2.21

18. Spot versus futures transaction Spot transaction: Now Futures transaction: NowT Agreement is reached.Item is exchanged for $.Agreement is reached.Item is exchanged for $.

19. Spot versus futures transaction – during the delivery period Spot transaction: Now Futures transaction: NowT Agreement is reached. Item is exchanged for $. T

20. Convergence of F to S Ignore transaction costs. If F > S during the delivery period: –Buy the asset for S in the spot market. –Short a futures contract. –Make delivery, selling the asset for F. Arbitrage profit per unit of underlying asset = (F -S) S rises and F falls. 1 st trading day DP Normal Market F S 1 st trading day F DP Inverted Market F S

21. Convergence of F to S Ignore transaction costs. If F < S during the delivery period: –Go long a futures contract, agreeing to buy the asset at F. –Wait for the short to make delivery. –Sell the asset in the spot market at the spot price at that time, S *. Profit per unit of underlying asset = (S*-F) F rises and S falls. 1 st trading day DP Normal Market F S 1 st trading day DP Inverted Market F S F

22. Futures price At any given time, a number of (canola) futures contracts are trading, identified by their delivery months. Mar08 and Nov08 contracts are trading currently. Assuming a normal market: Now Mar08 Nov08 S F Mar08 F Nov08

23. Cancelling a futures position Futures contract: a legally binding agreement. A position can be easily terminated: –Making/taking delivery. –Closing out or offsetting. –Undertaking an exchange-for-physicals (EFP) transaction.

24. Offsetting Action: Short (sell) five May 2008 cocoa futures Obligation: Deliver 50 metric tons of cocoa to the buyer in May 2008 Offsetting action: Go long (buy) five May 2008 cocoa futures Obligation: Zero Action: Go long (buy) two December 2009 US T-note futures Obligation: Buy $200,000 worth of US T-notes in December 2009 Offsetting action: Short (sell) two December 2009 US T-note futures Obligation: Zero

25. EFP transaction Trader ATrader B Buys 1 wheat futures contract on CBOT Sells 1 wheat futures contract on CBOT Wants to acquire actual wheatOwns wheat and wishes to sell Before EFP: EFP transaction: Exchange cancels B’s short futures position Exchange cancels A’s long futures position Reports EFP to the exchange Delivers wheat and receives payment from A Receives wheat and pays B Agrees with A to sell wheat and cancel futures Agrees with B to purchase wheat and cancel futures Trader BTrader A

26. Cancelling a futures position Very few traders (less than 2%) ever take or make delivery on a futures contract: –Inconvenient, expensive. –Not required to realize the benefits of hedging. –Speculators and arbitrageurs only want to trade the contract.

27. Light sweet crude oil futures www.nymex.com

28. Futures trading Clearinghouse CH member Broker Trader Broker Trader CH member Broker Trader Broker Trader

29. Operation of margins Margin accounts: –Clearinghouse member (with the clearinghouse) –Broker (with a CH member) –Trader (with a broker) Margin: good faith or security deposit. Initial margin: the initial amount put in a margin account by a trader to establish a futures position. Maintenance margin: the minimum amount that a trader must keep in a margin account to maintain a futures position.

30. Operation of margins Margin accounts are marked to market daily: they are adjusted daily for net gains/losses realized on a futures position. Trader: at the end of each day, his/her margin account is increased by the amount of the daily gain or reduced by the amount of the daily loss. Broker: his/her margin account is adjusted for daily net gains/losses over the accounts of all of his/her clients. Clearinghouse member: his/her margin account is adjusted daily for net gains/losses over the accounts of all of his/her clients. Purpose of margining system: To reduce credit risk, that is, to reduce the probability of market participants sustaining losses because of defaults.

31. Operation of margins Daily marking to market is equivalent to: –Closing a futures contract at the end of each day. –Opening a new contract at the beginning of the next business day with zero value to the trader.

32. Example A trader buys two November frozen orange juice futures contracts through her broker. Each contract is for the delivery of 15,000 pounds of orange juice. F 1, the current futures price, is 160 cents per pound. Initial margin: $6,000 per contract Maintenance margin: $4,500 per contract The contract is entered into on September 8 at 160 cents/pound (F 1 ) and closed out on September 14 at 161 cents/pound (F 2 ).

33. Example (continued) Futures price Daily gain (loss) Cumulative gain (loss) Margin account balance Margin call ($) Sept. 81.6012,000 Sept. 9 Sept. 10 Sept. 11 Sept. 12 Sept. 13 Sept. 14 1.857,500

34. Gain/loss on futures The long : F1F1 The long gains $-for-$ as F rises. The long loses $-for-$ as F falls. The short : F1F1 The short loses $-for-$ as F rises. The short gains $-for-$ as F falls. A futures contract is a zero-sum game.

35. Gain/loss on futures Example: Price at beginning of day = F1 = $1.50 Price at end of day = F2 = $1.60 Long’s gain (per unit of UA) on the day = (F2 – F1) = $0.10 Short’s gain (per unit of UA) on the day = (F1 – F2) = -$0.10 Long’s gain + short’s gain = 0 Example: Price at beginning of day = F1 = $1.50 Price at end of day = F2 = $1.30 Long’s gain (per unit of UA) on the day = (F2 – F1) = -$0.20 Short’s gain (per unit of UA) on the day = (F1 – F2) = $0.20 Long’s gain + short’s gain = 0

36. Example (continued) Futures price Daily gain (loss) Cumulative gain (loss) Margin account balance Margin call ($) Sept. 81.6012,000 Sept. 9 Sept. 10 Sept. 11 Sept. 12 Sept. 13 Sept. 14 Cumulative gain on September 14 = (F 2 -F 1 )×30,000 = ($1.61-$1.60)×30,000 = $300. 1.857,500 19,500 1.70(4,500)3,00015,000 1.35(10,500)(7,500)4,5007,500 1.566,300(1,200)18,300 1.560(1,200)18,300 1.611,50030019,800

37. Newspaper quotes The National Post web site, May 25, 2007: www.canada.com/national/nationalpost/financialpost/fpmarketdata HighLowMonthOpenHighLowSettleChgPrev OpInt 404.60298.10Nov07395.30404.60395.30401.40+6.2065,613 416.60349.00Mar08411.20416.60411.20413.90+3.901,404 410.00350.00Nov08407.30410.00407.30411.50+1.602,522 CANOLA (WPG) 20 metric tons, C$ per metric ton; 10 cents = $2 per contract Prev. vol. 9,635Prev. open int. 120,758 Question: Is the market normal, inverted, or mixed?

38. Making/taking delivery F 1 : futures price at the time a position is taken. The trader agrees to buy/sell at this price. Hull, page 33: “For all contracts the price (received by the short and paid by the long) is usually based on the settlement price immediately preceding the date of the notice of intention to deliver.” Contradiction?

39. Making/taking delivery T: the business day immediately preceding the date of the notice of intention to deliver F T : the settlement price at time T Effective price received by the short: F T + gain on futures = F T + (F 1 – F 2 ) + (F 2 – F 3 ) + (F 3 – F 4 ) … + (F T-1 – F T ) = F 1 Effective price paid by the long: F T + loss on futures = F T + (F 1 – F 2 ) + (F 2 – F 3 ) + (F 3 – F 4 ) … + (F T-1 – F T ) = F 1 Note: F 1 is paid/received via a sequence of daily instalments over the period the position is held, because of marking to market.

40. Example The benefits of hedging can be realized by closing out a futures position just prior to the delivery period.

41. Example Notation: F 1 : futures price at time position is taken F 2 : futures price at time position is closed S 1 : Spot price at time futures position is taken S 2 : Spot price at time futures position is closed

42. Example (continued) It is June 15. A hog farmer expects to have 90,000 pounds of hogs to sell at the end of August. To hedge, he shorts three September hog futures contracts, each for the delivery of 30,000 pounds of live hogs. F 1 = $0.75225 per pound The farmer plans to close out his short futures position on August 26 and to sell his hogs in the spot market at that time. Note: This strategy will yield the farmer a price for his hogs that is close to $0.75225 per pound. Consider two cases: S 2 = $0.73000 < $0.75225 S 2 = $0.80000 > $0.75225

43. Case 1: S 2 < F 1 Spot price Gain on futures September F1F1 F2F2 S1S1 S2S2 August 26 June 15 Effective price received by the farmer

44. Case 2: S 2 > F 1 September August 26 June 15 F1F1 F2F2 S1S1 S2S2 Spot price Loss on futures Effective price received by the farmer

45. Newspaper quotes The National Post web site, May 25, 2007: www.canada.com/national/nationalpost/financialpost/fpmarketdata HighLowMonthOpenHighLowSettleChgPrev OpInt 404.60298.10Nov07395.30404.60395.30401.40+6.2065,613 416.60349.00Mar08411.20416.60411.20413.90+3.901,404 410.00350.00Nov08407.30410.00407.30411.50+1.602,522 CANOLA (WPG) 20 metric tons, C$ per metric ton; 10 cents = $2 per contract Prev. vol. 9,635Prev. open int. 120,758

46. Hull: #2.22, page 43 “When a futures contract trades on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one.” (a)Suppose OI = 65,613 A trade takes place: A goes long entering into a new contract. B goes short entering into a new contract. OI = ? ΔOI = ?

47. Hull: #2.22, page 43 (b) Suppose OI = 65,613 A trade takes place: A goes long closing out a previous short position. B goes short closing out a previous long position. OI = ? ΔOI = ?

48. Hull: #2.22, page 43 (c) Suppose OI = 65,613 A trade takes place: A goes long entering into new contract. B goes short entering into a new contract. OI = ? ΔOI = ? Another trade occurs. C goes long entering into a new contract. A goes short closing out the previous long position. OI = ? ΔOI?

49. Open interest Open interest = 3 $290 B1 S1 $295 B2 S2 $300 B3 S3

50. Open interest A trade takes place: B4 goes long entering into a new position B3 goes short closing out her previous long position $290 B1 S1 $295 B2 S2 $300 B3 S3 $298 B4 B3

51. Open interest Open interest = 3 B4 is agreeing to buy at $298. S3 is agreeing to sell at $300. But if they take/make delivery, they will exchange the underlying asset at F T. The effective counterparty is the clearinghouse. $290 B1 S1 $295 B2 S2 $300 B3 S3 $298 B4 B3

52. Forward contract An agreement between two parties (a buyer and a seller) to exchange a specified quantity of an asset (the underlying asset) at a specified future time (the delivery date of the contract) for a price (the delivery price) agreed to in advance (when the contract is first entered into).

53. Forwards versus futures Futures contractForward contract Trades on organized futures exchange Trades OTC Has delivery periodHas a precise delivery date Usually closed out earlyUsually delivered on Settled (marked to market) daily Settled at maturity Margin requiredUsually no margin required RegulatedNot closely regulated Little credit riskCredit risk

54. Delivery price and forward price Delivery price: –The price specified in a forward contract. –Negotiated at inception; makes the contract have zero value to both parties. –Doesn’t change over the life of the contract. Forward price: –The price that, at any point in time during the life of a contract, makes the contract have zero value to both parties. –Changes over the life of the contract.

55. Forward contract Notation: K : the delivery price F : the forward price S : the spot price of the underlying asset f : the value of the contract to the long -f : the value of the contract to the short Note: A forward contract is a zero-sum game: f + (-f ) = 0

56. Life of a forward contract Without any loss of generality, assume an inverted market. 0: Inception of contract T: delivery date S0S0 F0F0 F T = S T K f -f-f Life of forward contract

57. Payoff & profit at maturity Payoff = Profit – price paid Forward contract: price paid = 0 Thus: Payoff = Profit The following terms are used interchangeably: payoff profit value gain

58. Payoff to the long at maturity Payoff at time T = F T – K = S T – K (F T = S T ) = f T STST K -K-K 0

59. Payoff to the short at maturity Payoff at time T = K – F T = K – S T (F T = S T ) = -f T STST K K 0

60. Zero-sum game Payoff to the long + payoff to the short = 0 f T + (-f T ) = 0 STST K -K-K 0 K

61. Next class Determination of forward and futures prices