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Chapter 12 Interest Rate Futures: Fundamentals. Definition Futures are marketable forward contracts. Forward contracts are agreements to buy or sell a.

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Presentation on theme: "Chapter 12 Interest Rate Futures: Fundamentals. Definition Futures are marketable forward contracts. Forward contracts are agreements to buy or sell a."— Presentation transcript:

1 Chapter 12 Interest Rate Futures: Fundamentals

2 Definition Futures are marketable forward contracts. Forward contracts are agreements to buy or sell a specified asset (commodity, index, debt security, currency, etc.) at an agreed- upon price (f) for purchase or delivery on a specified date (delivery date: T).

3 Futures Exchanges Futures are traded on organized exchanges;,such as the: –Chicago Board of Trade, CBOT –Chicago Mercantile Exchange, CME The exchanges provide marketability: –Listings –Standardization –Locals –Clearinghouse

4 Futures Exchanges U.S. Exchanges American Stock Exchange (AMEX) Chicago Board of Trade (CBOT) Chicago Board of Options Exchange (CBOE) Chicago Mercantile Exchange (CME) Coffee, Sugar, and Coca Exchange (NY) Commodity Exchange (COMEX) (NY) Kansas City Board of Trade (KCBT) Mid ‑ American Commodity Exchange (MidAm) Minneapolis Grain Exchange (MGE) New York Cotton Exchange (NYCE) New York Futures Exchange (NYFE) New York Mercantile Exchange (NYMEX) Pacific Exchange (PXS) Philadelphia Exchange (PHLX)

5 Futures Exchanges Non-U.S. Markets Amsterdam Exchange (AEX) Australian Stock Exchange (ASX) Brussels Exchange (BXS) Bolsa de Mercadorias y Futuros, Brazil (BM&F) Copenhagen Stock Exchange (FUTOP) Deutsche Termin Borse, Germany (DTB) Eurex (EUREX) International Petroleum Exchange, London (IPE) Hong Kong Futures Exchange (HKFE) Kuala Lumpur Options and Financial Futures Exchange (KLOFFE) London International Financial Futures and Options Exchange (LIFFE) Marche a Terme International de France (MATIF) Marche des Options Negociables de Paris (MONEP) MEFF Renta Fija And Variable, Spain (MEFF) New Zealand Futures and Options Exchange (NZFOE) Osaka Securities Exchange (OSA) Singapore International Monetary Exchange (SIMEX) Stockholm Options Exchange (SOM) Sydney Futures Exchange (SFE) Tokyo International Financial Futures Exchange (TIFFE) Toronto Stock Exchange (TSE) Winnipeg Commodity Exchange (WCE)

6 Futures Exchanges Alliances Eurex is an alliance of DTB, CBOT, and exchanges in Switzerland and Finland GLOBEX is an alliance of CME, ME, MATIF, SIMEX and exchanges in Brazil and the Paris Bourse. Euronext is an alliance of exchanges in Amsterdam, Brussels, and Paris

7 Futures Exchanges Futures exchanges are typically structured as membership organization with a fixed number of seats and with the seat being a precondition for direct trading on the exchange. On most futures exchanges, there are two major types of futures traders/members: commission brokers and locals. –Commission brokers buy and sell for their customers. They carry out most of the trading on the exchanges, serving the important role of linking futures traders. –Locals, on the other hand, trade from their own accounts, acting as speculators or arbitrageurs. They serve to make the market operate more efficiently.

8 Futures Exchanges Standardization –The futures exchanges provide standardization by specifying the grade or type of each asset and the size of the underlying asset. –Exchanges also specify how contract prices are quoted. For example: The contract prices on T ‑ bill futures are quoted in terms of an index equal to one hundred minus a discount yield. A T ‑ bond is quoted in terms of dollars and 1/32s of a T ‑ bond with a face value of $100.

9 Futures Exchanges Continuous Trading –Many security exchanges use market ‑ makers or specialists to ensure a continuous market. –On many futures exchanges, continuous trading also is provided, but not with market ‑ makers or specialists assigned by the exchange to deal in a specific contract. –Instead, futures exchanges such as the CBOT, CME, and LIFFE provide continuous trading through locals who are willing to take temporary positions in one or more futures.

10 Futures Exchanges Delivery Procedures –Only a small number of contracts that are entered into lead to actual delivery. –Most futures contracts are closed prior to expiration. –Nevertheless, detailed delivery procedures are important to ensure that the contract price on a futures contract are determined by the spot price on the underlying asset and that the futures price converges to the spot price at expiration.

11 Futures Exchanges Alliances and 24-Hour Trading –In addition to providing off-hour trading via electronic trading systems, 24-hour trading is also possible by using futures exchanges that offer trading on the same contract. –The CME, LIFFE, and SIMEX all offer identical contracts on 90-day Eurodollar deposits. –This makes it possible to trade the contract in the U.S., Europe, and the Far East. –Moreover, these exchanges have alliance agreements making it possible for traders to open a position in one market and close it in another. A similar alliance exists between SFE, CBOT, and LIFFE on U.S. T-bond contracts.

12 Futures Exchanges The exhibit on the next slide lists various interest rate futures contracts traded on the CBOT, CME, LIFFE, and other exchanges. Of these contracts, the four most popular are –T ‑ bonds –T ‑ notes –Eurodollar deposits –T ‑ bills

13 ContractExchangeContract Size Treasury Bond 5-Year Treasury Note Treasury Note 3-Month Treasury Bill 3-Month Eurodollar 1-Month LIBOR Municipal Bond Index 3-Month Euroyen 10-year Japanese Government Bond Index Long Gilt 3-Month Sterling Interest Rate CBOT CME CBOT SIMEX TSE LIFFE T-bond with $100,000 face value (or multiple of that) T-note with $100,000 face value (or multiple of that) $1,000,000 $3,000,000 $1,000 times the closing value of the Bond Buyer TM Municipal Bond Index (a price of 95 means a contract size of $95,000) 100,000,000 yen 100,000,000 yen face value 50,000 British pound 500,000 British pound Futures Exchanges

14 T ‑ Bill Futures T ‑ bill futures contracts call for the delivery (short position) or purchase (long position) of a T ‑ bill with a maturity of 91days and a face value (F) of $1 million. Futures prices on T ‑ bill contracts are quoted in terms of an index. This index, I, is equal to 100 minus the annual percentage discount rate, R D, for a 90-day T-bill:

15 T ‑ Bill Futures Given a quoted index value or discount yield, the actual contract price on the T ‑ bill futures contract is:

16 T ‑ Bill Futures Example: A T-bill futures contract quoted at a settlement index value of (R D = 4.38%) would have a futures contract price (f 0 ) of $989,050 and an implied YTM f of 4.515%:

17 T ‑ Bill Futures Expiration months on T ‑ bill futures are March, June, September, and December, and extend out about two years. The last trading day occurs during the third week of the expiration month, on the business day preceding the issue of spot T ‑ bills. Under the terms of the contract, delivery may occur on one of three successive business days with the delivered T-bill having a maturity of 89, 90, and 91 days.

18 Eurodollar Futures Contract A Eurodollar deposit is a time deposit in a bank located or incorporated outside the United States. A Eurodollar interest rate is the rate that one large international bank is willing to lend to another large international bank. The average rate paid by a sample of London Euro ‑ banks is known as the London Interbank Offer Rate (LIBOR). The LIBOR is higher than the T-bill rate, and is used as a benchmark rate on bank loans and deposits.

19 Eurodollar Futures Contract The CME's futures contract on the Eurodollar deposit calls for the delivery or purchase of a Eurodollar deposit with a face value of $1 million and a maturity of 90 days. The expiration months on Eurodollar futures contracts are March, June, September, and December and extend up to ten years.

20 Eurodollar Futures Contract Like T ‑ bill futures contracts, Eurodollar futures are quoted in terms of an index equal to 100 minus the annual discount rate, with the actual contract price found by using the following equation:

21 Eurodollar Futures Contract Example, given a settlement index value of on a Eurodollar contract, the actual futures price would be $987,725:

22 Eurodollar Futures Contract The major difference between the Eurodollar and T ‑ bill contracts is that Eurodollar contracts have cash settlements at delivery, while T ‑ bill contracts call for the actual delivery of the instrument. When a Eurodollar futures contract expires, the cash settlement is determined by the futures price and the settlement price.

23 Eurodollar Futures Contract The settlement price or expiration futures index price is 100 minus the average three ‑ month LIBOR offered by a sample of designated Euro-banks on the expiration date: Expiration Futures Price = 100 ‑ LIBOR

24 T ‑ Bond Futures Contracts The most heavily traded long-term interest rate futures contract is the CBOT’s T-bond contract. The contract calls for the delivery or purchase of a T ‑ bond with a maturity of at least 15 year. The CBOT has a conversion factor to determine the actual price received by the seller. The futures contract is based on the delivery of a T- bond with a face value of $100,000.

25 T ‑ Bond Futures Contracts The delivery months on the contracts are March, June, September, and December, going out approximately two years. Delivery can occur at any time during the delivery month. To ensure liquidity, any T ‑ bond with a maturity of 15 years is eligible for delivery, with a conversion factor used to determine the actual price of the deliverable bond. Since T ‑ bonds futures contracts allow for the delivery of a number of T ‑ bonds at any time during the delivery month, the CBOT's delivery procedure on such contracts is more complicated than the procedures on other futures contracts.

26 T ‑ Bond Futures Contracts T ‑ bond futures prices are quoted in dollars and 32nds for T ‑ bonds with a face value of $100. Thus, if the quoted price on a T-bond futures were of (i.e., /32 or ), the price would be $106,437 for a face value of $100,000.

27 T ‑ Bond Futures Contracts The actual price paid on the T-bond or revenue received by the seller in delivering the bond on the contract is equal to the quoted futures price times the conversion factor, CFA, on the delivered bond plus any accrued interest: Seller’s Revenue = (Quoted Futures Price)(CFA) + Accrued Interest

28 T ‑ Bond Futures Contracts Example: At the time of delivery, if the delivered bond has a CFA of 1.3 and accrued interest of $2 and the quoted futures price is 94-16, then the cash received by the seller of the bond and paid by the futures purchaser would be $ per $100 face value: Seller’s Revenue = (94.5)(1.3) + 2 =

29 T ‑ Note Futures Contracts T ‑ note contracts are similar to T-bond contracts, except that they call for the delivery of any T ‑ note with maturities between 6 1/2 and 10 years; The five-year T-note contracts are also similar to T- bond and T-note contracts except that they require delivery of the most recently auctioned five-year T- note. Both contracts, though, have delivery procedures similar to T-bond contracts.

30 Forward Contracts and Forward Rate Agreements (FRA) Forward contracts for interest rate products are private, customized contracts between two financial institutions or between a financial institution and one of its clients. Interest rate forward contracts predate the establishment of the interest rate futures market. A good example of an interest rate forward product is a forward rate agreement, FRA.

31 Forward Contracts and Forward Rate Agreements (FRA) A FRA requires a cash payment or provides a cash receipt based on the difference between a realized spot rate such as the LIBOR and a pre-specified rate. For example, the contract could be based on a specified rate of R k = 6% (annual) and the three- month LIBOR (annual) in five months and a notional principal, NP (principal used only for calculation purposes) of $10M.

32 Forward Contracts and Forward Rate Agreements (FRA) In five months the payoff would be –If the LIBOR at the end of five months exceeds the specified rate of 6%, the buyer of the FRA (or long position holder) receives the payoff from the seller. –If the LIBOR is less than 6%, the seller (or short position holder) receives the payoff from the buyer.

33 Forward Contracts and Forward Rate Agreements (FRA) If the LIBOR were at 6.5%, the buyer would be entitled to a payoff of $12,267 from the seller; If the LIBOR were at 5.5%, the buyer would be required to pay the seller $12,297.

34 Forward Contracts and Forward Rate Agreements (FRA) In general, a FRA that matures in T months and is written on a M-month LIBOR rate is referred to as a T x (T+M) agreement. Thus, in this example the FRA is a 5 x 8 agreement. At the maturity of the contract (T), the value of the contract, V T is

35 Forward Contracts and Forward Rate Agreements (FRA) FRAs originated in 1981 amongst large London Eurodollar banks that used these forward agreements to hedge their interest rate exposure. Today, FRAs are offered by banks and financial institutions in major financial centers and are often written for the bank’s corporate customers. They are customized contracts designed to meet the needs of the corporation or financial institution.

36 Forward Contracts and Forward Rate Agreements (FRA) Most FRAs do follow the guidelines established by the British Banker’s Association. Settlement dates do tend to be less than one year (e.g., 3, 6, or 9 months), although settlement dates going out as far as four years are available. The NP on a FRA can be as high as a billion and can be drawn in dollars, British pounds and other currencies.

37 Forward Contracts and Forward Rate Agreements (FRA) FRAs are used by corporations and financial institutions to manage interest rate risk in the same way as financial futures are used. Different from financial futures, FRAs are contracts between two parties and therefore are subject to the credit risk of either party defaulting. The customized FRAs are also less liquid than standardized futures contracts.

38 Futures Positions A futures holder can take one of two positions on a futures contract: a long position (or futures purchase) or a short position (futures sale). –In a long futures position, the holder agrees to buy the contract's underlying asset at a specified price, with the payment and delivery to occur on the expiration date (also referred to as the delivery date). –In a short futures position, the holder agrees to sell an asset at a specific price, with delivery and payment occurring at expiration.

39 Clearinghouse To provide contracts with marketability, futures exchanges use clearinghouses. The exchange clearinghouse is an adjunct of the exchange. It consists of clearinghouse members (many of whom are brokerage firms) who guarantee the performance of each party of the transaction and act as intermediaries by breaking up each contract after the trade has taken place.

40 Clearinghouse: Example Suppose in early June Speculator A buys a September T-bill Futures contract from Speculator B for f 0 = $987,500 (IMM = 95, R D = 5) –A is long –B is Short

41 Clearinghouse The clearinghouse (CH) would come in after Speculators A and B have reached an agreement on the price of the September T-bill contract, becoming the effective seller on A's long position and the effective buyer on B's short position. Once the clearinghouse has broken up the contract, then A's and B's contracts would be with the clearinghouse. The clearinghouse, in turn, would record the following entries in its computers.

42 Clearinghouse Clearinghouse Record: Speculator A agrees to buy September T-bill at $987,500 from the clearinghouse. Speculator B agrees to sell September T-bill at $987,500 to the clearinghouse.

43 Clearinghouse The intermediary role of the clearinghouse makes it easier for futures traders to close their positions before expiration. To see this, suppose that in June, short-term interest rates drop, leading speculators such as C to want to take a long position in the September T-bill contract.

44 Clearinghouse Seeing a profit potential from the increased demand for long positions in the September contract, suppose Speculator A agrees to sell a September T-bill futures contract to Speculator C for $988,750 (R D = 4.5% and Index = 95.5). Upon doing this, Speculator A now would be short in the new September contract, with Speculator C having a long position, and there now would be two contracts on September T-bills. After the new contract between A and C has been established, the clearinghouse would step in and break it up. For Speculator A, the clearinghouse's records would now show the following.

45 Clearinghouse Clearinghouse Records for Speculator A: Speculator A agrees to BUY September T-bill from the clearinghouse for $987,500. Speculator A agrees to SELL September T-bill to the clearinghouse for $988,750. The clearinghouse accordingly would close Speculator A's positions by paying her $1,250 at expiration.

46 Clearinghouse Since Speculator A's short position effectively closes her position, it is variously referred to as a closing, reversing out, or offsetting position or simply as an offset. Thus, the clearinghouse makes it easier for futures contracts to be closed prior to expiration. The expense and inconvenience of delivery causes most futures traders to close their positions instead of taking delivery.

47 Clearinghouse As the delivery date approaches, the number of outstanding contracts, referred to as open interest, declines, with only a relatively few contracts still outstanding at delivery.

48 Clearinghouse At expiration (T), the contract prices on futures contracts established on that date (f T ) should be equal (or approximately equal for some contracts) to the prevailing spot price on the underlying asset (S T ). If f T does not equal S T at expiration, an arbitrage opportunity would exist. Arbitrageurs could take a position in the futures market and an opposite position in the spot market.

49 Clearinghouse For example, if the September T-bill futures contracts were trading at $990,000 on the delivery date in September and the spot price on T-bills were trading at $990,500, an arbitrageur could –go long in the September contract, –take delivery by buying the T-bill at $990,000 on the futures contract, –then sell the bill on the spot at $990,500 to earn a risk-free profit of $500. The arbitrageur’s efforts to take a long position, though, would drive the contract price up to $990,500.

50 Clearinghouse On the other hand, if f T exceeds $990,500, then an arbitrageur would reverse their strategy, pushing f T down to $990,500. Thus at delivery, arbitrageurs will ensure that the price on an expiring contracts is equal to the spot price. As a result, closing a futures contract with an offsetting position at expiration will yield the same profits or losses as purchasing (selling) the asset on the spot and selling (buying) it on the futures contract.

51 Clearinghouse Example: Suppose near the delivery date on the September contract the spot T-bill price and the price on the expiring September futures contracts are $990,000 (R D = 4% or Index = 96). To close his existing short contract, Speculator B would need to take a long position in the September contract, while to offset her existing long contract, Speculator C would need to take a short position.

52 Clearinghouse Suppose Speculators B and C take their offsetting positions with each other on the expiring September T-bill contract priced at f T = S T = $990,000. After the clearinghouse breaks up the new contract, Speculator B would owe the clearinghouse $2,500 and Speculator C would receive $1,250 from the clearinghouse.

53 Clearinghouse Clearinghouse Records for Speculator B: Speculator B agrees to SELL September T-bill to CH for $987,500. Speculator B agrees to BUY September T-bill from CH at $990,000. Speculator B would pay the CH $2,500.

54 Clearinghouse Clearinghouse Records for Speculator C: Speculator C agrees to BUY September T-bill at $988,750. Speculator C agrees to SELL September T-bill for $990,000. CH would pay Speculator C $1,250.

55 Clearinghouse To recapitulate: –The contract prices on September T-bill contracts went from $987,500 on the A and B contract, to $988,750 on the A and C contract, to $990,000 on the B and C contract at expiration. –Speculators A and C each received $1,250 from the clearinghouse. –Speculator B paid $2,500 to the clearinghouse. –The clearinghouse with a perfect hedge on each contract received nothing (other than clearinghouse fees attached to the commission charges). –No T-bill was actually purchased or delivered.

56 Margins Since a futures contract is an agreement, it has no initial value. Futures traders, however, are required to post some margin -- security or good faith money with their brokers. Depending on the brokerage firm, the customer's margin requirement can be satisfied either in the form of cash or cash ‑ equivalents. Futures contracts have both initial and maintenance margin requirements.

57 Margins The initial (or performance) margin is the amount of cash or cash equivalents that must be deposited by the investor on the day the futures position is established. The futures trader does this by setting up a margin (or commodity) account with the broker and depositing the required cash or cash equivalents. The amount of the margin is determined by the margin requirement, defined as a proportion (m) of the contract value (usually 3% to 5%).

58 Margins Example: If the initial margin requirement is 5%, then Speculators A and B in our example would be required to deposit $49,375 in cash or cash equivalents in their commodity accounts as good faith money on their September futures contracts: m[Contract Value] =.05[$987,500] = $49,375

59 Margins At the end of each trading day, the futures trader’s account is adjusted to reflect any gains or losses based on the settlement price on new contracts. In our example, suppose the day after Speculators A and B established their respective long and short positions, the settlement index value on the September T-bill was 95.5 (f t = 988,750, R D = 4.5%). The value of A's and B's margin accounts would therefore be: A: Account Value = $49,375 + ($988,750 - $987,500) = $50,625 B: Account Value = $49,375 + ($987,500 - $988,750) = $48,125

60 Margins With a lower rate and higher futures price, A’s long position has increase in value by $1,250 and B’s short position has decreased by $1,250. When there is a decrease in the account value, the futures trader’s broker has to exchange money through the clearing firm equal to the loss on the position to the broker and clearinghouse with the gain. This process is known as marking to market. Thus in our case, B’s broker and clearing firm would pass on $1,250 to A’s broker and clearing firm.

61 Margins To ensure that the balance in the trader’s account does not become negative, the brokerage firm requires a margin to be maintained by the futures traders. The maintenance (or variation) margin is the amount of additional cash or cash equivalents that futures traders must deposit to keep the equity in their commodity account equal to a certain percentage (e.g., 75%) of the initial margin value.

62 Margins If the maintenance margin requirements were equal to 100% of the initial margin, then A and B would have to keep the equity values of their accounts equal to $49,375. If Speculator B did not deposit the required margin immediately, then he would receive a margin call from the broker instructing him to post the required amount of funds. If Speculator B did not comply with the margin call, the broker would close the position.

63 Futures Hedging Futures markets provide corporations, financial institutions, and others with –a tool for hedging their particular spot positions against adverse price movements, –for speculating on expected spot price changes, and –for creating synthetic debt and investment positions with better rates than direct positions. Of theses uses, the most extensive one is hedging.

64 Futures Hedging Two hedging positions exist: Long hedge Short hedge

65 Futures Hedging In a long hedge (or hedge purchase), a hedger takes a long position in a futures contract to protect against an increase in the price of the underlying asset or commodity. Long hedge positions on debt securities are used by money-market managers, fixed-income managers, and dealers to lock in their costs on future security purchases.

66 Futures Hedging In a short hedge, a hedger takes a short futures position to protect against a decrease in the price of the underlying asset. Short hedge positions are used: –by bond and money market managers, investment bankers, and dealers who are planning to sell securities in the future –by banks and other intermediaries to lock in the rates they pay on future deposits –by corporate treasurers and other borrowers who want to lock in the future rates on their loans or who want to fix the rates on the floating rate loans.

67 Long Futures Hedge: Example Consider the case of a money market manager who is expected a cash inflow of $9,875,000 in September that he plans to invest in a 90-day jumbo certificates of deposit, CD, with a face value of $10M. Fearing that short-term rates could decrease (causing CD prices to increase), suppose the manager goes long in ten September Eurodollar futures trading at R D = 5% or f 0 = $987,500.

68 Long Futures Hedge: Example Given equal spot and expiring futures prices at expiration, the manager will find that –Any additional costs of buying the jumbo CD above the $9,875,000 price on the spot market will be offset by a profit from his futures position. –Any benefits from the costs of the CD being less than the $9,875,000 price would be negated by losses on the Eurodollar futures position. As a result, the manager’s costs of buying CDs on the spot and closing his futures position would be $9,875,000.

69 Long Futures Hedge: Example In the exhibit on the next slide, the third row shows three possible costs of buying the $10M face value CD at the September delivery date of $9,850,000 $9,875,000 and $9,900,000 given settlement LIBORs of 6%, 5%, and 4%. The fourth row shows the profits and losses from the long futures position in which the offset position has a contract or cash settlement price (f T ) equal to the spot price (S T ). The last row shows the net costs of $9,875,000 resulting from purchasing the CDs and closing the futures position.

70 Long Futures Hedge: Example Positions6%5%4% (1) September Spot R D (2) September Spot and futures Price (3) Cost of $10M face value 90-day CD (4) Profit on Futures 6% $985,000 $9,850,000 ($25,000) 5% $987,500 $9,875, % $990,000 $9,900,000 $25,000 Net Costs: Row (3) – Row (4)$9,875,000 Initial Position: Long in 10 September Eurodollar futures contracts at R D = 5 (Index = 95, f 0 = $987,500) to hedge $9,875,000 CD investment in September. Profit on futures = 10 (Spot Price - $987,500)

71 Short Futures Hedge: Example Consider the case of a fixed-income manager who in July anticipates needing cash in September that she plans to obtain by selling ten 6% T-bonds, each with a face value of $100,000 and currently trading at par. Suppose that the September T-bond futures contract is trading at 100, and at the time of the anticipated September sale, the T-bonds will be at a coupon date with a maturity of exactly 15 years and no accrued interest at that date. If the manager wants to lock in a September selling price on her T-bonds of $100,000 per bond, she could go short in 10 September T-bond futures contracts.

72 Short Futures Hedge: Example At the September expiration, if the cheapest-to- deliver bond is the 15-year, 6% coupon bond with a conversion factor of 1, then the treasurer would receive $1M in revenue at delivery from selling her T-bonds on the spot market and closing the futures contract by going long in the expiring September contract trading at price equal to the spot price on the 15-year, 6% T-bond.

73 Short Futures Hedge: Example In the exhibit on the next slide: –The second row shows three revenue amounts from selling the ten T-bonds at three possible spot T-bond prices of 95, 100, 105. –The third row shows the profits and losses from the futures position. –The last row shows the hedged revenue from aggregating both positions. Thus, regardless of the spot price, the manager receives $1,000,000 from selling the bonds and closing the futures positions.

74 Short Futures Hedge: Example Initial Position: Short in 10 September T-bond futures contracts at f 0 = 100 to hedge a September sale of 10 T-bonds. At the delivery date the 10 T-bonds each have a maturity of 15 years, no accrued interest, and can be delivered on the futures contracts with a conversion factor of 1. Positions (1) September spot and futures Price (2) Revenue from sale of 10 T-bonds (3) Profit on futures $95,000 $950,000 $50,000 $100,000 $1,000,000 0 $105,000 $1,050,000 ($50,000) Net Revenue: Row (2) + Row (3)$1,000,000 Profit on futures = 10 ($100,000 – Spot Price)

75 Short Futures Hedge: Example It should be noted that in determining the futures positions, hedgers need to take into account the cheapest-to-deliver bond, accrued interest, and a conversion factor that is likely to be different than 1.

76 Hedging Risk The above examples represent perfect hedging cases in which certain revenues or costs can be locked in at a future date. In practice, perfect hedges are the exception and not the rule.

77 Hedging Risk There are three types of hedging risk that preclude one from obtaining a zero risk position: 1.Quality Risk 2.Timing Risk 3.Quantity Risk

78 Hedging Risk Quality Risk Quality risk exists when the commodity or asset being hedged is not identical to the one underlying the futures contract. The manager in our long hedge example, for instance, may be planning to purchase commercial paper instead of a T-bill. In such hedging cases, futures contracts written on a different underlying asset are often used to hedge the spot asset. These types of hedges are known as cross hedges. Unlike direct hedges in which the future's underlying asset is the same as the asset being hedged, cross ‑ hedging cannot eliminate risk, but can minimize it.

79 Hedging Risk Timing risk Timing risk occurs when the delivery date on the futures contract does not coincide with the date the hedged asset needs to be purchased or sold. For example, timing risk would exist in our long hedging example if the manager needed to buy the CDs on the first of September instead of at the futures' expiration at the end of the September.

80 Hedging Risk Timing Risk If the spot asset is purchased or sold at a date that differs from the expiration date on the futures contract, then the price on the futures (f t ) and the spot price (S t ) will not necessarily be equal. The difference between the futures and spot price is called the basis (B t ). The basis tends to narrow as expiration nears, converging to zero at expiration (B T = 0). Prior to expiration, the basis can vary, with greater variability usually observed the longer the time is to expiration.

81 Hedging Risk Timing Risk Given basis risk, the greater the time difference between buying or selling the hedged asset and the futures' expiration date, the less perfect the hedge. To minimize timing risk or basis risk, hedgers often select futures contracts that mature before the hedged asset is to be bought or sold but as close as possible to that date. For very distant horizon dates, though, hedgers sometimes follow a strategy known as rolling the hedge forward. This hedging strategy involves taking a futures position, then at expiration closing the position and taking a new one.

82 Hedging Risk Quantity Risk Because of the standardization of futures contracts, futures hedging also is subject to quantity risk.

83 Websites Chicago Mercantile Exchange: Chicago Board of Trade: Commodity Futures Trading Commission: National Futures Association:

84 Websites For more information on futures and links to other sites with futures information go to Current prices on futures contracts on Eurodollar and T- bill and other futures can be obtained by going to and clicking on “Quotes” in “Market Data” and then clicking on “Interest Rate Products.” For T-bonds, T-notes, and other futures go to and click on “Quotes and Data.”

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