Tài chính doanh nghiệp - Chapter 11: Fundamentals of interest rate futures

© 2004 South-Western Publishing1Chapter 11Fundamentals of Interest Rate Futures2OutlineInterest rate futuresTreasury bills, eurodollars, and their futures contractsHedging with eurodollar futuresTreasury bonds and their futures contractsPricing interest rate futures contractsSpreading with interest rate futures3Interest Rate FuturesExist across the yield curve and on many different types of interest ratesT-bond contractsEurodollar (ED) futures contracts30-day Federal funds contractsOther Treasury contracts4Treasury Bills, Eurodollars, and Their Futures ContractsCharacteristics of U.S. Treasury billsThe Treasury bill futures contractCharacteristics of eurodollarsThe eurodollar futures contractSpeculating with eurodollar futures5Characteristics of U.S. Treasury BillsSell at a discount from par using a 36-day year and twelve 30-day months91-day (13-week) and 182-day (26-week) T-bills are sold at a weekly auction6Characteristics of U.S. Treasury Bills (cont’d)Treasury Bill Auction Results TermIssue DateAuction DateDiscount Rate %Investment Rate %Price Per $10013-week01-02-200412-29-20030.8850.90199.77926-week01-02-200412-29-20030.9951.01699.5004-week12-26-200312-23-20030.8700.88299.93513-week12-26-200312-22-20030.8700.88499.78326-week12-26-200312-22-20030.9700.99299.5124-week12-18-200312-16-20030.8300.85099.9357Characteristics of U.S. Treasury Bills (cont’d)The “Discount Rate %” is the discount yield, calculated as:8Characteristics of U.S. Treasury Bills (cont’d)Discount Yield Computation Example For the first T-bill in the table on slide 6, the discount yield is: 9Characteristics of U.S. Treasury Bills (cont’d)The discount yield relates the income to the par value rather than to the price paid and uses a 360-day year rather than a 365-day yearCalculate the “Investment Rate %” (bond equivalent yield):10Characteristics of U.S. Treasury Bills (cont’d)Bond Equivalent Yield Computation Example For the first T-bill in the table on slide 6, the bond equivalent yield is:11The Treasury Bill Futures ContractTreasury bill futures contracts call for the delivery of $1 million par value of 91-day T-bills on the delivery date of the futures contractOn the day the Treasury bills are delivered, they mature in 91 days12The Treasury Bill Futures Contract (cont’d)Futures position 91-day T-bill T-bill established delivered matures 91 days Time13The Treasury Bill Futures Contract (cont’d)T-Bill Futures QuotationsSeptember 15, 2000  OpenHighLowSettleChangeSettleChangeOpen InterestSept94.0394.0394.0294.02-.015.98+.011,311Dec94.0094.0093.9693.97-.026.03+.021,08314Characteristics of EurodollarsApplies to any U.S. dollar deposited in a commercial bank outside the jurisdiction of the U.S. Federal Reserve BoardBanks may prefer eurodollar deposits to domestic deposits because:They are not subject to reserve requirement restrictionsEvery ED received by a bank can be reinvested somewhere else15The Eurodollar Futures ContractThe underlying asset with a eurodollar futures contract is a three-month, $1 million face value instrumentA non-transferable time deposit rather than a securityThe ED futures contract is cash settled with no actual delivery16The Eurodollar Futures Contract (cont’d)Treasury Bill vs Eurodollar Futures Treasury BillsEurodollarsDeliverable underlying commodityUndeliverable underlying commoditySettled by deliverySettled by cashTransferableNon-transferableYield quoted on discount basisYield quoted on add-on basisMaturities out to one yearMaturities out to 10 yearsOne tick is $25One tick is $2517The Eurodollar Futures Contract (cont’d)The quoted yield with eurodollars is an add-on yieldFor a given discount, the add-on yield will exceed the corresponding discount yield:18The Eurodollar Futures Contract (cont’d)Add-On Yield Computation Example An add-on yield of 1.24% corresponds to a discount of $3,124.66:19The Eurodollar Futures Contract (cont’d)Add-On Yield Computation Example (cont’d) If a $1 million Treasury bill sold for a discount of $3,124.66 we would determine a discount yield of 1.236%:20Speculating With Eurodollar FuturesThe price of a fixed income security moves inversely with market interest ratesIndustry practice is to compute futures price changes by using 90 days until expiration21Speculating With Eurodollar Futures (cont’d)Speculation Example Assume a speculator purchased a MAR 05 ED futures contract at a price of 97.26. The ED futures contract has a face value of $1 million. Suppose the discount yield at the time of purchase was 2.74%. In the middle of March 2005, interest rates have risen to 7.00%. What is the speculator’s dollar gain or loss?22Speculating With Eurodollar Futures (cont’d)Speculation Example (cont’d) The initial price is:23Speculating With Eurodollar Futures (cont’d)Speculation Example (cont’d) The price with the new interest rate of 7.00% is:24Speculating With Eurodollar Futures (cont’d)Speculation Example (cont’d) The speculator’s dollar loss is therefore:25Hedging With Eurodollar FuturesUsing the futures market, hedgers can lock in the current interest rate26Hedging With Eurodollar Futures (cont’d)Hedging Example Assume you are a portfolio managers for a university’s endowment fund which will receive $10 million in 3 months. You would like to invest the money now, as you think interest rates are going to decline. Because you want a money market investment, you establish a long hedge in eurodollar futures. Using the figures from the earlier example, you are promising to pay $993,150.00 for $1 million in eurodollars if you buy a futures contract at 98.76. Using the $10 million figure, you decide to buy 10 MAR ED futures, promising to pay $9,969,000. 27Hedging With Eurodollar Futures (cont’d)Hedging Example (cont’d) When you receive the $10 million in three months, assume interest rate have fallen to 1.00%. $10 million in T-bills would then cost: This is $6,000 more than the price at the time you established the hedge.28Hedging With Eurodollar Futures (cont’d)Hedging Example (cont’d) In the futures market, you have a gain that will offset the increased purchase price. When you close out the futures positions, you will sell your contracts for $6,000 more than you paid for them.29Treasury Bonds and Their Futures ContractsCharacteristics of U.S. Treasury bondsPricing of Treasury bondsThe Treasury bond futures contractDealing with coupon differencesThe matter of accrued interestDelivery proceduresThe invoice priceCheapest to deliver30Characteristics of U.S. Treasury BondsVery similar to corporate bonds:Pay semiannual interestHave a maturity of up to 30 yearsAre readily traded in the capital marketsDifferent from Treasury notes:Notes have a life of less than ten yearsSome T-bonds may be callable fifteen years after issuance31Characteristics of U.S. Treasury Bonds (cont’d)Bonds are identified by:The issuerThe couponThe year of maturityE.g., “U.S. government six and a quarters of 23” means Treasury bonds with a 6¼% coupon rate that mature in 2023 32Pricing of Treasury BondsTo find the price of a bond, discount the cash flows of the bond at the appropriate spot rates:33Pricing of Treasury Bonds (cont’d)Bond Pricing Example Suppose we have a government bond with one year remaining to maturity and a coupon rate of 6%. 6-months spot rates are 5.73% and 12 months spot rates are 5.80%. What is the price of the bond?34Pricing of Treasury Bonds (cont’d)Bond Pricing Example (cont’d) This corresponds to a newspaper price of about 100 8/32nds. 35Pricing of Treasury Bonds (cont’d)Bond Pricing Example (cont’d) To solve for the yield to maturity, we can either look at a “bond book,” use a spreadsheet package, or use a trial and error approach. The yield to maturity in this example is 5.72%.36Dealing With Coupon DifferencesTo standardize the $100,000 face value T-bond contract traded on the Chicago Board of Trade, a conversion factor is used to convert all deliverable bonds to bonds yielding 6%37Dealing With Coupon Differences (cont’d)38The Matter of Accrued InterestThe Treasury only mails interest payment checks twice a year, but bondholders earn interest each calendar day they hold a bondWhen someone buys a bond, they pay the accrued interest to the seller of the bondCalculated using a 365-day year39Delivery ProceduresDelivery actually occurs with Treasury securitiesFirst position day is two business days before the first business day of the delivery monthEveryone with a long position in T-bond futures must report to the Clearing Corporation a list of their long positions40Delivery Procedures (cont’d)On intention day, a short seller notifies the Clearing Corporation of intent to deliverThe next day is notice of intention day, when the Clearing Corporation notifies both parties of the other’s identity and the short seller prepares an invoiceThe next day is delivery day, when the final instrument actually changes hands41The Invoice PriceThe cash that changes hands at futures settlement equals the futures settlement price multiplied by the conversion factors, plus any accrued interestThe invoice price is the amount that the deliverer of the bond receives from the purchaser42Cheapest to DeliverNormally, only one bond eligible for delivery will be cheapest to deliverA hedger will collect information on all the deliverable bonds and select the one most advantageous to deliver43Pricing Interest Rate Futures ContractsComputationRepo ratesArbitrage with T-bill futuresDelivery options44ComputationInterest rate futures prices come from the implications of cost of carry:45Computation (cont’d)Cost of carry is the net cost of carrying the commodity forward in time (the carry return minus the carry charges)If you can borrow money at the same rate that a Treasury bond pays, your cost of carry is zeroSolving for C in the futures pricing equation yields the implied repo rate (implied financing rate)46Arbitrage With T-Bill FuturesIf an arbitrageur can discover a disparity between the implied financing rate and the available repo rate, there is an opportunity for riskless profitIf the implied financing rate is greater than the borrowing rate, then he/she could borrow, buy T-bills, and sell futuresIf the implied financing rate is lower than the borrowing rate, he/she could borrow, buy T-bills, and buy futures47Delivery OptionsThe Quality OptionA person with a short futures position has the prerogative to deliver any T-bond that satisfies the delivery requirementPeople with the long position do not know which particular Treasury security they will receive48Delivery Options (cont’d)The Timing OptionThe holder of a short position can initiate the delivery process any time the exchange is open during the delivery monthValuable to the arbitrageur who seeks to take advantage of minor price discrepancies49Delivery Options (cont’d)The Wild Card OptionT-bonds cease trading at 3 p.m.A person may choose to initiate delivery any time between the 3 p.m. settlement and 9 p.m. that eveningIn essence, the short hedger may make a transaction and receive cash based on a price determined up to six hours earlier50Spreading With Interest Rate FuturesTED spreadThe NOB spreadOther spreads with financial futures51TED spreadInvolves the T-bill futures contract and the eurodollar futures contractUsed by traders who are anticipating changes in relative riskiness of eurodollar deposits52TED spread (cont’d)The TED spread is the difference between the price of the U.S. T-bill futures contract and the eurodollar futures contract, where both futures contracts have the same delivery monthIf you think the spread will widen, buy the spread53The NOB SpreadThe NOB spread is “notes over bonds”Traders who use NOB spreads are speculating on shifts in the yield curveIf you feel the gap between long-term rates and short-term rates is going to narrow, you could buy T-note futures contracts and sell T-bond futures54Other Spreads With Financial FuturesLED spreadMOB spread55LED SpreadLED spread is the LIBOR-eurodollar spreadLIBOR is the London Inter-Bank Offered RateTraders adopt this strategy because of a belief about a change in the slope of the yield curve or because of apparent arbitrage in the forward rates associated with the implied yields56MOB SpreadThe MOB spread is “municipals over bonds”It is a play on the taxable bond market (Treasury bonds) versus the tax-exempt bond market (municipal bonds)Trader buys the futures contract that is expected to outperform the other and sells the weaker contract