Chapter 11 Fundamentals of Interest Rate Futures 1 © 2004 South-Western Publishing Outline Interest rate futures – yield curve http://www.bank-banque-canada.ca/cgi-bin/famecgi_fdps Treasury bills, eurodollars, and their futures contracts Discount yield vs. Investment Rate %” (bond equivalent yield): Pricing interest rate futures contracts Spreading with interest rate futures 2 Interest Rate Futures Exist across the yield curve and on many different types of interest rates – U.S. Treasury Bills – – – 3 Eurodollar (ED) futures contracts 30-day Federal funds contracts Other Treasury contracts Characteristics of U.S. Treasury Bills 4 Sell at a discount from par using a 360-day year and twelve 30-day months 91-day (13-week) and 182-day (26-week) Tbills are sold at a weekly auction Characteristics of U.S. Treasury Bills (cont’d) Treasury Bill Auction Results 5 Term Issue Date Auction Date Discount Rate % Investment Rate % Price Per $100 13-week 01-02-2004 12-29-2003 0.885 0.901 99.779 26-week 01-02-2004 12-29-2003 0.995 1.016 99.500 4-week 12-26-2003 12-23-2003 0.870 0.882 99.935 13-week 12-26-2003 12-22-2003 0.870 0.884 99.783 26-week 12-26-2003 12-22-2003 0.970 0.992 99.512 4-week 12-18-2003 12-16-2003 0.830 0.850 99.935 Characteristics of U.S. Treasury Bills (cont’d) The “Discount Rate %” is the discount yield, calculated as: Discount Yield 6 Par Value - Market Price 360 Par Value Days Characteristics 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: Par Value - Market Price 360 Discount Yield Par Value Days 10,000 9,977.90 360 0.884% 10,000 90 7 Characteristics 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 year – Calculate the “Investment Rate %” (bond equivalent yield): Bond Equivalent Yield 8 Discount Amount 365 Discount Price Days to maturity Characteristics 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: Discount Amount 365 Bond Equivalent Yield Discount Price Days to maturity 10,000 9,977.90 365 0.90% 9,977.90 90 9 The Treasury Bill Futures Contract Treasury bill futures contracts call for the delivery of $1 million par value of 91-day T-bills on the delivery date of the futures contract – 10 On the day the Treasury bills are delivered, they mature in 91 days The Treasury Bill Futures Contract (cont’d) Futures position 91-day T-bill T-bill established delivered matures 91 days Time 11 The Treasury Bill Futures Contract (cont’d) T-Bill Futures Quotations September 15, 2000 12 Open High Low Settle Change Settle Change Open Interest Sept 94.03 94.03 94.02 94.02 -.01 5.98 +.01 1,311 Dec 94.00 94.00 93.96 93.97 -.02 6.03 +.02 1,083 Characteristics of Eurodollars Applies to any U.S. dollar deposited in a commercial bank outside the jurisdiction of the U.S. Federal Reserve Board Banks may prefer eurodollar deposits to domestic deposits because: – – 13 They are not subject to reserve requirement restrictions Every ED received by a bank can be reinvested somewhere else The Eurodollar Futures Contract The underlying asset with a eurodollar futures contract is a three-month, $1 million face value instrument – A non-transferable time deposit rather than a security 14 The ED futures contract is cash settled with no actual delivery The Eurodollar Futures Contract (cont’d) Treasury Bill vs Eurodollar Futures Treasury Bills 15 Eurodollars Deliverable underlying commodity Undeliverable underlying commodity Settled by delivery Settled by cash Transferable Non-transferable Yield quoted on discount basis Yield quoted on add-on basis Maturities out to one year Maturities out to 10 years One tick is $25 One tick is $25 The Eurodollar Futures Contract (cont’d) The quoted yield with eurodollars is an addon yield For a given discount, the add-on yield will exceed the corresponding discount yield: Discount 360 Add - on Yield Pr ice Days to Maturity 16 The 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: Discount 360 Add - on Yield Pr ice Days to Maturity Discount 360 .0124 $1,000,000 Discount 91 Discount $3,124.66 17 The 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%: $3,124.66 360 Discount Yield 1.236% $1,000,000 91 18 Speculating With Eurodollar Futures 19 The price of a fixed income security moves inversely with market interest rates Industry practice is to compute futures price changes by using 90 days until expiration Speculating 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? 20 Speculating With Eurodollar Futures (cont’d) Speculation Example (cont’d) The initial price is: Discount Yield 90 Price Face Value 1 360 .0274 90 Price $1,000,0001 $993,150 360 21 Speculating With Eurodollar Futures (cont’d) Speculation Example (cont’d) The price with the new interest rate of 7.00% is: Discount Yield 90 Price Face Value 1 360 .0700 90 Price $1,000,000 1 $982,500.00 360 22 Speculating With Eurodollar Futures (cont’d) Speculation Example (cont’d) The speculator’s dollar loss is therefore: $982,500.00 $993,150.00 $10,650.00 23 Hedging With Eurodollar Futures 24 Using the futures market, hedgers can lock in the current interest rate Hedging 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. 25 Hedging 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: .01 90 Price $10,000,0001 $9,975,000.00 360 This is $6,000 more than the price at the time you established the hedge. 26 Hedging 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. 27 Characteristics of U.S. Treasury Bonds Very similar to corporate bonds: – – – Different from Treasury notes: – – 28 Pay semiannual interest Have a maturity of up to 30 years Are readily traded in the capital markets Notes have a life of less than ten years Some T-bonds may be callable fifteen years after issuance Characteristics of U.S. Treasury Bonds (cont’d) Bonds are identified by: – – – 29 The issuer The coupon The year of maturity E.g., “U.S. government six and a quarters of 23” means Treasury bonds with a 6¼% coupon rate that mature in 2023 Pricing of Treasury Bonds To find the price of a bond, discount the cash flows of the bond at the appropriate spot rates: Ct P0 t t 1 (1 Rt ) N 30 Pricing 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? 31 Pricing of Treasury Bonds (cont’d) Bond Pricing Example (cont’d) $30 $1,030 P0 $1,002.71 0.5 1.0 (1.0573) (1.0580) This corresponds to a newspaper price of about 100 8/32nds. 32 Pricing 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 financial calculator. The yield to maturity in this example is 5.72%. 33 Dealing With Coupon Differences 34 To 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% The Matter of Accrued Interest The Treasury only mails interest payment checks twice a year, but bondholders earn interest each calendar day they hold a bond When someone buys a bond, they pay the accrued interest to the seller of the bond – 35 Calculated using a 365-day year Cheapest to Deliver 36 Normally, only one bond eligible for delivery will be cheapest to deliver A hedger will collect information on all the deliverable bonds and select the one most advantageous to deliver Pricing Interest Rate Futures Contracts Interest rate futures prices come from the implications of cost of carry: Ft S (1 C0,t ) where Ft futures price for delivery at time t C0 , t 37 S spot commodity price cost of carry from time zero to time t Computation Cost of carry is the net cost of carrying the commodity forward in time (the carry return minus the carry charges) – 38 If you can borrow money at the same rate that a Treasury bond pays, your cost of carry is zero Solving for C in the futures pricing equation yields the implied repo rate (implied financing rate) Arbitrage With T-Bill Futures If an arbitrageur can discover a disparity between the implied financing rate and the available repo rate, there is an opportunity for riskless profit – – 39 If the implied financing rate is greater than the borrowing rate, then he/she could borrow, buy Tbills, and sell futures If the implied financing rate is lower than the borrowing rate, he/she could borrow, buy T-bills, and buy futures Spreading With Interest Rate Futures TED spread Involves the T-bill futures contract and the eurodollar futures contract 40 TED spread (different yield curves) 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 month (T-bill yield<ED yield) – 41 If you think the spread will widen, buy the spread (buy T-bill, sell ED) Maturity Spread 42 NOB spread ( change of slope) The NOB Spread The NOB spread is “notes over bonds” Traders who use NOB spreads are speculating on shifts in the yield curve – 43 If 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 futures Summary 44 Discount vs. investment (bond, add-on) yield Bond pricing (new based on yield curve) Pricing of Interest rate future and Arbitrage Spreading Interest rate futures