1. © 2004 South-Western Publishing 1 Chapter 11 Fundamentals of Interest Rate Futures

2. 2 Summary Reconcile expectation and Cost of Carry hypothesis of pricing future contracts on foreign exchange Find forward exchange rate based on IRP and PPP Learn term structure of interest rates and its use in pricing financial assets

3. 3 Outline Interest rate futures – yield curve 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

4. 4 Interest Rate Futures Exist across the yield curve and on many different types of interest rates – U.S. Treasury Bills – Eurodollar (ED) futures contracts – 30-day Federal funds contracts – Other Treasury contracts

5. 5 Characteristics of U.S. Treasury Bills 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) T- bills are sold at a weekly auction

6. 6 Characteristics of U.S. Treasury Bills (cont’d) Treasury Bill Auction Results TermIssue DateAuction Date Discount Rate % Investment Rate % Price Per $100 13-week01-02-200412-29-20030.8850.90199.779 26-week01-02-200412-29-20030.9951.01699.500 4-week12-26-200312-23-20030.8700.88299.935 13-week12-26-200312-22-20030.8700.88499.783 26-week12-26-200312-22-20030.9700.99299.512 4-week12-18-200312-16-20030.8300.85099.935

7. 7 Characteristics of U.S. Treasury Bills (cont’d) The “Discount Rate %” is the discount yield, calculated as:

8. 8 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:

9. 9 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):

10. 10 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:

11. 11 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 – On the day the Treasury bills are delivered, they mature in 91 days

12. 12 The Treasury Bill Futures Contract (cont’d) Futures position 91-day T-bill T-bill established delivered matures 91 days Time

13. 13 The Treasury Bill Futures Contract (cont’d) T-Bill Futures Quotations September 15, 2000 OpenHighLowSettleChangeSettleChangeOpen Interest Sept 94.03 94.02 -.015.98+.011,311 Dec94.00 93.9693.97-.026.03+.021,083

14. 14 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: – They are not subject to reserve requirement restrictions – Every ED received by a bank can be reinvested somewhere else

15. 15 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 The ED futures contract is cash settled with no actual delivery

16. 16 The Eurodollar Futures Contract (cont’d) Treasury Bill vs Eurodollar Futures Treasury BillsEurodollars Deliverable underlying commodityUndeliverable underlying commodity Settled by deliverySettled by cash TransferableNon-transferable Yield quoted on discount basisYield quoted on add-on basis Maturities out to one yearMaturities out to 10 years One tick is $25

17. 17 The Eurodollar Futures Contract (cont’d) The quoted yield with eurodollars is an add- on yield For a given discount, the add-on yield will exceed the corresponding discount yield:

18. 18 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:

19. 19 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%:

20. 20 Speculating With Eurodollar Futures 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

21. 21 Hedging With Eurodollar Futures Using the futures market, hedgers can lock in the current interest rate

22. 22 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.

23. 23 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: This is $6,000 more than the price at the time you established the hedge.

24. 24 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.

25. 25 Characteristics of U.S. Treasury Bonds Very similar to corporate bonds: – Pay semiannual interest – Have a maturity of up to 30 years – Are readily traded in the capital markets Different from Treasury notes: – Notes have a life of less than ten years – Some T-bonds may be callable fifteen years after issuance

26. 26 Characteristics of U.S. Treasury Bonds (cont’d) Bonds are identified by: – 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

27. 27 Pricing of Treasury Bonds To find the price of a bond, discount the cash flows of the bond at the appropriate spot rates:

28. 28 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?

29. 29 Pricing of Treasury Bonds (cont’d) Bond Pricing Example (cont’d) This corresponds to a newspaper price of about 100 8/32nds.

30. 30 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%.

31. 31 Dealing With Coupon Differences 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%

32. 32 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 – Calculated using a 365-day year

33. 33 Cheapest to Deliver 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

34. 34 Pricing Interest Rate Futures Contracts Interest rate futures prices come from the implications of cost of carry:

35. 35 Computation 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 zero Solving for C in the futures pricing equation yields the implied repo rate (implied financing rate)

36. 36 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 – If the implied financing rate is greater than the borrowing rate, then he/she could borrow, buy T- bills, and sell futures – If the implied financing rate is lower than the borrowing rate, he/she could borrow, buy T-bills, and buy futures

37. 37 Spreading With Interest Rate Futures TED spread Involves the T-bill futures contract and the eurodollar futures contract

38. 38 Maturity Spread NOB spread ( change of slope)

39. 39 Summary 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