Chapter 11

1. Chapter 11 Fundamentals of Interest Rate Futures

2. Outline • Interest rate futures • Treasury bills, eurodollars, and their futures contracts • Hedging with eurodollar futures • Treasury bonds and their futures contracts • Pricing interest rate futures contracts • Spreading with interest rate futures

3. Interest Rate Futures • Exist across the yield curve and on many different types of interest rates • T-bond contracts • Eurodollar (ED) futures contracts • 30-day Federal funds contracts • Other Treasury contracts

4. Treasury Bills, Eurodollars, and Their Futures Contracts • Characteristics of U.S. Treasury bills • The Treasury bill futures contract • Characteristics of eurodollars • The eurodollar futures contract • Speculating with eurodollar futures

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. 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) Treasury Bill Auction Results

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

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

13. 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 The Treasury Bill Futures Contract (cont’d) T-Bill Futures Quotations September 15, 2000

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. 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. Treasury Bills 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) Treasury Bill vs Eurodollar Futures

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. 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. 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. 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. 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?

22. Speculating With Eurodollar Futures (cont’d) Speculation Example (cont’d) The initial price is:

23. Speculating With Eurodollar Futures (cont’d) Speculation Example (cont’d) The price with the new interest rate of 7.00% is:

24. Speculating With Eurodollar Futures (cont’d) Speculation Example (cont’d) The speculator’s dollar loss is therefore:

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

26. 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.

27. 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.

28. 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.

29. Treasury Bonds and Their Futures Contracts • Characteristics of U.S. Treasury bonds • Pricing of Treasury bonds • The Treasury bond futures contract • Dealing with coupon differences • The matter of accrued interest • Delivery procedures • The invoice price • Cheapest to deliver

30. 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

31. 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

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

33. 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?

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

35. 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%.

36. 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%

37. Dealing With Coupon Differences (cont’d)

38. 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

39. Delivery Procedures • Delivery actually occurs with Treasury securities • First position day is two business days before the first business day of the delivery month • Everyone with a long position in T-bond futures must report to the Clearing Corporation a list of their long positions

40. Delivery Procedures (cont’d) • On intention day, a short seller notifies the Clearing Corporation of intent to deliver • The 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 invoice • The next day is delivery day, when the final instrument actually changes hands

41. The Invoice Price • The cash that changes hands at futures settlement equals the futures settlement price multiplied by the conversion factors, plus any accrued interest • The invoice price is the amount that the deliverer of the bond receives from the purchaser

42. 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

43. Pricing Interest Rate Futures Contracts • Computation • Repo rates • Arbitrage with T-bill futures • Delivery options

44. Computation • Interest rate futures prices come from the implications of cost of carry:

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

46. 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

47. Delivery Options • The Quality Option • A person with a short futures position has the prerogative to deliver any T-bond that satisfies the delivery requirement • People with the long position do not know which particular Treasury security they will receive

48. Delivery Options (cont’d) • The Timing Option • The holder of a short position can initiate the delivery process any time the exchange is open during the delivery month • Valuable to the arbitrageur who seeks to take advantage of minor price discrepancies

49. Delivery Options (cont’d) • The Wild Card Option • T-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 evening • In essence, the short hedger may make a transaction and receive cash based on a price determined up to six hours earlier

50. Spreading With Interest Rate Futures • TED spread • The NOB spread • Other spreads with financial futures