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

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

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

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

Characteristics of U.S. Treasury Bills Sell at a discount from par using a 36-day year and twelve 30-day months 91-day (13-week) and 182-day (26-week) T-bills are sold at a weekly auction

Characteristics of U.S. Treasury Bills (cont’d) Treasury Bill Auction Results 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 0.995 1.016 99.500 4-week 12-26-2003 12-23-2003 0.870 0.882 99.935 12-22-2003 0.884 99.783 0.970 0.992 99.512 12-18-2003 12-16-2003 0.830 0.850

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

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:

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):

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:

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

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

The Treasury Bill Futures Contract (cont’d) T-Bill Futures Quotations September 15, 2000   Open High Low Settle Change Open Interest Sept 94.03 94.02 -.01 5.98 +.01 1,311 Dec 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: 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 The ED futures contract is cash settled with no actual delivery

The Eurodollar Futures Contract (cont’d) Treasury Bill vs Eurodollar Futures 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

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:

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:

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%:

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

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?

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

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

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

Hedging With Eurodollar Futures 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.

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.

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.

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

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

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

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

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?

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

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 trial and error approach. The yield to maturity in this example is 5.72%.

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%

Dealing With Coupon Differences (cont’d)

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

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

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

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

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

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

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

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)

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

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

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

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

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

TED spread Involves the T-bill futures contract and the eurodollar futures contract Used by traders who are anticipating changes in relative riskiness of eurodollar deposits

TED 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 month If you think the spread will widen, buy the spread

The NOB Spread The NOB spread is “notes over bonds” Traders who use NOB spreads are speculating on shifts in the yield curve 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

Other Spreads With Financial Futures LED spread MOB spread

LED Spread LED spread is the LIBOR-eurodollar spread LIBOR is the London Inter-Bank Offered Rate Traders 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 yields

MOB Spread The 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