© 2004 South-Western Publishing 1

Chapter 11

Fundamentals of Interest Rate Futures

2

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

3

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

4

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

5

Characteristics of U.S. Treasury Bills (cont’d)

Treasury Bill Auction ResultsTerm Issue Date Auction

DateDiscount 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

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Characteristics of U.S. Treasury Bills (cont’d)

The “Discount Rate %” is the discount yield, calculated as:

Days

360

ValuePar

PriceMarket - ValuePar YieldDiscount

7

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:

%884.090

360

000,10

90.977,9000,10

Days

360

ValuePar

PriceMarket - ValuePar YieldDiscount

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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):

maturity toDays

365

PriceDiscount

AmountDiscount Yield Equivalent Bond

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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:

%90.090

365

90.977,9

90.977,9000,10

maturity toDays

365

PriceDiscount

AmountDiscount Yield Equivalent Bond

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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

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The Treasury Bill Futures Contract (cont’d)

Futures position 91-day T-bill T-bill

established delivered matures

91 days

Time

12

The Treasury Bill Futures Contract (cont’d)

T-Bill Futures Quotations

September 15, 2000

  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

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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

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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

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The Eurodollar Futures Contract (cont’d)

Treasury Bill vs Eurodollar FuturesTreasury 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

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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:

Maturity toDays

360

icePr

DiscountYieldon -Add

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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:

$3,124.66Discount

91

360

Discount000,000,1$

Discount0124.

Maturity toDays

360

icePr

DiscountYieldon -Add

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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%:

%236.191

360

$1,000,000

$3,124.66 YieldDiscount

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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

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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?

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Speculating With Eurodollar Futures (cont’d)

Speculation Example (cont’d)

The initial price is:

150,993$360

900274.1000,000,1$Price

360

90YieldDiscount -1Value FacePrice

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Speculating With Eurodollar Futures (cont’d)

Speculation Example (cont’d)

The price with the new interest rate of 7.00% is:

00.500,982$360

900700.1000,000,1$Price

360

90YieldDiscount -1Value FacePrice

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Speculating With Eurodollar Futures (cont’d)

Speculation Example (cont’d)

The speculator’s dollar loss is therefore:

00.650,10$00.150,993$00.500,982$

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Hedging With Eurodollar Futures

Using the futures market, hedgers can lock in the current interest rate

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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.

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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.

00.000,975,9$360

9001.1000,000,10$Price

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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.

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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

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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

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Pricing of Treasury Bonds

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

N

tt

t

t

R

CP

10 )1(

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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?

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Pricing of Treasury Bonds (cont’d)

Bond Pricing Example (cont’d)

This corresponds to a newspaper price of about 100 8/32nds.

71.002,1$)0580.1(

030,1$

)0573.1(

30$0.15.00 P

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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%.

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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%

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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

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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

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Pricing Interest Rate Futures Contracts

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

tC

S

tF

CSF

t

t

tt

time tozero timefromcarry ofcost

pricecommodity spot

at timedelivery for price futures

where

)1(

,0

,0

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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)

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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

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Spreading With Interest Rate Futures

TED spread Involves the T-bill futures contract and the eurodollar futures contract

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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)– If you think the spread will widen, buy the

spread (buy T-bill, sell ED)

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Maturity Spread

NOB spread ( change of slope)

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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

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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