Chapter 11
Fundamentals of
Interest Rate
Futures
1
© 2002 South-Western Publishing
Outline
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2
Interest rate futures
Treasury bills, Eurodollars, and their
futures contracts
Hedging with T-bill 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
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3
T-bond contracts
Eurodollar (ED) futures contracts
T-bill contracts
Federal funds contracts
LIBOR contracts
Treasury Bills, Eurodollars, and
Their Futures Contracts
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4
Characteristics of U.S. Treasury bills
The Treasury bill futures contract
Characteristics of eurodollars
The eurodollar futures contract
Speculating with T-bill futures
Characteristics of U.S. Treasury
Bills
5

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) Tbills are sold at a weekly auction
Characteristics of U.S. Treasury
Bills (cont’d)
Treasury Bill Auction Results
6
Term
Issue Date
Maturity
Date
Discount
Rate %
Investment
Rate %
Price Per
$100
91-day
09-21-2000
12-21-2000
5.960
6.137
98.493
182-day
09-21-2000
03-22-2001
5.935
6.203
97.000
91-day
09-14-2000
12-14-2000
5.945
6.121
98.497
182-day
09-14-2000
03-15-2001
5.955
6.226
96.989
14-day
09-01-2000
09-15-2000
6.44
6.53
99.750
364-day
08-31-2000
08-30-2001
5.880
6.241
94.055
Characteristics of U.S. Treasury
Bills (cont’d)

The “Discount Rate %” is the discount
yield, calculated as:
Par Value - Market Price 360
Discount Yield 

Par Value
Days
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:
Par Value - Market Price 360
Discount Yield 

Par Value
Days
10,000  9,849.30 360


 5.96%
10,000
91
8
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 
9
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  9,849.30 365


 6.14%
9,849.30
91
10
The Treasury Bill Futures
Contract

Treasury bill futures contracts call for the
delivery of $1 million par value of 91-day Tbills on the delivery date of the futures
contract
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11
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
12
The Treasury Bill Futures
Contract (cont’d)
T-Bill Futures Quotations
September 15, 2000
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
Characteristics of Eurodollars
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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:
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14
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
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A non-transferable time deposit rather than a
security
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15
The ED futures contract is cash settled with no actual
delivery
The Eurodollar Futures Contract
(cont’d)
Treasury Bill vs Eurodollar Futures
Treasury Bills
16
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)
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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
17
The Eurodollar Futures Contract
(cont’d)
Add-On Yield Computation Example
An add-on yield of 6.74% corresponds to a discount of
$16,569.97:
Discount
360
Add - on Yield 

Pr ice
Days to Maturity
Discount
360
.0674 

$1,000,000  Discount 90
Discount  $16,569.97
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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 $16,569.97
we would determine a discount yield of 6.56%:
$16,569.97 360
Discount Yield 

 6.56%
$1,000,000 91
19
Speculating With T-Bill Futures
20

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 T-Bill Futures
(cont’d)
Speculation Example
Assume a speculator purchased a DEC T-Bill
futures contract at a price of 93.97. The T-bill
futures contract has a face value of $1 million.
Suppose the discount yield at the time of purchase
was 6.03%. In the middle of December, interest
rates have risen to 7.00%. What is the speculators
dollar gain or loss?
21
Speculating With T-Bill Futures
(cont’d)
Speculation Example (cont’d)
The initial price is:
 Discount Yield  90 
Price  Face Value 1 
360

 .0603  90 
Price  $1,000,000 1 
 $984,925.00

360 

22
Speculating With T-Bill 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 

23
Speculating With T-Bill Futures
(cont’d)
Speculation Example (cont’d)
The speculator’s dollar loss is therefore:
$982,500.00  $984,925.00  $2,425.00
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Hedging With T-Bill Futures
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25
Using the futures market, hedgers can lock
in the current interest rate
Hedging With T-Bill 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 in T-bills, as you think interest rates
are going to decline. Because you want the T-bills, you
establish a long hedge in T-bill futures. Using the figures from
the earlier example, you are promising to pay $984,925.00 for
$1 million in T-bills if you buy a futures contract at 93.97.
Using the $10 million figure, you decide to buy 10 DEC T-bill
futures, promising to pay $9,849,250.
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Hedging With T-Bill Futures
(cont’d)
Hedging Example (cont’d)
When you receive the $10 million in three months, assume
interest rate have fallen to 5.50%. $10 million in T-bills would
then cost:
 .055  90 
Price  $10,000,000 1 
 $9,862,500.00

360 

This is $13,250 more than the price at the time you
established the hedge.
27
Hedging With T-Bill 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 $13,250 more than
you paid for them.
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Treasury Bonds and Their
Futures Contracts
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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
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Very similar to corporate bonds:
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Different from Treasury notes:
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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)
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Bonds are identified by:
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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
32
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)
$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.
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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 trial and error approach. The yield to maturity
in this example is 5.72%.
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Dealing With Coupon
Differences
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36
To standardize the $100,000 face value
Tbond 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)
CF 
1
x
C
 C 6X

C 
1
1
1 

 

 
2N 
2N 
 2 0.06  (1.03)  (1.03)  2  6 
(1.03) 6
where
CF  conversion factor
C  annual coupon in decimal form
N  number of whole years to maturity
X  the number of months in excess of the whole N
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The Matter of Accrued Interest
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The Treasury only mails interest payment
checks twice a year, but bondholders earn
interest each calendar day they hold a bond
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When someone buys a bond, they pay the
accrued interest to the seller of the bond
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Calculated using a 365-day year
Delivery Procedures
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Delivery actually occurs with Treasury
securities
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First position day is two business days
before the first business day of the delivery
month
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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)
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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
41

The cash that changes hands at futures
settlement equals the futures settlement
price multiplied by the conversion factors,
plus any accrued interest
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The invoice price is the amount that the
deliverer of the bond receives from the
purchaser
Cheapest to Deliver
42

Normally, only one bond eligible for delivery
will be cheapest to deliver
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A hedger will collect information on all the
deliverable bonds and select the one most
advantageous to deliver
Pricing Interest Rate Futures
Contracts
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Computation
Repo rates
Arbitrage with T-bill futures
Delivery options
Computation

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
S  spot commodity price
C0,t  cost of carry from time zero to time t
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Computation (cont’d)

Cost of carry is the net cost of carrying the
commodity forward in time (the carry return
minus the carry charges)
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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
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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
Delivery Options
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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)
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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
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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
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TED spread
The NOB spread
Other spreads with financial futures
TED spread
51

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
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If you think the spread will widen, buy the
spread
The NOB Spread
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The NOB spread is “notes over bonds”
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Traders who use NOB spreads are
speculating on shifts in the yield curve
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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
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LED spread
MOB spread
LED Spread

LED spread is the LIBOR-Eurodollar spread
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55
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
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56
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