Chapter 11
Fundamentals of
Interest Rate
Futures
1
© 2002 South-Western Publishing
Outline







2

Interest rate futures
Treasury bills, Eurodollars, and their
futures contracts
Speculating & Hedging with T-bill futures
Hedging with Eurodollar Futures
Swap Futures Contracts - overview
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/instruments
Canada (Montreal Exchange)
–
–
–

United States
–
–
–
–
–
–
–
3
30 day Overnight ‘Repo’ rate
3 month Ba’s
2 & 10 year Gov’t of Canada bonds
Overnight fed funds and 30 day fed funds (CBOT)
Eurodollar (ED) futures contracts (CME)
T-bill contracts - 13 week (CME)
LIBOR contracts (CME)
2/5/10 year Swap Futures (CME/CBOT)
T-Notes contracts – 2/5/10 year Treasury notes (CBOT)
T-bond contracts - 30 year Treasury bonds (CBOT)
Treasury Bills, Eurodollars, and
Their Futures Contracts







4
Characteristics of U.S. Treasury bills
The Treasury bill futures contract
Characteristics of eurodollars
The eurodollar futures contract
Speculating with T-bill futures
Hedging with T-Bill futures
Pricing of interest rate futures contracts
Characteristics of U.S. Treasury
Bills
5

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) 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 360day year rather than a 365-day year
 The investment Rate or bond equivalent yield
relates the income to the discounted price paid and
uses a 365 day year
 Calculate the “Investment Rate %” (bond
equivalent yield):
Discount Amount
365
Bond Equivalent Yield 

Discount Price
Days to maturity

9
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
–
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
Speculating With T-Bill 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
–
14
a one basis point change (.01%) in the price of a
t-bill futures contract =‘s $25 change in the value
of the contract
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?
15
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 

16
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 

17
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
A 97 basis point change * $25/basis point
= - $2,425.00
18
Hedging With T-Bill Futures

Using the futures market, hedgers can lock in the
current interest rate
–
–
19
a portfolio manager who is long cash ie has cash to invest
(but not priced i.e. the investment rate is not established,
or is floating) - risk is with decreasing rates - need a long
hedge (buy futures)
a borrower is short in the cash market (loan rate not
established or is floating)- risk is with increasing rates requires a short hedge (sell futures)
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.
20
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.
21
Hedging With T-Bill Futures
(cont’d)
Hedging Example (cont’d)


22
In the futures market, you have a gain that will offset the
increased purchase price. When you close out the futures
positions, you will have effectively sold your contracts for
$13,250 more than you paid for them.
(Or you will hold on to maturity and actually take delivery of
the 10 1 million dollar t-bills)
This will be offset by a ‘loss’ in the cash market as you can
now invest the $ 10 million at the lower interest rate of 5.5%
Pricing Interest Rate Futures
Contracts




23
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
24
Computation (cont’d)

Cost of carry is the net cost of carrying the
commodity forward in time (the carry return
minus the carry charges)
–

25
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


26
If an arbitrageur can discover a disparity between the implied
financing rate and the available repo or financing rate, there
is an opportunity for riskless profit
Example-Page 248
– If the implied financing rate is greater than the borrowing
rate
 borrow for 45 days and buy 136 day bills
 sell futures contract due in 45 days
– If the implied financing rate is less than the borrowing rate
 Borrow for 136 days and buy the 45 day t-bill
 Buy futures contract due in 45 days
The Eurodollar Futures Contract

The underlying asset with a Eurodollar
futures contract is a three-month time
deposit with a $1 million face value
–
A non-transferable time deposit rather than a
security

27
The ED futures contract is cash settled with no actual
delivery
Characteristics of Eurodollars


U.S. dollars deposited in a commercial bank
outside the jurisdiction of the U.S. Federal
Reserve Board- foreign banks or foreign
branches of U.S. banks
Banks may prefer Eurodollar deposits to
domestic deposits because:
–
28
They are not subject to reserve requirement
restrictions- banks can put the full amount of the
ED amount to work without setting aside reserve
dollars
The Eurodollar Futures Contract
(cont’d)
Treasury Bill vs Eurodollar Futures
Treasury Bills
29
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)



Trade on the IMM of the Chicago Mercantile
Exchange
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
30
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:
Discount
360
Add - on Yield 

Pr ice
Days to Maturity
Discount
360
.0124 

$1,000,000  Discount 91
Discount  $3,124.66
31
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%:
$3,124.66 360
Discount Yield 

 1.236%
$1,000,000 91
32
Eurodollar Futures Contract
Settlement Procedures



33
Based on the 3 month LIBOR (London
Interbank Offered Rate)
Libor is the rate at which banks are willing
to lend funds to other banks in the
interbank market
Many floating rate U.S. dollar loans are
priced at Libor plus a margin (Libor is the
floating rate indice)
Eurodollar Futures Contract
34
Settlement Procedures
 the final settlement price is determined
by the Clearing House at the termination
of trading and at a randomly selected
time within the last 90 minutes of trading
 the settlement price is 100 minus the
mean of the LIBOR at these two times
 12 bank quotes are used
Speculating With Eurodollar
Futures
35

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?
36
Speculating With Eurodollar
Futures (cont’d)
Speculation Example (cont’d)
The initial price is:
 Discount Yield  90 
Price  Face Value 1 
360

 .0274  90 
Price  $1,000,0001 
 $993,150

360 

37
Speculating With Eurodollar
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 

38
Speculating With Eurodollar
Futures (cont’d)
Speculation Example (cont’d)
The speculator’s dollar loss is therefore:
$982,500.00  $993,150.00  $10,650.00
39
Hedging With Eurodollar Futures

40
Using the futures market, hedgers can lock
in the current interest rate
Hedging with Eurodollar
Futures
Hedging Opportunities
 hedging an expected future investment
 hedging a future commercial paper issue
 hedging a floating rate loan
41
Hedging - a floating rate loan

Same concepts and principles apply with
hedging with t-bills

long cash position
– Floating rate loan is equivalent to a long cash position e.g.
holding bonds where the risk is with increasing interest
rates
go short ED futures
– as interest rates increase- the value of the ED contract
decreases in price - a short position generates gains
futures gains offset the higher cost of borrowing in the cash
market


42
Eurodollar Hedge Example

$100 million floating rate loan as of Dec 05
–
–
–

Hedge
–
–
43
floats with 3 month libor
Rates set end of each calendar quarter
Risk – upward pressure on short term interest rates
Establish hedge – short (sell) Eurodollar futures strip –
Dec./March, June and Sept. ‘ 06 contracts
Lock in rates of 4.245%, 4.355%, 4.355% and 4.395%
respectively
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.
44
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:
 .01 90 
Price  $10,000,0001 
 $9,975,000.00

360 

This is $6,000 more than the price at the time you established
the hedge.
45
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.
46
Swap Futures Contracts




47
Recent development by both the CBOT and CME in
response to a need/opportunity
Designed to provide a means of hedging market
interest rate swaps across the 2/5/10 year horizon.
Better correlation with corporate market rates vs
Treasuries
Settle or priced to the International Swaps and
Derivatives Association (ISDA) benchmark swap
survey interest rate
Swap Futures Contracts – Pricing
Prices are established in a similar fashion to the
Eurodollar contract – index points of 100 minus the
swap rate
e.g. 94.70 represents a 10 year swap rate of 5.3%
 10 year swap rate – 10 year term for a notional
$100,000
 Price movement – one tick (1 basis point) =‘s $100.

–
Minimum movement of ¼ of one tick or $25.00
e.g. interest rates move from 5.30 % to 5.29% (one basis
point) - index moves from 94.70 to 94.71
$100,000 *.0001 * 10 (years) = $100
48
Treasury Bonds and Their
Futures Contracts








49
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:
–
–
–

Different from Treasury notes:
–
–
50
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)

Bonds are identified by:
–
–
–

51
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
52
The Treasury Bond Futures
Contract
The T-Bond contract calls for the delivery of
$100,000 face value of U.S. Treasury bonds
that have a minimum of 15 years until
maturity - if callable, they must have a
minimum of 15 years of call protection
 There are, therefore, a number of different
bonds that meet this criteria
53
Treasury Bond Futures Contract –
Pricing




54
Quoted as a percentage of par e.g. 105’14
means 105 14/32 % of par
Par is $100,000
The contract price then for a contract
quoted at 105’14 would be 105.4375 *
$100,000 =‘s $105,437.50
Assumes 6% coupon and a minimum of 15
years to maturity
Dealing With Coupon
Differences


55
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%
see table 11-7
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
56
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
–

57
Calculated using a 365-day year
Impacts the invoice price the buyer (holder
of a long futures position) must pay to the
seller (holder of the short futures position)
Delivery Procedures

Delivery actually occurs with Treasury
securities

First position day is two business days
before the first business day of the delivery
month
–
58
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)



59
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
60

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
61

Normally, only one bond eligible for delivery
will be cheapest to deliver but there will be
many that will be eligible

A short hedger will collect information on
all the deliverable bonds and select the one
most advantageous to deliver
Delivery Options

62
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)

63
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-bond futures cease trading at 3 p.m.
….but the spot market continues to trade
– 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 (2 days later)based
on a price determined up to six hours earlier
–
64
Spreading With Interest Rate
Futures - Trading Strategies


65
TED spread
The NOB spread
TED spread - trading strategy



66
Involves the T-bill futures contract and the
Eurodollar futures contract
Now with swap futures contracts – new
‘TED’ spread can be put into place on
longer dated rates e.g. 5 or 10 year
Used by traders who are anticipating
changes in relative riskiness of Eurodollar
deposits –or corporate spreads vs
treasuries
TED spread (cont’d)

67
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
– essentially a play on the changing risk structure
of interest rates
– If you think the spread will widen (eurodollar
rates less t-bill rates increasing) , buy the
spread by selling ED futures and buying t-bill
futures
The NOB Spread - trading
strategy


The NOB spread is “notes over bonds”
Traders who use NOB spreads are
speculating on shifts in a) level of the yield
curve and or b) the shape of the yield curve
(remember t-bonds have a longer
maturity/duration vs t-notes.
–
68
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