1
Chapter 11
Fundamentals of
Interest Rate
Futures
© 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

3
Interest Rate Futures



Exist across the yield curve and on many different types of interest rates/instruments
Canada (Montreal Exchange)
–
–
30 day Overnight ‘Repo’ rate
3 month Ba’s
–
2 & 10 year Gov’t of Canada bonds
United States
– 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)

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 T-bill futures
 Hedging with T-Bill futures
 Pricing of interest rate futures contracts

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) Tbills are sold at a weekly auction

6
Characteristics of U.S. Treasury
Bills (cont’d)
Term
91-day
182-day
91-day
182-day
14-day
364-day
Treasury Bill Auction Results
Issue Date Maturity
Date
Discount
Rate %
Investment
Rate %
09-21-2000 12-21-2000 5.960
6.137
09-21-2000
09-14-2000
03-22-2001
12-14-2000
5.935
5.945
6.203
6.121
09-14-2000
09-01-2000
08-31-2000
03-15-2001
09-15-2000
08-30-2001
5.955
6.44
5.880
6.226
6.53
6.241
Price Per
$100
98.493
97.000
98.497
96.989
99.750
94.055

7
Characteristics of U.S. Treasury
Bills (cont’d)

The “Discount Rate %” is the discount yield , calculated as:
Discount Yield

Par Value Market
Par Value
Price

360
Days

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:
Discount Yield

Par Value Market
Par Value
Price

10 , 000

9 , 849 .
30
10 , 000

360
91

360
Days

5 .
96 %

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 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) :
Bond Equivalent Yield

Discount
Discount
Amount
Price

365
Days to maturity

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:
Bond Equivalent Yield

Discount
Discount
Amount
Price

Days to maturity

10 , 000

9 , 849 .
30
9 , 849 .
30

365
91

365
6 .
14 %

11
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
– On the day the Treasury bills are delivered, they mature in 91 days

12
The Treasury Bill Futures
Contract (cont’d)
Futures position established
91-day T-bill delivered
91 days
T-bill matures
Time

13
The Treasury Bill Futures
Contract (cont’d)
Open High
T-Bill Futures Quotations
September 15, 2000
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
14
 Industry practice is to compute futures price changes by using 90 days until expiration
– a one basis point change (.01%) in the price of a tbill futures contract =‘s $25 change in the value of the contract

15
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?

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Speculating With T-Bill Futures
(cont’d)
Speculation Example (cont’d)
The initial price is:
Price
Price

Face Value

 1 -
Discount Yield
360

$ 1 , 000 , 000

 1

.
0603

360
90




90


$ 984 , 925 .
00

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Speculating With T-Bill Futures
(cont’d)
Speculation Example (cont’d)
The price with the new interest rate of 7.00% is:
Price
Price

Face Value

 1 -
Discount Yield
360

$ 1 , 000 , 000

 1

.
0700

90
360




90


$ 982 , 500 .
00

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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

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Hedging With T-Bill Futures
 Using the futures market, hedgers can lock in the current interest rate
–
– 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)

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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:
Price

$ 10 , 000 , 000

 1

.
055

360
90



$ 9 , 862 , 500 .
00
This is $13,250 more than the price at the time you established the hedge.

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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.
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%

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

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Computation
 Interest rate futures prices come from the implications of cost of carry:
F t

S ( 1

C
0 , t
)
C
0
F
S t where
 futures price for delivery at time t
 spot commodity price
 cost of carry from time zero to time t
, 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)
– 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 or financing rate, there is an opportunity for riskless profit
Example-Page 285
– 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

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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
 The ED futures contract is cash settled with no actual delivery

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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:
– 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)
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Treasury Bill vs Eurodollar Futures
Treasury Bills
Deliverable underlying commodity
Settled by delivery
Transferable
Yield quoted on discount basis
Maturities out to one year
One tick is $25
Eurodollars
Undeliverable underlying commodity
Settled by cash
Non-transferable
Yield quoted on add-on basis
Maturities out to 10 years
One tick is $25

The Eurodollar Futures Contract
(cont’d)
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 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:
Add on Yield

Discount
Pr ice

360
Days to Maturity

The Eurodollar Futures Contract
(cont’d)
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Add-On Yield Computation Example
An add-on yield of 6.74% corresponds to a discount of
$16,569.97:
Add on Yield

Discount
Pr ice

360
Days to Maturity
.
0674
Discount

Discount
$ 1 , 000 , 000

Discount

$16,569.97

360
90

32
The Eurodollar Futures Contract
(cont’d)
AddOn 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%:
Discount Yield

$16,569.97
$1,000,000

360
91

6 .
56 %

Eurodollar Futures Contract
33
Settlement Procedures
 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

35
Hedging with Eurodollar
Futures
Hedging Opportunities
 hedging an expected future investment
 hedging a future commercial paper issue
 hedging a floating rate loan

Hedging - a floating rate loan
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



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

37
Eurodollar Hedge Example


$100 million floating rate loan as of June 04
– floats with 3 month libor
–
–
Rates set end of each calendar quarter
Risk – upward pressure on short term interest rates
Hedge
– Establish hedge – short (sell) Eurodollar futures strip –
Sept/Dec./March and June. 05 contracts
– Lock in rates of 2.055%, 2.565%, 3.02% and 3.415% respectively

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Swap Futures Contracts




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

39
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

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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

41
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

42
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

43
Pricing of Treasury Bonds
 To find the price of a bond, discount the cash flows of the bond at the appropriate spot rates:
P
0
 t
N


1
( 1

C t
R t
) t

44
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

45
Treasury Bond Futures Contract –
Pricing

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

46
Dealing With Coupon
Differences
 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

47
Dealing With Coupon
Differences (cont’d)
CF

1
(1.03) x
6



C
2

C
0 .
06


1

1
( 1 .
03 )
2N



1
( 1 .
03 )
2N




C
2 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
6
X

The Matter of Accrued Interest
48
 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
 Impacts the invoice price the buyer (holder of a long futures position) must pay to the seller (holder of the short futures position)

49
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

50
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

51
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

52
Cheapest to Deliver
 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

53
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

54
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

55
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 (2 days later)based on a price determined up to six hours earlier

56
Spreading With Interest Rate
Futures - Trading Strategies
 TED spread
 The NOB spread

57
TED spread - trading strategy
 Involves the T-bill futures contract and the
Eurodollar futures contract
 Used by traders who are anticipating changes in relative riskiness of Eurodollar deposits

58
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
– 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
59
 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.
– 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