1. Fundamentals of Interest Rate Futures
Chapter 11
Fundamentals of Interest Rate Futures
© 2002 South-Western Publishing

2. Outline 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) T-bills are sold at a weekly auction

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

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

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:

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 360-day 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):

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:

11. 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

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

13. 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

14. 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
a one basis point change (.01%) in the price of a t-bill 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 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?

16. Speculating With T-Bill Futures (cont’d)
Speculation Example (cont’d)
The initial price is:

17. Speculating With T-Bill Futures (cont’d)
Speculation Example (cont’d)
The price with the new interest rate of 7.00% is:

18. Speculating With T-Bill Futures (cont’d)
Speculation Example (cont’d)
The speculator’s dollar loss is therefore:
A 97 basis point change * $25/basis point
= - $2,425.00

19. 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)

20. 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, for $1 million in T-bills if you buy a futures contract at Using the $10 million figure, you decide to buy 10 DEC T-bill futures, promising to pay $9,849,250.

21. 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:
This is $13,250 more than the price at the time you established the hedge.

22. 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%

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

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

25. 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)

26. 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

27. 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

28. 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

29. 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

30. The Eurodollar Futures Contract (cont’d)
Trade on the IMM of the Chicago Mercantile Exchange
The quoted yield with eurodollars is an add-on yield
For a given discount, the add-on yield will exceed the corresponding discount yield:

31. 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:

32. 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, we would determine a discount yield of 6.56%:

33. Eurodollar Futures Contract
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)

34. Eurodollar Futures Contract
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

36. 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

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

38. 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 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 to 94.71
$100,000 *.0001 * 10 (years) = $100

40. 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:

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 /32 % of par
Par is $100,000
The contract price then for a contract quoted at 105’14 would be * $100,000 =‘s $105,437.50

46. 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%
see table 11-7

47. Dealing With Coupon Differences (cont’d)

48. 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
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

59. 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.
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