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

© 2002 South-Western Publishing 1

Chapter 11

Fundamentals of Interest Rate Futures

2

Outline

Interest rate futures Treasury bills, Eurodollars, and their futures

contracts Speculating & Hedging with T-bill futures Hedging with Eurodollar Futures 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

– Eurodollar (ED) futures contracts– T-bill contracts– LIBOR contracts– T-Notes contracts - 10 year Treasury notes– T-bond contracts - 30 year Treasury bonds

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

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 ResultsTerm Issue Date Maturity

DateDiscount 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

7


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

Days

360

ValuePar

PriceMarket - ValuePar YieldDiscount

8


Discount Yield Computation Example

For the first T-bill in the table on slide 6, the discount yield is:

%96.591

360

000,10

30.849,9000,10

Days

360

ValuePar

PriceMarket - ValuePar YieldDiscount

9


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):

maturity toDays

365

PriceDiscount

AmountDiscount Yield Equivalent Bond

10


Bond Equivalent Yield Computation Example

For the first T-bill in the table on slide 6, the bond equivalent yield is:

%14.691

365

30.849,9

30.849,9000,10

maturity toDays

365

PriceDiscount

AmountDiscount Yield Equivalent Bond

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 91-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 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

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 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?

16


Speculation Example (cont’d)

The initial price is:

00.925,984$360

900603.1000,000,1$Price

360

90YieldDiscount -1Value FacePrice

17



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

00.500,982$360

900700.1000,000,1$Price

360

90YieldDiscount -1Value FacePrice

18



The speculator’s dollar loss is therefore:

00.425,2$00.925,984$00.500,982$

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 $984,925.00 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.

21


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.

00.500,862,9$360

90055.1000,000,10$Price

22


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:

tC

S

tF

CSF

t

t

tt

time tozero timefromcarry ofcost

pricecommodity spot

at timedelivery for price futures

where

)1(

,0

,0

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 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

30


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:

Maturity toDays

360

icePr

DiscountYieldon -Add

31


Add-On Yield Computation Example

An add-on yield of 6.74% corresponds to a discount of $16,569.97:

$16,569.97Discount

90

360

Discount000,000,1$

Discount0674.

Maturity toDays

360

icePr

DiscountYieldon -Add

32


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%:

%56.691

360

$1,000,000

$16,569.97 YieldDiscount

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 indicie)

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 an expected floating rate loan

36

Hedging - a floating rate loan

Same concepts and principles apply long cash position

– risk is with higher 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

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

38

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

39

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

40

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(

41

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

42

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

43

Dealing With Coupon Differences (cont’d)

N whole theof excessin months ofnumber theX

maturity toyears wholeofnumber N

form decimalin coupon annualC

factor conversion CF

where

6

X6

2)03.1(

1

)03.1(

11

06.02(1.03)

1 CF

2N2N6

x

CCC

44

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)

45

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

46

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

47

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

48

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

49

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

50

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

51

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

52

Spreading With Interest Rate Futures - Trading Strategies

TED spread The NOB spread

53

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

54

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

55

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

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

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