11
Fundamentals Chapter of Interest Rate Futures
1
2002 South-Western Publishing
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
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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
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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
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Characteristics of U.S. Treasury Bills
Sell
at a discount from par using a 360-day year and twelve 30-day months (13-week) and 182-day (26-week) Tbills are sold at a weekly auction
91-day
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Characteristics of U.S. Treasury Bills (contd)
Treasury Bill Auction Results
Term 91-day 182-day 91-day 182-day 14-day 364-day Issue Date 09-21-2000 09-21-2000 09-14-2000 09-14-2000 09-01-2000 08-31-2000 Maturity Date 12-21-2000 03-22-2001 12-14-2000 03-15-2001 09-15-2000 08-30-2001 Discount Rate % 5.960 5.935 5.945 5.955 6.44 5.880 Investment Rate % 6.137 6.203 6.121 6.226 6.53 6.241 Price Per $100 98.493 97.000 98.497 96.989 99.750 94.055
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Characteristics of U.S. Treasury Bills (contd)
The
Discount Rate % is the discount yield, calculated as:
Par Value - Market Price 360 Discount Yield = Par Value Days
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Characteristics of U.S. Treasury Bills (contd)
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
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Characteristics of U.S. Treasury Bills (contd)
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):
Discount Amount 365 Bond Equivalent Yield = Discount Price Days to maturity
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Characteristics of U.S. Treasury Bills (contd)
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
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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
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The Treasury Bill Futures Contract (contd)
Futures position established 91-day T-bill delivered T-bill matures
91 days
Time
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The Treasury Bill Futures Contract (contd)
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
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Speculating With T-Bill Futures
The
price of a fixed income security moves inversely with market interest rates practice is to compute futures price changes by using 90 days until expiration
Industry
a one basis point change (.01%) in the price of a t-bill futures contract =s $25 change in the value of the contract
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Speculating With T-Bill Futures (contd)
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 (contd)
Speculation Example (contd)
The initial price is:
Discount Yield 90 Price = Face Value1 360 .0603 90 Price = $1,000,0001 = $984,925.00 360
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Speculating With T-Bill Futures (contd)
Speculation Example (contd)
The price with the new interest rate of 7.00% is:
Discount Yield 90 Price = Face Value1 360 .0700 90 Price = $1,000,0001 = $982,500.00 360
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Speculating With T-Bill Futures (contd)
Speculation Example (contd)
The speculators 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, risk is with decreasing rates need a long hedge (buy futures) a borrower is short in the cash market, risk is with increasing rates - requires a short hedge (sell futures)
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Hedging With T-Bill Futures (contd)
Hedging Example
Assume you are a portfolio managers for a universitys 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 (contd)
Hedging Example (contd)
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.
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Hedging With T-Bill Futures (contd)
Hedging Example (contd)
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:
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 (contd)
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 rate, there is an opportunity for riskless profit
If the implied financing rate is greater than the borrowing rate (example - page 285)
borrow for 45 days and buy 136 day bills sell futures contract due in 45 days
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Futures Pricing - The Introductory Math
Work
through the text examples 284-286
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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 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 because:
They deposits are not subject to reserve requirement restrictions- banks can put the full amount of the ED amount to work without setting aside reserve dollars
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The Eurodollar Futures Contract (contd)
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
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The Eurodollar Futures Contract (contd)
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
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The Eurodollar Futures Contract (contd)
Add-On Yield Computation Example
An add-on yield of 6.74% corresponds to a discount of $16,569.97:
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Discount 360 Add - on Yield = Pr ice Days to Maturity Discount 360 .0674 = $1,000,000 Discount 90 Discount = $16,569.97
The Eurodollar Futures Contract (contd)
Add-On Yield Computation Example (contd)
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
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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
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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
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Hedging with Eurodollar Futures
Hedging Opportunities hedging an expected future investment hedging a future commercial paper issue hedging an expected floating rate loan
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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 increases in price - a short position generates gains
futures
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gains offset the higher cost of borrowing in the cash market
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
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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
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Characteristics of U.S. Treasury Bonds (contd)
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 6% coupon rate that mature in 2023
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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
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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
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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
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Dealing With Coupon Differences (contd)
CF = 1
x
(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
C C 1 1 + 2 0.06 (1.03) 2N
C 6X 1 + (1.03) 2N 2 6
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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
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the invoice price the buyer (holder of a long futures position) must pay to the seller (holder of the short futures po...