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Chapter 11. Fundamentals of Interest Rate Futures. 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

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chapter 11

Chapter 11

Fundamentals of Interest Rate Futures

outline
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
interest rate futures
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
treasury bills eurodollars and their futures contracts
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
characteristics of u s treasury bills
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
characteristics of u s treasury bills cont d

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)

Treasury Bill Auction Results

characteristics of u s treasury bills cont d7
Characteristics of U.S. Treasury Bills (cont’d)
  • The “Discount Rate %” is the discount yield, calculated as:
characteristics of u s treasury bills cont d8
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:

characteristics of u s treasury bills cont d9
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):
characteristics of u s treasury bills cont d10
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:

the treasury bill futures contract
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
the treasury bill futures contract cont d
The Treasury Bill Futures Contract (cont’d)

Futures position 91-day T-bill T-bill

established delivered matures

91 days

Time

the treasury bill futures contract cont d13

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

The Treasury Bill Futures Contract (cont’d)

T-Bill Futures Quotations

September 15, 2000

speculating with t bill futures
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
speculating with t bill futures cont d
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?

speculating with t bill futures cont d16
Speculating With T-Bill Futures (cont’d)

Speculation Example (cont’d)

The initial price is:

speculating with t bill futures cont d17
Speculating With T-Bill Futures (cont’d)

Speculation Example (cont’d)

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

speculating with t bill futures cont d18
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

hedging with t bill futures
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)
hedging with t bill futures cont d
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.

hedging with t bill futures cont d21
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.

hedging with t bill futures cont d22
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%
pricing interest rate futures contracts
Pricing Interest Rate Futures Contracts
  • Computation
  • Repo rates
  • Arbitrage with T-bill futures
  • Delivery options
computation
Computation
  • Interest rate futures prices come from the implications of cost of carry:
computation cont d
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)
arbitrage with t bill futures
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
the eurodollar futures contract
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
characteristics of eurodollars
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

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

One tick is $25

The Eurodollar Futures Contract (cont’d)

Treasury Bill vs Eurodollar Futures

the eurodollar futures contract cont d30
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:
the eurodollar futures contract cont d31
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:

the eurodollar futures contract cont d32
The Eurodollar Futures Contract (cont’d)

Add-On Yield Computation Example (cont’d)

If a $1 million Treasury bill sold for a discount of $16,569.97 we would determine a discount yield of 6.56%:

eurodollar futures contract
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)
eurodollar futures contract34
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
hedging with eurodollar futures
Hedging with Eurodollar Futures

Hedging Opportunities

  • hedging an expected future investment
  • hedging a future commercial paper issue
  • hedging an expected floating rate loan
hedging a floating rate loan
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
treasury bonds and their futures contracts
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
characteristics of u s treasury bonds
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
characteristics of u s treasury bonds cont d
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
pricing of treasury bonds
Pricing of Treasury Bonds
  • To find the price of a bond, discount the cash flows of the bond at the appropriate spot rates:
the treasury bond futures contract
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
dealing with coupon differences
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
the matter of accrued interest
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)
delivery procedures
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
delivery procedures cont d
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
the invoice price
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
cheapest to deliver
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
delivery options
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
delivery options cont d
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
delivery options cont d51
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
ted spread trading strategy
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
ted spread cont d
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
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
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