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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
- Pricing interest rate futures contracts
- Spreading with 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

- 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

- 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

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’d)

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

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’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’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

- 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)

Futures position 91-day T-bill T-bill

established delivered matures

91 days

Time

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

- 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)

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’d)

Speculation Example (cont’d)

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

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

- 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 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’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’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

- Computation
- Repo rates
- Arbitrage with T-bill futures
- Delivery options

Computation

- Interest rate futures prices come from the implications of cost of carry:

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

- 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 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

- 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

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’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’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’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

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 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 Opportunities

- hedging an expected future investment
- hedging a future commercial paper issue
- hedging an expected 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

- 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

- 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)

- 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

- 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 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

- 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 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 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)

- 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 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

- 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

- 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)

- 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’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

Spreading With Interest Rate Futures - Trading Strategies

- TED spread
- The NOB spread

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)

- 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 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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