Interest Rate Futures

Professor Brooks

BA 444

02/14/08

The Underlying Asset

Bonds or Interest Bearing Accounts These can be real or fictitious bonds They are interest rate sensitive

As interest rates change the value of the underlying changes

Therefore can be used to hedge interest rates

PriceRate

Interest Rate Futures

Domestic Set of Underlyings U.S. Treasury Bills, Notes, and Bonds For Delivery

T-Bill, 91-Day Notes, 2 and 5 years Bonds, 10 and 30 years

Around the World Eurodollars (most popular) – U.S. dollars in a

foreign bank Euroyen, Euroswiss, Euibor, etc.

T-Bill as the Underlying Asset

T-Bills -- sold with maturities of 4 weeks, 13 weeks and 26 weeks Pure Discount Bill Pay “market price” today and it grows to

maturity or face value with no interest payments

Quoted on a Bank Discount Basis

360

Maturity toDaysyielddiscount -1 ValuePar Price

Auctions for T-Bills

All buyers get the same price Bids are in yields…

Use yield to find price, Example, discount yield is 1.5% on 13 week T-bill, Price of T-bill: $9,962.08

08.962,9$360

91015.0-1 000,10$Price

True Yield on the T-Bill

Correcting for 360 days a year (should be 365) Correcting for using maturity as investment price (should be the

purchase price) Bond Equivalent Yield

BEY = (Par – Price)/(Price) x 365/(Days to Maturity) Example: BEY = ($10,000 - $9962.08) / $9,962.08 x 365/91 BEY = 0.0152662 or 1.5266% This is simple interest

Correcting for compound interest True Yield = (Par Value / Price) (365 / Days to Maturity) - 1 True Yield = ($10,000 / $9662.08)(365 / 91) -1 = 0.0153539 True Yield = 1.5354%

T-Bill as Underlying Asset

At Delivery, you will deliver (take delivery) T-Bill with 91 days to maturity (13-weeks) Par Value of the T-Bill is $1,000,000

Futures Price is the Bank Discount Yield The anticipated 13-week T-Bill rate Remember when you enter the Futures

contract it has a delivery date for the T-Bill with 13 weeks t maturity

See Figure 11-1 on page 234

T-Bill Futures Prices

On CME Look at February ‘08 – Settle at (9)96920

My best guess on CME prices is that the first nine is not displayed…

http://www.cme.com What is the implied discount for the T-Bill for

delivery? 0.01218 or 1.218% discount This annualized as BEY is 1.239%

Eurodollars as Underlying

The interest rate on U.S. dollars deposited in a foreign bank (main activity in London) Not a security Nontransferable bank deposit You are buying or selling a “savings account” Three month savings account with $1,000,000

maturity (or other maturities) Savings rate is LIBOR…an average of a

survey of banks Add-On yield – but again simple interest

Futures Price of ED Underlying

Let’s assume quote for Futures is 2.00% or that at the maturity of the Futures contract you will get savings account that in three months will mature at $1,000,000 with a current price that implies a 2% interest rate.

360

Day x Yield x Price Discount

Eurodollar Underlying

To find the Value of the savings account at deposit… Price is present value of the Par Value At the periodic discount rate

Convert the annual yield to periodic rate and find price of underlying “savings account”

360Days

discount1

ValuePar Price

Eurodollar Underlying

Add-on Yield is quoted as 0.0124 or 1.24% Convert to periodic yield

0.0124 x 91/360 (three month savings) 0.00313444444 Find price with periodic rate Price = $1,000,000 / 1.003134444 Price = $996,875.35

On a calculator N=1, I/Y = 0.313444, FV = 1,000,000, PMT = 0 Compute PV = $996,875.35

Speculating in T-Bills or Eurodollar

Belief – Interest Rates will rise… You are betting that the T-Bill or ED will fall in price You sell the T-Bill or ED futures contract Proof with ED…

Sell Futures ED – June ’08 with current discount at 3% (implied price of delivery $992,473.75)

Wait five months… Discount rate rises to 3.5% Cost to deliver at 3.5% is $991,230.35 Profit $1,243.38

Hedging with T-Bill Or Eurodollar

You need an inventory position that is interest rate sensitive for the period you would have a futures position…

Assume you just won the lottery and will get $1,000,000 in six months

Afraid interest rates will fall before you can invest $ Falling interest rates hurt you (rising T-Bill prices are

more expensive) You will buy a futures contract to hedge “short” lottery

position

Longer Term Interest Rates

The underlying asset for longer interest rates are Treasury Notes (2 to 10 years) and Treasury Bonds (up to 20 years now)

Pricing of the underlying asset

YTM

YTM1

1-1

CouponYTM 1

ValuePar Price

N

N

What is Yield to Maturity (YTM)

YTM is the weighted average discount rate over the life of the note or bond…

Based on the concept of stripping a bond Each future cash flow is discounted back to

the present at the discount rate for that “period”

Present Value of all future cash flow is added up to find price

Known price is used to find the YTM

Problems with T-Notes and T-Bonds

The coupon rate impacts the reaction of the price of the bond to changes in interest rates

The fictitious T-Notes or T-Bonds in the futures contracts have an implied coupon rate of 6%.

Example: T-Note, 4% coupon rate 5 years to maturity T-Note, 9% coupon rate 5 years to maturity What happens when rates change?

T-Notes Price Changes

Five-Year T-Note YTM is 6% Coupon rate at 4% N=10, I/Y = 6.0, FV = 1,000,000, PMT = 20,000 Compute Price = $914,698 Coupon rate at 9% N=10, I/Y = 6.0, FV = 1,000,000, PMT = 45,000 Compute Price = $1,127,953

YTM goes down during to 4% 4% Coupon price $1,000,000, change of $85,302 9% Coupon price $1,224,566, change of $96,613

The Asymmetric Reaction Implies

The T-Notes and T-Bonds have different values when delivered

There is a conversion table to account for the difference in the coupon rates…

Same is true for different maturities… The conversion table accounts for the

difference in maturities… See pages 241, 6% conversion factors

Problem #2 with T-Notes and T-Bonds

Accrued interest… Because coupon payments are paid every six

months Holders of the bond believe they are earning

the coupon over the six month period Selling before the coupon payment date

means they lose their “accrued” interest Price includes accrued interest

What does this mean at delivery?

The Price at Delivery

Function of The futures settlement price Contract size Correction Factor (from table or equation) Accrued Interest

Price is Settlement Price x Contract Size x Correction

Factor + Accrued Interest See page 244…example

Delivery Procedures

First Position Day (2 business days before first businesses day of delivery month) Long position reports by trade date To Clearinghouse

Short position notifies “Intention” to deliver Settlement in 3 business days Clearinghouse matches oldest long position

Notice Day …both parties are revealed Delivery day…transaction completed

Delivery

Short Position will deliver Treasury Note or Bond…based on the original futures contract

Now, short position will deliver the cheapest bond

Invoice will be prepared (with correction factor and accrued interest)

Invoice will indicate the price the long position will pay…

Short delivers the bonds, Long pays $

Flexibility in Delivery to Short

Because the short position “elects” to deliver the position has an options value

Quality Option Can deliver any T-Bond that satisfies futures

delivery conditions (picks cheapest to deliver Timing Option

Can deliver anytime during the month Wild Card Option

Prices are determined at 3 p.m. but decision to deliver can be made up to 9 p.m.

Arbitrage and Spreads

Arbitrage with interest rate futures happens when repo rates and financing rates have too large a spread… Repo is a repurchase agreement where you sell an

asset one day with a contract to buy it back at a later date at a pre-set price

Difference in price is repo rate Spreads

TED (T-Bill and Eurodollar) NOB (Notes over Bonds LED (LIBOR and Eurodollar)

Interest Rate Futures

Reverse Logic for Short and Long Position if you are thinking in terms of interest rates If you believe interest rates will rise – short If you believe interest rates will fall – long

Portion of Interest Rate Futures are actually delivered Adjustment to the underlying for bonds and

notes based on conversion factor and accrued interest

Delivery during the month…not at expiration