Interest Rate Futures

1
Interest Rate Futures

• Professor Brooks
• BA 444
• 02/14/08

2
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

3
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.

4
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

5
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

6
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

7
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

8
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

9
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 LIBORan average of a survey of
  banks
• Add-On yield but again simple interest

10
Futures Price of ED Underlying

• Lets 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.

11
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

12
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
• N1, I/Y 0.313444, FV 1,000,000, PMT 0
• Compute PV 996,875.35

13
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

14
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

15
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

16
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

17
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?

18
T-Notes Price Changes

• Five-Year T-Note YTM is 6
• Coupon rate at 4
• N10, I/Y 6.0, FV 1,000,000, PMT 20,000
• Compute Price 914,698
• Coupon rate at 9
• N10, 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

19
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

20
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?

21
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 244example

22
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 daytransaction completed

23
Delivery

• Short Position will deliver Treasury Note or
  Bondbased 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

24
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.

25
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)

26
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 monthnot at expiration