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Interest Rate Futures


This is simple interest. Correcting for compound interest ... On a calculator. N=1, I/Y = 0.313444, FV = 1,000,000, PMT = 0. Compute PV = $996,875.35 ... – PowerPoint PPT presentation

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Title: Interest Rate Futures

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

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

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

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
  • Example BEY (10,000 - 9962.08) / 9,962.08 x
  • 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
  • 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//
  • What is the implied discount for the T-Bill for
  • 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 LIBORan average of a survey of
  • Add-On yield but again simple interest

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.

Eurodollar Underlying
  • To find the Value of the savings account at
  • 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

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

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
  • 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

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
  • 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

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 244example

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

  • Short Position will deliver Treasury Note or
    Bondbased on the original futures contract
  • Now, short position will deliver the cheapest
  • 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
  • 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
  • Adjustment to the underlying for bonds and notes
    based on conversion factor and accrued interest
  • Delivery during the monthnot at expiration