Interest Rate Futures Professor Brooks BA 444 021408

Interest Rate Futures Professor Brooks BA 444 02/14/08

The Underlying Asset n Bonds or Interest Bearing Accounts n These can be real or fictitious bonds n They are interest rate sensitive n n As interest rates change the value of the underlying changes Therefore can be used to hedge interest rates Rate Price

Interest Rate Futures n Domestic Set of Underlyings U. S. Treasury Bills, Notes, and Bonds n For Delivery n T-Bill, 91 -Day n Notes, 2 and 5 years n Bonds, 10 and 30 years n Around the World n Eurodollars (most popular) – U. S. dollars in a foreign bank n Euroyen, Euroswiss, Euibor, etc. n

T-Bill as the Underlying Asset n T-Bills -- sold with maturities of 4 weeks, 13 weeks and 26 weeks Pure Discount Bill n Pay “market price” today and it grows to maturity or face value with no interest payments n Quoted on a Bank Discount Basis n

Auctions for T-Bills n All buyers get the same price n Bids are in yields… Use yield to find price, n Example, discount yield is 1. 5% on n 13 week T-bill, Price of T-bill: $9, 962. 08 n

True Yield on the T-Bill n Correcting for 360 days a year (should be 365) n Correcting for using maturity as investment price (should be the purchase price) n Bond Equivalent Yield n BEY = (Par – Price)/(Price) x 365/(Days to Maturity) n Example: BEY = ($10, 000 - $9962. 08) / $9, 962. 08 x 365/91 n BEY = 0. 0152662 or 1. 5266% n This is simple interest n Correcting for compound interest n True Yield = (Par Value / Price) (365 / Days to Maturity) - 1 n True Yield = ($10, 000 / $9662. 08)(365 / 91) -1 = 0. 0153539 n True Yield = 1. 5354%

T-Bill as Underlying Asset n At Delivery, you will deliver (take delivery) T-Bill with 91 days to maturity (13 -weeks) n Par Value of the T-Bill is $1, 000 n n Futures Price is the Bank Discount Yield The anticipated 13 -week T-Bill rate n Remember when you enter the Futures contract it has a delivery date for the T-Bill with 13 weeks t maturity n See Figure 11 -1 on page 234 n

T-Bill Futures Prices n On CME n Look at February ‘ 08 – Settle at (9)96920 n My best guess on CME prices is that the first nine is not displayed… n http: //www. cme. com n What is the implied discount for the T-Bill for delivery? 0. 01218 or 1. 218% discount n This annualized as BEY is 1. 239% n

Eurodollars as Underlying n The interest rate on U. S. dollars deposited in a foreign bank (main activity in London) Not a security n Nontransferable bank deposit n You are buying or selling a “savings account” n Three month savings account with $1, 000 maturity (or other maturities) n Savings rate is LIBOR…an average of a survey of banks n n Add-On yield – but again simple interest

Futures Price of ED Underlying n 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 with a current price that implies a 2% interest rate.

Eurodollar Underlying n To find the Value of the savings account at deposit… n Price is present value of the Par Value n At the periodic discount rate n Convert the annual yield to periodic rate and find price of underlying “savings account”

Eurodollar Underlying n Add-on Yield is quoted as 0. 0124 or 1. 24% n Convert to periodic yield n n n 0. 0124 x 91/360 (three month savings) 0. 00313444444 Find price with periodic rate Price = $1, 000 / 1. 003134444 Price = $996, 875. 35 n On a calculator n n N=1, I/Y = 0. 313444, FV = 1, 000, PMT = 0 Compute PV = $996, 875. 35

Speculating in T-Bills or Eurodollar n Belief – Interest Rates will rise… n You are betting that the T-Bill or ED will fall in price n You sell the T-Bill or ED futures contract n Proof with ED… n Sell Futures ED – June ’ 08 with current discount at n n 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 n You need an inventory position that is interest rate n n sensitive for the period you would have a futures position… Assume you just won the lottery and will get $1, 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 n The underlying asset for longer interest rates are Treasury Notes (2 to 10 years) and Treasury Bonds (up to 20 years now) n Pricing of the underlying asset

What is Yield to Maturity (YTM) n YTM is the weighted average discount rate over the life of the note or bond… n Based on the concept of stripping a bond n Each future cash flow is discounted back to the present at the discount rate for that “period” n Present Value of all future cash flow is added up to find price n Known price is used to find the YTM

Problems with T-Notes and T-Bonds n The coupon rate impacts the reaction of the price of the bond to changes in interest rates n The fictitious T-Notes or T-Bonds in the futures contracts have an implied coupon rate of 6%. n Example: T-Note, 4% coupon rate 5 years to maturity n T-Note, 9% coupon rate 5 years to maturity n What happens when rates change? n

T-Notes Price Changes n Five-Year T-Note YTM is 6% n Coupon rate at 4% n n n N=10, I/Y = 6. 0, FV = 1, 000, PMT = 20, 000 Compute Price = $914, 698 Coupon rate at 9% N=10, I/Y = 6. 0, FV = 1, 000, PMT = 45, 000 Compute Price = $1, 127, 953 n YTM goes down during to 4% n 4% Coupon price $1, 000, change of $85, 302 n 9% Coupon price $1, 224, 566, change of $96, 613

The Asymmetric Reaction Implies n The T-Notes and T-Bonds have different values when delivered n There is a conversion table to account for the difference in the coupon rates… n Same is true for different maturities… n The conversion table accounts for the difference in maturities… n See pages 241, 6% conversion factors

Problem #2 with T-Notes and T-Bonds n Accrued interest… n Because coupon payments are paid every six months Holders of the bond believe they are earning the coupon over the six month period n Selling before the coupon payment date means they lose their “accrued” interest n Price includes accrued interest n n What does this mean at delivery?

The Price at Delivery n Function of n The futures settlement price n Contract size n Correction Factor (from table or equation) n Accrued Interest n Price is n Settlement Price x Contract Size x Correction Factor + Accrued Interest n See page 244…example

Delivery Procedures n First Position Day (2 business days before first businesses day of delivery month) Long position reports by trade date n To Clearinghouse n n Short position notifies “Intention” to deliver n Settlement in 3 business days n Clearinghouse matches oldest long position n Notice Day …both parties are revealed n Delivery day…transaction completed

Delivery n Short Position will deliver Treasury Note or Bond…based on the original futures contract n Now, short position will deliver the cheapest bond n Invoice will be prepared (with correction factor and accrued interest) n Invoice will indicate the price the long position will pay… n Short delivers the bonds, Long pays $

Flexibility in Delivery to Short n Because the short position “elects” to deliver the position has an options value n Quality Option n Can deliver any T-Bond that satisfies futures delivery conditions (picks cheapest to deliver n Timing Option n Can deliver anytime during the month n Wild Card Option n Prices are determined at 3 p. m. but decision to deliver can be made up to 9 p. m.

Arbitrage and Spreads n Arbitrage with interest rate futures happens when repo rates and financing rates have too large a spread… n n 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 n Spreads n TED (T-Bill and Eurodollar) n NOB (Notes over Bonds n LED (LIBOR and Eurodollar)

Interest Rate Futures n Reverse Logic for Short and Long Position if you are thinking in terms of interest rates If you believe interest rates will rise – short n If you believe interest rates will fall – long n n Portion of Interest Rate Futures are actually delivered Adjustment to the underlying for bonds and notes based on conversion factor and accrued interest n Delivery during the month…not at expiration n