# Interest Rate Futures Chapter 6, excluding Sec. 6.4-6.5 for 7 th edition; excluding Sec. 6.5 – 6.6 for pre 7 th editions.

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Interest Rate Futures Chapter 6, excluding Sec. 6.4-6.5 for 7 th edition; excluding Sec. 6.5 – 6.6 for pre 7 th editions

Day Count Conventions Treasury Bonds: Corporate Bonds: Money Market (T-bills) Instruments: Actual/Actual (in period) 30/360 Actual/360 Day count defines the way in which interest accrues over time expressed as X/Y. X = defines the way in which the number of days between two dates is calculated Y = defines the way that the total number of days in the reference period is measures Number of days between dates x Interest Number of days in reference period Three day count conventions used:

Treasury Bond Price quoted is often not the same as the cash price you would pay if you purchased an interest bearing instrument. Treasury bonds are quoted in dollars and thirty-seconds of a dollar (eg. 90-05 means 90 + 5/32 = 90.15625). Quoted price = clean price Cash price = dirty price Cash price = Quoted price + Accrued Interest

Treasury Bills Short term, non-coupon bearing instrument issued by the government to finance its debt Price quotes are for a Treasury bill with a face value of \$100 If Y is the cash price of a Treasury bill that has n days to maturity the quoted price (discount rate) is The quoted price (discount rate is not the same as rate of return earned on the Treasury Bill) Eg. 6.8

Treasury Bond Futures Cash price received by party with short position = Quoted futures price × Conversion factor + Accrued interest Most popular contract is the Treasury bond futures contract traded on the CBOT (CME Group; Chicago Mercantile Ex) Any government bond that has more than 15 years to maturity on the first day of the delivery month and is not callable within 15 years from that day can be delivered. Treasury bond futures prices are quoted the same way as Treasury bond prices, in dollars and thirty-seconds of a dollar Each contract is for the delivery of \$100,000

Conversion Factor A parameter that is used to define the price received by the party with the short position given that any bond can be chosen that has a maturity of more than 15 years and is not callable within 15 years. The conversion factor for a bond is approximately equal to the value of the bond on the assumption that the yield curve is flat at 6% with semiannual compounding Bond maturities and times to coupon payments are rounded down to the nearest three months. If after rounding, the bond lasts for an exact number of 6 month periods, the first coupon is after 6 months. If after rounding, there is an extra 3 months, first coupon is assumed after 3 months and accrued interest is subtracted.

Cheapest-to-Deliver Bond Cash price received by party with short position = Quoted futures price × Conversion factor + Accrued interest Cost of purchasing a bond = Quoted bond price + Accrued Interest Cheapest to deliver = Quoted bond price – (Quoted futures price × Conversion factor) Example on page 136 (7 th edition), 133 (6 th edition)

Determine the Futures Price Difficult to determine given that the party with the short position can choose which bond to deliver If we assume that we know the cheapest-to-deliver bond and the delivery date, the Treasury bond futures contract is a futures contract providing the holder with known income. F 0 = (S 0 – I)e rT Where I is the present value of the coupons during the life of the futures contract and T is the time to futures contract maturity Example on page 138 (7 th edition), page 135 (6 th edition)

Questions: 7 th edition: 6.1, 6.2, 6.9, 6.10, 6.11, 6.12, 6.25 6 th edition: 6.1, 6.2, 6.10, 6.11, 6.12

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