HullFund8eCh06ProblemSolutions

HullFund8eCh06ProblemSolutions - CHAPTER 6 Interest Rate...

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CHAPTER 6 Interest Rate Futures Practice Questions Problem 6.8. The price of a 90-day Treasury bill is quoted as 10.00. What continuously compounded return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-day period? The cash price of the Treasury bill is 90 100 10 97 50 360 $ The annualized continuously compounded return is 365 2 5 ln 1 10 27 90 97 5 % Problem 6.9. It is May 5, 2013. The quoted price of a government bond with a 12% coupon that matures on July 27, 2024, is 110-17. What is the cash price? The number of days between January 27, 2013 and May 5, 2013 is 98. The number of days between January 27, 2013 and July 27, 2013 is 181. The accrued interest is therefore 98 6 3 2486 181 The quoted price is 110.5312. The cash price is therefore 110 5312 3 2486 113 7798 or $113.78. Problem 6.10. Suppose that the Treasury bond futures price is 101-12. Which of the following four bonds is cheapest to deliver? Bond Price Conversion Factor 1 125-05 1.2131 2 142-15 1.3792 3 115-31 1.1149 4 144-02 1.4026 The cheapest-to-deliver bond is the one for which Quoted Price Futures Price Conversion Factor is least. Calculating this factor for each of the 4 bonds we get
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Bond1 125 15625 101 375 1 2131 2 178 Bond 2 142 46875 101 375 1 3792 2 652 Bond 3 115 96875 101 375 1 1149 2 946 Bond 4 144 06250 101 375 1 4026 1 874           Bond 4 is therefore the cheapest to deliver. Problem 6.11. It is July 30, 2015. The cheapest-to-deliver bond in a September 2015 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2015. Coupon payments on the bond are made on February 4 and August 4 each year. The term structure is flat, and the rate of interest with semiannual compounding is 12% per annum. The conversion factor for the bond is 1.5. The current quoted bond price is $110. Calculate the quoted futures price for the contract. There are 176 days between February 4 and July 30 and 181 days between February 4 and August 4. The cash price of the bond is, therefore: 176 110 6 5 116 32 181   The rate of interest with continuous compounding is 2ln1 06 0 1165 or 11.65% per annum. A coupon of 6.5 will be received in 5 days (= 0.01370 years) time. The present value of the coupon is 49 . 6 5 . 6 1165 . 0 01370 . 0 e The futures contract lasts for 62 days (= 0.1699 years). The cash futures price if the contract were written on the 13% bond would be 03 . 112 ) 49 . 6 32 . 116 ( 1165 . 0 1699 . 0 e At delivery there are 57 days of accrued interest. The quoted futures price if the contract were written on the 13% bond would therefore be 01 . 110 184 57 5 . 6 03 . 112 Taking the conversion factor into account the quoted futures price should be: 110 01 73 34 1 5 Problem 6.12. An investor is looking for arbitrage opportunities in the Treasury bond futures market. What complications are created by the fact that the party with a short position can choose to deliver any bond with a maturity of over 15 years?
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