It is May 5, 2013. The quoted price of a government bond with a 12% coupon that
ID: 2615790 • Letter: I
Question
It is May 5, 2013. The quoted price of a government bond with a 12% coupon that matures on July 27, 2024, is 110-24. What is the cash price?
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.
Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum.
Show that both portfolios have the same duration.
Show that the percentage changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same.
What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?
Explanation / Answer
1) The Govt bond is semi annual. Maturity is 27 Jul 2024. So Semiannual payments are on 27 Jan and 27 Jul
Number of days between Jan 27, 2017 and May 5, 2017 is 98. The number of days between 27 Jan and 27 Jul is 181. Semiannual rate is 6%
The accrued interest = Semi annual rate X (Number of days from last coupon)/ Number of days between coupon paymments
The Accrued Interest = 6% X 98/181 = 3.2486
Quoted price is 110-17 = 110+17/32 = 110.5312
The cash price = 110.5312 + 3.2486 = 113.7798 = $113.78
2) Number of days between 4 Feb and 30 Jul = 176 (Days formula in excel)
Number of days between 4 Feb and 4 Aug = 181
Cash price =110 + 6.5% *176/181 = 116.32
Rate of interest with continous compounding is = 2 ln 1.06 = 0.1165 = 11.65%
A coupon of 6.5 will be recieved in 5 days. Thus 6.5e (-5*0.1165/365) = 6.49
The number of days between 30 Jul and 30 Sep = 62 days = 62/365 =0.1699 years
The Cash price = (116.32- 6.49)e(0.1699*0.1165) = 112.03
At delivery there are 57 days left for interest.The quoted price for 13% bond will be
112.03-6.5 * 57/184 = 110.01
Taking conversion factor into account , quoted futures price will be 110.01/1.5 = 73.34
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