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# P1.T3.719. Quoted versus cash bond prices (Hull Chapter 6)

#### Nicole Seaman

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Learning objectives: Identify the most commonly used day count conventions, describe the markets that each one is typically used in, and apply each to an interest calculation. Calculate the conversion of a discount rate to a price for a US Treasury bill. Differentiate between the clean and dirty price for a US Treasury bond; calculate the accrued interest and dirty price on a US Treasury bond.

Questions:

719.1. Suppose it is April 20, 2018 and we want to infer the quoted price of a government bond that accrues interest on an actual/actual basis. The bond under consideration is a 12.0% semi-annual coupon bond that matures on July 10th, 2025. The bond has a semi-annual yield of 8.0%; i.e., 8.0% per annum with semi-annual compounding. Because coupons are paid semiannually on government bonds (and the final coupon is at maturity), the most recent coupon date is January 10, 2018, and the next coupon date is July 10, 2018. The (actual) number of days between January 10, 2018, and April 20, 2018, is 100; and the (actual) number of days between January 10, 2018, and July 10, 2018, is 181. What is nearest to the the bond's quoted price?

a. $121.60 b.$124.91
c. $127.13 d.$135.57

719.2. The price of a 72-day Treasury bill is quoted as 7.00. Which is nearest to the continuously compounded return (on an actual/365 basis) that an investor will earn on the Treasury bill for the 72-bay period? (note: inspired by Hull's EOC Problem 6.8)

a. 1.40000% per annum with continuous compounding
b. 5.60000% per annum with continuous compounding
c. 5.71790% per annum with continuous compounding
d. 7.00000% per annum with continuous compounding

719.3. A U.S. Treasury bond with a face value of $1,000.00 pays a 12.0% coupon on January 1st and July 1st. The bond settles on March 1st, such that interest accrues from January 1st to March 1st; call this amount of accrued interest, AI(T). If the bond were instead a corporate bond, the accrued interest on the same settlement date would instead be given by AI(Corp). What is nearest to the INCREASE in accrued interest, if we switched from a U.S. Treasury to a corporate bond; i.e., what is AI(Corp) - AI(T)? (note: inspired by Hull's EOC Problem 6.1) a. Zero b.$0.4420
c. $1.2970 d.$3.8020