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. Explain and calculate a US Treasury bond futures contract conversion factor. Calculate the cost of delivering a bond into a Treasury bond futures contract.
Questions:
23.5.1. A U.S. Treasury bond with a face value of $1,000.00 pays a semi-coupons on April 1st and October 1st matures on Oct 1st, 2028. The coupon rate is 8.00% per annum, and the yield is 6.40%. The bond settles on Sept 4th, 2023. Which of the following is nearest to the difference between the dirty (aka, full) and clean (aka, quoted) price of the bond on the settlement date?
a. Zero
b. $17.05
c. $34.10
d. $68.20
23.5.2. Which of the following is nearest to the cash price of Treasury bill with a quoted price of 6.30 that matures in 240 days?
a. $93.67
b. $95.80
c. $99.94
d. $104.29
23.5.3. Suppose that it is known that a bond will be delivered in 180 days under the terms of a futures contract. The timing of coupon payments is shown below. The last coupon on the bond was paid 76 days ago, and the next coupon will be paid in 108 days. The coupon after the next one will be paid in 290 days (i.e., 110 days after delivery). Here is the timeline:
Assume that the risk-free interest rate for all maturities is 5.0% with continuous compounding and that the delivered bond pays a coupon of 9.0% semi-annually with a current quoted (clean) price of USD 124.80 and a conversion factor of 1.300.
Which of the following is nearest to the quoted futures price?
a, $95.00
b. $98.22
c. $123.50
d. $125.27
Answers here:
Questions:
23.5.1. A U.S. Treasury bond with a face value of $1,000.00 pays a semi-coupons on April 1st and October 1st matures on Oct 1st, 2028. The coupon rate is 8.00% per annum, and the yield is 6.40%. The bond settles on Sept 4th, 2023. Which of the following is nearest to the difference between the dirty (aka, full) and clean (aka, quoted) price of the bond on the settlement date?
a. Zero
b. $17.05
c. $34.10
d. $68.20
23.5.2. Which of the following is nearest to the cash price of Treasury bill with a quoted price of 6.30 that matures in 240 days?
a. $93.67
b. $95.80
c. $99.94
d. $104.29
23.5.3. Suppose that it is known that a bond will be delivered in 180 days under the terms of a futures contract. The timing of coupon payments is shown below. The last coupon on the bond was paid 76 days ago, and the next coupon will be paid in 108 days. The coupon after the next one will be paid in 290 days (i.e., 110 days after delivery). Here is the timeline:
Assume that the risk-free interest rate for all maturities is 5.0% with continuous compounding and that the delivered bond pays a coupon of 9.0% semi-annually with a current quoted (clean) price of USD 124.80 and a conversion factor of 1.300.
Which of the following is nearest to the quoted futures price?
a, $95.00
b. $98.22
c. $123.50
d. $125.27
Answers here:
