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# P1.T4.900. Discount function and the Law of One Price (Tuckman, Ch.1)

#### Nicole Seaman

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Learning objectives: Define discount factor and use a discount function to compute present and future values. Define the “law of one price,” explain it using an arbitrage argument, and describe how it can be applied to bond pricing. Identify the components of a US Treasury coupon bond, and compare and contrast the structure to Treasury STRIPS, including the difference between P-STRIPS and C-STRIPS.

Questions:

900.1. Displayed below (in the rightmost column) is a discount function implied by six U.S. Treasury bonds with various maturities. The bonds (one per row) pay a semi-annual coupon and mature at six-month intervals over the next three years:

Consider a new U.S. Treasury bond issued on May 28, 2018 with a maturity of three years that pays an annual coupon of 6.0% per annum. Unlike the Treasury bonds in the exhibit, this new bond pays coupons once per year and therefore has only three cash flows before maturing on 5/31/2021. Which is nearest to the bond's present value; aka, theoretical price?

a. $88.22 b.$97.34
c. $100.99 d.$105.05

900.2. Consider the following two U.S. Treasury bonds:
• Bond #1 has a remaining maturity of exactly five years, has a coupon rate of 2.0% per annum and pays a semi-annual coupon. Its current price is $81.600. • Bond #2 has a remaining maturity of exactly five years, has a coupon rate of 7.0% per annum and pays a semi-annual coupon. Its current price is$104.050.
If we can assume the validity of the Law of One Price, then which of the following must be the price of a third bond (aka, Bond #3) that has a remaining maturity of exactly five years and a semi-annual (i.e., payable) coupon rate of 5.0% per annum?

a. $90.580 b.$95.070
c. \$101.356