What's new

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

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
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

900.3. In regard to Tuckman's discussion of the components and structure of U.S. Treasury STRIPS, which of the following statements is TRUE?

a. The holder of a U.S. Treasury STRIP is immunized against inflation risk but exposed to significant liquidity risk and call risk
b. The Law of One Price says an arbitrage profit is necessarily available when two securities offer identical cash flows but sell at different market prices
c. If we apply the discount function implied only by C-STRIPS (i.e., without P-STRIPS) to infer the price of a U.S. Treasury bond, we are likely to undervalue the security relative to its actual market price
d. Because C-STRIPS and P-STRIPS are perfect commodities, arbitrage enforces the law of one price to ensure that, with respect to U.S. Treasury bonds, theoretical (aka, model) prices equal market prices

(Source: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011))