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# L1.T4.11. Treasury STRIPS

#### David Harper CFA FRM

##### David Harper CFA FRM
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AIMs: Discuss the components of a U.S. Treasury coupon bond, and compare and contrast the structure to Treasury STRIPS, including the difference between P-STRIPS and C-STRIPS. Compute the price of a fixed income security with certain cash-flows and compare its value to fixed-income securities with different, but certain, cash flow characteristics. Identify arbitrage opportunities for fixed income securities with certain cash flows.

Questions:

11.1. A $10 million Treasury bond (note) with a 10-year maturity pays semi-annual coupons at a coupon rate of 4.0% per annum. If the bond is fully "stripped" such that STRIPS are created, each of the following is TRUE except: a. The stripping creates 21 zero-coupon bonds b. Each of the C-STRIPS and the P-STRIP implies an exact spot (a.k.a., zero) interest rate c. The duration of the P-STRIP is greater than the duration of the original Treasury bond d. The C-STRIPS each have durations near to zero 11.2. A U.S. Treasury note with 1.5 years to maturity has a market price of$105.75 and pays a semi-annual coupon with a coupon rate of 5.50%. The market's discount function is the following set of discount factors: d(0.5) = 0.970, d(1.0) = 0.950, and d(1.5) = 0.920. Is the bond trading cheap, rich, or fair?
d. Cheap at six months, fair at one year, and rich at 1.5 years.

11.3. Which of the following would be the most likely reason for a C- or P-STRIP to "trade rich" or "trade cheap?"
a. Arbitrageurs
b. Technical (non-fundamental) factors; e.g., liquidity, supply/demand
c. A shift in the spot rates which changes discount rate(s) abruptly
d. Individual investors have different views (preferences) with respect to the time value of money

11.4. A fixed income manager has determined that an eighteen-month (1.5 year maturity) Treasury note with a market price at $102 that pays a 4.0% semi-annual coupon is overvalued. She conducts an arbitrage by shorting the bond and buying the replicating portfolio, as it trades cheap, that consists of positions in the following three bonds: 1. Bond B(1): A six-month (0.5 year to maturity) bond with a market price of$99.80 that pays a 1.0% semi-annual coupon (i.e., 1.0% per annum coupon rate pays 0.5% every six months)
2. Bond B(2): A one-year (1.0 year to maturity) bond with a market price of $99.40 that pays a 2.0% semi-annual coupon 3. Bond B(3): A 1.5-year bond with a market price of$98.00 that pays a 3.0% semi-annual coupon
What are face amounts, respectively, of the replicating portfolio? (note: more tedious than a typical exam question)
a. B(1) = 0.00, B(2) = 0.10, B(3) = 103.54
b. B(1) = 1.60, B(2) = 2.85, B(3) = 4.67
c. B(1) = 2.43, B(2) = 2.44, B(3) = 102.46
d. B(1) = 1.43, B(2) = 99.65, B(3) = 103.66