Question

U.S. Treasury STRIPS, close of business November 15, 2015:

Maturity	Price			Maturity	Price
November ’16		99.471		November ’19		95.035
November ’17		98.782		November ’20		92.570
November ’18		96.827		November ’21		89.342

a. According to the pure expectations theory of interest rates, how much do you expect to pay for a five-year STRIPS on November 15, 2016? (Do not round intermediate calculations. Enter your answer as a percent rounded to 3 decimal places.)

b. According to the pure expectations theory of interest rates, how much do you expect to pay for a two-year STRIPS on November 15, 2018? (Do not round intermediate calculations. Enter your answer as a percent rounded to 3 decimal places.)

Answer 1

Maturity	Yield
1	0.53%
2	0.61%
3	1.08%
4	1.28%
5	1.56%
6	1.90%

Firstly, calculate the yields given the prices. Rate, Rn= (100 / P)^(1/n) - 1, where P - Price and n - maturity

a) Using expectation theory,

(1 + 1F5)^5 = (1 + R6)^6 / (1 + R1)

where, 1F5 - five year rate, one year from now, R6 - Current 6-year rate = 1.9% and R1 - 1-year rate = 0.53%

=> (1 + 1F5)^5 = (1 + 1.90%)^6 / (1 + 0.53%) = 1.1134

=> 1F5 = 2.171%

b) (1 + 3F2)^2 = (1 + R5)^5 / (1 + R3)^3 = (1 + 1.56%)^5 / (1 + 1.08%)^3 = 1.0459

=> 3F2 = 2.273%