Question

Today, interest rates on 1-year T-bonds yield 1.5%, interest rates on 2-year T-bonds yield 2.55%, and interest rates on 3-year T-bonds yield 3.4%.

a. If the pure expectations theory is correct, what is the yield on 1-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations. ________ %

b. If the pure expectations theory is correct, what is the yield on 2-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations. ___________%

c. If the pure expectations theory is correct, what is the yield on 1-year T-bonds two years from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations. ________%

Answer 1

Interest rates on 1-year T-bonds yield, S_0,1 = 1.5%

Interest rates on 2-year T-bonds yield, S_0,2 = 2.55%, and

Interest rates on 3-year T-bonds yield, S_0,3 = 3.4%.

a. If the pure expectations theory is correct, what is the yield on 1-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations. ________ %

Let's assume the yield on 1-year T-bonds one year from now = F_1,2

Hence, by no arbitrage rule,

(1 + S_0,2)² = (1 + S_0,1).(1 + F_1,2)

Hence, (1 + 2.55%)² = (1 + 1.5%).(1 + F_1,2)

Hence, F_1,2 = 1.0255² / 1.015 - 1 = 3.6109%

b. If the pure expectations theory is correct, what is the yield on 2-year T-bonds one year from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations. ___________%

Let's assume the yield on 2-year T-bonds one year from now = F_1,3

(1 + S_0,3)³ = (1 + S_0,1).(1 + F_1,3)²

Hence, (1 + 3.4%)³ = (1 + 1.5%).(1 + F_1,3)²

Hence, F_1,3 = [1.034³ / 1.015]^1/2 - 1 = 4.3633%

c. If the pure expectations theory is correct, what is the yield on 1-year T-bonds two years from now? Be sure to use a geometric average in your calculations. Round your answer to four decimal places. Do not round intermediate calculations. ________%

Let's assume the yield on 1-year T-bonds two years from now = F_2,3

(1 + S_0,3)³ = (1 + S_0,2)².(1 + F_2,3)

Hence, (1 + 3.4%)³ = (1 + 2.55%)².(1 + F_2,3)

Hence, F_2,3 = [1.034³ / 1.0255²] - 1 = 5.1212%