Question

Today, interest rates on 1-year T-bonds yield 1.7%, interest rates on 2-year T-bonds yield 2.5%, 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. Do not round intermediate calculations. Round your answer to four decimal places.

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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. Do not round intermediate calculations. Round your answer to four decimal places.

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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. Do not round intermediate calculations. Round your answer to four decimal places.

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Answer 1

For treasury bonds we consider semiannual compounding. The equations are as follows:

a. 1.0085^2 * (1+r/2)^2 = 1.0125^4 gives r = 3.3032%

b. 1.0085^2 * (1+r/2)^4 = 1.017^6 gives r = 4.2554%

c. 1.0125^4 * (1+r/2)^2 = 1.017^6 gives r = 5.2120%

Answer 2

Here, Interest Rate (R1) on 1 year T - Bonds is 1.7% Interest Rate (R2) on 2 year T-Bonds is 2.5% Interest Rate (R3) on 3 year T-Bonds is 3.4% Step 2 of 4: According to the Pure Expectation Theory, Calculation of yield on 1-year T-bonds one year from now is as follows:   Yeild on 1 year T-bond one year from now = (1+R2)21+R1-1=(1+0.025)21+0.017-1=1.03306293018-1=0.03306293018=3.3062%   Step 3 of 4: According to the Pure Expectation Theory, Calculation of yield on 2-year T-bonds one year from now is as follows: Yeild on 2 year T-bond one year from now = (1+R3)31+R11/2-1 =(1+0.034)31+0.0171/2-1 =1.04260626838-1 =0.04260626838 =4.2606%   Step 4 of 4: According to the Pure Expectation Theory, Calculation of yield on 1-year T-bonds two years from now is as follows: Yeild on 1 year T-bond two years from now = (1+R3)3(1+R2)2-1=(1+0.034)3(1+0.025)2-1=1.05223776704-1=0.05223776704= 5.2237% Answer: a) Yield on 1-year T-bonds one year from now is 3.3062% b) Yield on 2-year T-bonds one year from now is 4.2606% c) Yield on 1-year T-bonds two year from now is 5.2237%