Today, interest rates on 1-year T-bonds yield 1.4%, interest rates on 2-year T-bonds yield 2.4%, and interest rates on 3-year T-bonds yield 3.2%.

Using the Yield Curve to Estimate Future Interest Rates

Today, interest rates on 1-year T-bonds yield 1.4%, interest rates on 2-year T-bonds yield 2.4%, and interest rates on 3-year T-bonds yield 3.2%.

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.

a). Let the Yield on 1 Year T-bond one year from now be A.

(1 + 0.032)3 = (1 + A) * (1 + 0.024)2   (Pure expectation theory hold good in the question.)

(1.032)3 = (1 + A) * (1.024)2

1.099105 = (1 + A) * 1.048576

(1 + A) = 1.099105 / 1.048576

1 + A = 1.048188

A = 1.048188 – 1

A = 0.048188 i.e., 4.8188 %

Conclusion:-  Yield on 1 Year T-bond one year from now = 4.8188 %.

b). Let the Yield on 2 Year T-bond one year from now be B.

(1 + 0.032)3 = (1 + 0.014) * (1 + B)2   (Pure expectation theory hold good in the question.)

(1.032)3 = (1 + B)2 * (1.014)

1.099105 = (1 + B)2 * 1.014

(1 + B)2 = 1.099105 / 1.014

(1 + B)2 = 1.08393

(1 + B) = 1.041120 (Square root of 1.08393)

B = 1.041120 – 1

B = 0.041120 i.e., 4.1120 %

Conclusion:-  Yield on 2 Year T-bond one year from now = 4.1120 % (approx)

Asked on May 20, 2017 in