Today, interest rates on 1-year T-bonds yield 1.8%, interest rates on 2-year T-b

Question

Today, interest rates on 1-year T-bonds yield 1.8%, interest rates on 2-year T-bonds yield 2.6%, and interest rates on 3-year T-bonds yield 3.8%.

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.

Explanation / Answer

a) yield on 1-year T-bonds one year from now. Let x be the yield we require.

We have 1.026^2 = 1.018 * (1+x)

1.026^2/1.018 = 1 + x

1.034063 = 1 + x

x = 0.034063 = 3.41%

b) yield on 2-year T-bonds one year from now. Let x be the yield we require

We have 1.038^3= 1.018*(1+x)^2

1.038^3/1.018 = (1+x)^2

1.098612 = (1+x)^2

taking the square root of both sides we have 1.048147 = 1 + x; x = 0.048147 = 4.81%

c) yield on 1-year T-bonds two years from now. Let x be the yield we require.

Then, 1.038^3 = 1.026^2 * (1+x)

1.038^3/1.026^2 = 1+x

1.062423 - 1 = x

x = 0.062423 = 6.24%

Check: (1.018*1.0341*1.0624)^1/3 - 1 = 0.038005 = 3.8%, the yield on 3 year T Bonds as of today.

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