Today, interest rates on 1-year T-bonds yield 1.2%, interest rates on 2-year T-b

Question

Today, interest rates on 1-year T-bonds yield 1.2%, interest rates on 2-year T-bonds yield 2.1%, and interest rates on 3-year T-bonds yield 3.7%.

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

1) If bonds held for 2 years

For every dollar they invest today, they will have accumulated $1.042441 by the end of Year 2:

Funds at end of Year 2 $1(1.021)^2 = $1.042441

Now, buy security for 1 year and reinvest again for 1 year

(1.012)(1+x) = 1.042441

1+x = 1.0301

x = 0.0301 = 3.01%

2)

If bonds held for 3 years

For every dollar they invest today, they will have accumulated $1.115158 by the end of Year 3:

Funds at end of Year 2 $1(1.037)^3 = $1.115158

Now, buy security for 1 year and reinvest again for 2 year bond

(1.012)(1+x)^2 = 1.115158

(1+x)^2 = 1.1019

1+x = square root of 1.1019

1+x = 1.04973

x = 0.04973 = 4.973%

3)

Now invest in 2 year bond and reinvest the proceed in last 1 year bond

(1.021)^2 (1+x) = 1.115158

1+x = 1.0698

x = 0.0698 = 6.98%

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