Suppose 2-year Treasury bonds yield 5.3% while 1-year bonds yield 3.6%, r is 1%

Question

Suppose 2-year Treasury bonds yield 5.3% while 1-year bonds yield 3.6%, r is 1% and the maturity risk premium s zero. Use minus s or a ne ative expected in at rate. a. Using the expectations theory, what is the yield on a 1-year bond 1 year from now? Calculate the yield using a geometric average. Do not round intermediate calculations. Round your answer to two decimal places. b. What is the expected inflation rate in Year 1? Do not round intermediate calculations. Round your answer to two decimal places. What is the expected inflation rate in Year 2? Do not round intermediate calculations. Round your answer to two decimal places.

Explanation / Answer

a. According to pure expectations theory, short term interest rates are indicator of long term interest rates. According to this theory if you invest in a 2 year bond today or if you invest in a 1 year bond today and then after this bond matures, invest the proceeds in another 1 year bond (not total duration of investment remains 2 years in both cases), then the amount received after 2 years is equal.

(1 + Yield on 2yr bond)2 = (1 + Yield on 1yr Bond) * (1 + Yield on 1yr bond 1 yr from now)

(1 + 5.3%)2 = (1 + 3.6%) * (1 + Yield on 1yr bond 1 yr from now)

Yield on 1 Year bond, 1 Year from now = 7.03%

b. Expected Inflation in year 1 can be calculated usingFischer relation:

Nominal rate = Real rate + Inflation rate

Real rate = 1%, Nominal rate = 3.6%

Inflation Rate = 2.6%

c. Expected Inflation in year 2 can be calculated usingFischer relation:

Nominal rate = Real rate + Inflation rate

Real rate = 1%, Nominal rate = 7.02%

Inflation Rate = 6.02%

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