Due to a recession, expected inflation this year is only 2%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 2%. Assume that expectations theory holds and the real risk-free rate is r* = 2.25%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2.75%, what inflation rate is expected after Year 1? Round your answer to two decimal places.
To determine the expected inflation rate after Year 1, we can apply the expectations theory and use the relationship between the yields of 1-year and 3-year Treasury bonds.
According to the expectations theory, the yield on a long-term bond is equal to the average of the expected short-term interest rates over the holding period, plus a term premium. In this case, the term premium is given as 2.75% (or 0.0275).
Let's denote the expected inflation rate after Year 1 as "expected_inflation_2". According to the expectations theory, the yield on a 3-year Treasury bond would be equal to the 1-year yield plus the expected average short-term interest rate over the next 2 years, which includes the expected inflation rate after Year 1:
Yield on 3-year Treasury bond = 1-year yield + expected_inflation_2
Since the expected inflation in Year 1 is given as 2%, the 1-year yield would be the sum of the real risk-free rate (r*) and the expected inflation in Year 1:
1-year yield = r* + expected_inflation_1
= 2.25% + 2%
= 4.25% or 0.0425
Now we can use the given relationship between 1-year and 3-year yields to solve for the expected_inflation_2:
Yield on 3-year Treasury bond = 1-year yield + expected_inflation_2
0.0425 + expected_inflation_2 = 0.0425 + 0.0275
By rearranging the equation, we can isolate the expected_inflation_2:
expected_inflation_2 = 0.0275
Therefore, the expected inflation rate after Year 1 is 2.75%.