Due to a recession, expected inflation this year is only 2.75%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 2.75%. Assume that expectations theory holds and the real risk-free rate is r* = 3%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 3%, what inflation rate is expected after Year 1? Round your answer to two decimal places.
nn
To solve this question, we need to apply the expectations theory and the relationship between bond yields, inflation, and the risk-free rate.
According to the expectations theory, the yield on a long-term bond is equal to the average of the expected short-term yields over the bond's life, adjusted for a risk premium. In this case, we are comparing the yields on 3-year Treasury bonds and 1-year Treasury bonds.
Let's break down the given information:
- The real risk-free rate (r*) = 3%
- The expected inflation in Year 1 = 2.75%
- The expected inflation in Year 2 and thereafter is constant and above 2.75%
According to the expectations theory, the yield on the 3-year Treasury bond is equal to the 1-year yield plus the expected average inflation rate over the next two years. We can use this relationship to solve for the expected inflation rate after Year 1.
Let's set up the equation:
3-year yield = 1-year yield + average inflation rate
Using the information provided:
3-year yield = 1-year yield + 3% (since r* = 3%)
3-year yield = 1-year yield + average inflation rate
We know that:
1-year yield = 2.75% + r* = 2.75% + 3% = 5.75%
Substituting the values into the equation:
3-year yield = 5.75% + average inflation rate
Since we are given that the yield on 3-year Treasury bonds equals the 1-year yield plus 3%, we can substitute this into the equation:
5.75% + average inflation rate = 1-year yield + 3%
5.75% + average inflation rate = 5.75% + 3%
average inflation rate = 3%
Therefore, the expected inflation rate after Year 1 is 3%.