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 find the expected inflation rate after Year 1, we can use the Expectations Theory of the Yield Curve. According to the Expectations Theory, the yield on a long-term bond (in this case, the 3-year Treasury bond) is equal to the average of the current and future short-term yields.
Let's break down the information given:
- The yield on 3-year Treasury bonds equals the 1-year yield plus 2.75%.
- The real risk-free rate (r*) is given as 2.25%.
- Expected inflation this year is 2%.
- The inflation rate in Year 2 and thereafter is expected to be constant at some level above 2%.
Based on the Expectations Theory equation, we can set up the following equation:
3-year yield = 1-year yield + 2.75%
Let's substitute the components with their respective values:
3-year yield = 1-year yield + 2.75%
3-year yield = (r* + expected inflation) + 2.75%
3-year yield = (2.25% + 2%) + 2.75%
3-year yield = 7%
Now, we need to solve for the expected inflation rate after Year 1, which is represented by (r* + expected inflation).
7% = 2.25% + 2% + (r* + expected inflation)
7% = 4.25% + (r* + expected inflation)
To isolate (r* + expected inflation), we subtract 4.25% from both sides of the equation:
7% - 4.25% = r* + expected inflation
2.75% = r* + expected inflation
Now, let's substitute the value of the real risk-free rate (r*):
2.75% = 2.25% + expected inflation
To solve for expected inflation, we subtract 2.25% from both sides of the equation:
2.75% - 2.25% = expected inflation
expected inflation = 0.5%
Therefore, the expected inflation rate after Year 1 is 0.5% (or 0.005 when rounded to two decimal places).