Question

Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that the expectations theory holds and the real risk-free rate (r∗) is 2.5%. If the yield on 3 -year Treasury bonds equals the 1 -year yleld plus 1.0%, what inflation rate is expected after Year 1 ? Round your answer to two decimal places.

Answer 1

The expected inflation rate after Year 1 can be calculated using the expectations theory, the real risk-free rate, and the given bond yields. By factoring in the 3-year bond yield being 1.0% higher than the 1-year bond yield and a real risk-free rate of 2.5%, the expected inflation rate after Year 1 is found to be approximately 5.25%.

Step-by-step explanation:

The student is asking how to calculate the expected inflation rate after Year 1, assuming the expectations theory holds and given certain conditions. According to the expectations theory, the yield on longer-term bonds is determined by the market's expectations for the average future short-term interest rates. If the yield on a 3-year Treasury bond equals the 1-year yield plus 1.0%, and we know that the real risk-free rate (r*) is 2.5%, we can calculate the expected inflation rate after Year 1.

To find the expected inflation rate after Year 1, we can use the given information: the current year's expected inflation is 3.25%, and the real risk-free rate is 2.5%. The total expected return on a 1-year bond would be the sum of these two rates, so 5.75% (3.25% + 2.5%). The 3-year bond yield is 1.0% higher, making it 6.75%. Substract the real risk-free rate from this to get the average expected inflation over the next three years, which is 4.25% (6.75% - 2.5%). Since the first year's inflation is 3.25%, the average inflation for the next two years must be higher to result in an average of 4.25%. Using the average inflation rate formula, we can determine that the rate of inflation expected after Year 1 is approximately 5.25%.