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Inflation

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* = 2.25%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2.25%, what inflation rate is expected after Year 1? Round your answer to two decimal places.

User Jberg
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Final answer:

Using the expectations theory and the provided information, the expected inflation rate after Year 1 can be calculated, with the final answer rounded to two decimal places.

Step-by-step explanation:

According to the expectations theory, the yield curve reflects expectations of future inflation rates. Given that the real risk-free rate (r*) is 2.25%, and inflation for Year 1 is 2.75%, we can calculate the expected inflation rate after Year 1 using the provided yield information for 3-year Treasury bonds.

To find the expected inflation rate for Year 2 and beyond, we use the yield on the 1-year Treasury bond plus the given 2.25% addition to yield for the 3-year bond. Let's denote the 1-year rate (Year 1 real risk-free rate + Year 1 inflation) as i1 and the 3-year rate (average of Year 1 real risk-free rate + expected inflation over 3 years) as i3. We have:


  • i1 = r* + inflation rate for Year 1

  • i3 = (r* + expected inflation rate for Years 1-3) * 3

The 3-year yield is equal to the 1-year yield plus 2.25%. So:


i1 + 2.25% = i3

Solving for the unknown expected inflation rate, we get an expected inflation rate for Year 2 and thereafter. Remember the yield for the 3-year bond represents the average expected inflation over those three years.

The expected inflation rate after Year 1, rounded to two decimal places, can be calculated from the given information.

User Maxim Kasyanov
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