The real risk-free rate is 2.1%. Inflation is expected to be 2.2% this year, 3.95% next year, and then 3.05% thereafter. The maturity risk premium is estimated to be 0.05(t - 1)%, where t = number of years to maturity. What is the yield on a 7-year Treasury note? Round your answer to two decimal places.
To calculate the yield on a 7-year Treasury note, we need to consider various components, including the real risk-free rate, inflation expectations, and the maturity risk premium.
Step 1: Calculate the expected inflation for each year.
- Inflation for the current year is given as 2.2%.
- Next year's inflation is expected to be 3.95%.
- Inflation thereafter is expected to be 3.05%.
Step 2: Calculate the nominal risk-free rate for each year.
- Add the expected inflation to the real risk-free rate.
- For the current year, the nominal risk-free rate is 2.1% + 2.2% = 4.3%.
- For next year, it is 2.1% + 3.95% = 6.05%.
- For subsequent years, it is 2.1% + 3.05% = 5.15%.
Step 3: Determine the maturity risk premium for a 7-year Treasury note.
- The maturity risk premium is calculated using the formula 0.05(t - 1)%, where t is the number of years to maturity.
- For a 7-year note, the maturity risk premium is 0.05(7 - 1)% = 0.05(6)% = 0.3%.
Step 4: Calculate the yield on the 7-year Treasury note.
- The yield is the sum of the nominal risk-free rate and the maturity risk premium.
- For a 7-year note, the yield is 5.15% + 0.3% = 5.45%.
Therefore, the yield on a 7-year Treasury note is 5.45%.