Question

Due to a recession, expected inflation this year is only 3.75%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.75%. Assume that the expectations theory holds and the real risk-free rate (r*) is 3.5%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 0.5%, what inflation rate is expected after Year 1? Round your answer to two decimal places.

____ %

Answer 1

Yield on 1-year Treasury Bond = Real Risk-free Rate + Inflation Premium on 1-year Treasury Bond
Yield on 1-year Treasury Bond = 3.50% + 3.75%
Yield on 1-year Treasury Bond = 7.25%

Yield on 3-year Treasury Bond = Real Risk-free Rate + Inflation Premium on 3-year Treasury Bond
Yield on 3-year Treasury Bond = 3.50% + Inflation Premium on 3-year Treasury Bond

Yield on 3-year Treasury Bond = Yield on 1-year Treasury Bond + 0.50%
3.50% + Inflation Premium on 3-year Treasury Bond = 7.25% + 0.50%
3.50% + Inflation Premium on 3-year Treasury Bond = 7.75%
Inflation Premium on 3-year Treasury Bond = 4.25%

Inflation Premium on 3-year Treasury Bond = Average Inflation over next 3 years
4.25% = [3.75% + 2 * Inflation for Year 2 and thereafter] / 3
12.75% = 3.75% + 2 * Inflation for Year 2 and thereafter
9.00% = 2 * Inflation for Year 2 and thereafter
Inflation for Year 2 and thereafter = 4.50%