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 1.5%, what inflation rate is expected after Year 1? Round your answer to two decimal places.

Answer 1

Calculation of Inflation rate expected after Year 1 :

We first need to calculate treasury yield on 1 year Bond

1-year Treasury Security Yield = r* + Expected Inflation in year 1

= 3.5% + 3.75%

= 7.25%

3- year treasury yield security = 1-year Treasury Security Yield + 1.5%

= 7.25% + 1.5%

= 8.75%

Calculation of Yield on 2-year security :

(1 + Total Return earned on 1-year security )^1 * (1 + yield on two year security yielding 4-years)^2 = (1 + Total Return earned on 3-year security)^3

(1 + 0.0725)^1 * (1 + yield on two year security yielding 2-years)^2 = (1 + 0.0875)^3

==>  (1 + yield on two year security yielding 2-years)^2 = (1 + 0.0875)^3 / (1 + 0.0725)

Yield on year bond two year from now =[1.19919689684]^(1/2) - 1

  = 1.09507848883 - 1

= 9.51%

Inflation Premium expected after year 1 = 9.51% - 3.5% = 6.01%