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 2.5%. 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

Answer :

Here, we have

Real risk free rate (r*) = 2.5%

Inflation premium (IP1) = 3.75%

Yield on treasury bond = r* + IP1

= 2.5% + 3.75% = 6.25%

Yield on 3 year treasury bond = Yield on 1 year treasury bond + 0.5%

= 6.25% + 0.5% = 6.75%

Yield on 3 year treasury bond = r* + IP3

6.75% = 2.5% + IP3

IP3 = 6.75% - 2.5% = 4.25%

IP3 = ( IP1 + 2IP ) / 3

4.25 = ( 3.75 + 2IP ) / 3

4.25 * 3 = 3.75 + 2IP

( 12.75 - 3.75 ) / 2 = IP

IP = 4.50%

Inflation Rate expected after year 1 = 4.50%