Question

Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that the expectations theory holds and the real risk-free rate (r*) is 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.​

Answer 1

Basic relevant equations:

rt = r* + IPt + DRPt + MRPt + IPt.

But here IPt is the only premium, so rt = r* + IPt.

IPt = Avg. inflation = (I1 + I2 + . . .)/N.

We know that I1 = IP1 = 3.25% and r* = 2.25%. Therefore,

rT1 = 2.25% + 3.25% = 6%. rT3 = rT1 + 2.25% = 6% + 2.25% = 8.25%

But,

rT3 = r* + IP3 = 2.25% + IP3 = 8.25%, so

IP3 = 8.25% – 2.25% = 6%.

We also know that It = Constant after t = 1.

We can set up this table:

r* I Avg. I = IPt r = r* + IPt

IP3= 6% = (3.25% + 2IP)/3

18 = 3.25 + 2IP

2IP = 14.75%

IP = 7.375%