Question

Due to a recession, expected inflation this year is only 2.5%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 2.5%. Assume that the expectations theory holds and the real risk-free rate (r*) is 3%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 3%, 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 = 2.5% and r* = 3%. Therefore,

rT1 = 3% + 2.5% = 5.5%.

rT3 = rT1 + 3% = 5.5% + 3% = 8.5%.

But,

rT3 = r* + IP3 = 3% + IP3 = 8.5%,

so

IP3 = 8.5% – 3% = 5.5%.

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

We can set up this table:

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

IP3= 5.5% = (2.5% + 2IP)/3

16.5% = 2.5% + 2IP

2IP = 14%

IP = 7%

inflation rate is expected after year 1 = 7%