Because of a recession, the inflation rate expected for the coming year is only 3%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3%. Assume that the real risk-free rate is r* = 2% for all maturities and that there are no maturity premiums. If 3-year Treasury notes yield 2 percentage points more than 1-year notes, what inflation rate is expected after Year 1?

Basic equation is: r t = r* IP t DRP t MRP t LP t But, DRP t = MRP t = LP t = 0 So, r t = r* IP t IP t = Average

Inflation = (I 1 I 2 I 3 ..) / N It is given that I 1 = IP 1 = 3% and r*

= 2%. Therefore, r 1 =

2% 3% = 5% 3-year

Treasury notes yield 2 percentage points more than 1-year notes. So, r 3 =

r 1 2% = 5% 2% = 7% Also, r 3 =

r* IP 3 = 2% IP 3…

e 2% IP 3 = 7% So, IP 3 = 5% It is given that It is constant after t = 1. So I 2 = I 3 =I 4 = IP 3 = (I 1 I 2 I 3 )

/ 3 Or IP 3 = (I 1 2I) / 3 5% = (3% 2I) / 3 15% = 3% 2I I = (15% – 3%) / 2 = 6% Expected inflation rate after

Year 1 is 6%