Question

Problem 4-20
Inflation Risk Premiums

Because of a recession, the inflation rate expected for the coming year is only 4%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 4%. 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?

%

Answer 1

first we calculate yield of 1-year treasury note.

yield of 1-year treasury note = [(1+real risk-free rate)*(1+inflation in year 1)] - 1 = [(1+0.02)*(1+0.04)] - 1 = (1.02*1.04) - 1 = 1.0608 - 1 = 0.0608 or 6.08%

3-year Treasury notes yield 2 percentage points more than 1-year notes. so 3-year Treasury notes yield is 6.08% + 2% = 8.08%.

inflation rate expected after year 1 = [(1+3-year Treasury notes yield)/(1+real risk-free rate)] - 1 = [(1+0.0808)/(1+0.02)] - 1 = (1.0808/1.02) - 1 = 1.0596 - 1 = 0.0596 or 5.96%

inflation rate expected after Year 1 is 5.96%.