Question

Assume that a 3-year Treasury note has no maturity premium, and that the real, risk-free rate of interest is 3 percent. If the T-note carries a yield to maturity of 13 percent, and if the expected average inflation rate over the next 2 years is 11 percent, what is the implied expected inflation rate during Year 3?

please show work in written form (not excel) thank you.

Answer 1

Answer - 8%

Given real risk free rate = Rf = 3%,

3-year YTM = nominal rate = 13%

Average Inflation over next 2 years = 11%

Calculating, Average nominal rate over next 2 years =

Average Inflation over next 2 years + real risk free rate = 11% + 3% = 14% [ linear approximation of Fischer equation]

Assume, Implied Inflation during 3rd year = i  

so, Implied nominal rate during 3rd year = Implied Inflation during 3rd year + real risk free rate = i + 3% = i + 0.03

Using nominal rate formula from Fischer equation,

(1+ 3-year nominal rate)³ = (1+Average nominal rate over next 2 years)² * (1+Implied nominal rate during 3rd year)

or, (1+13%)³ = (1+14%)² * (1+ i + 0.03)

or, i + 1.03 = 1.11

so, i = 1.11 -1.03 = 0.08 = 8%

Implied Inflation during 3rd year = i = 8%