Question

The real risk-free rate of interest is 2%. Inflation is expected to be 3.5% the next 2 years and 6% during the next 3 years after that. Assume that the maturity risk premium is zero. What is the yield on 3-year Treasury securities? What is the yield on 5-year Treasury securities?

PLEASE SHOW WORK, EXPLANATION, AND EQUATION

Answer 1

Given that,

Real risk free rate r* = 2%

Inflation is expected to be 3.5% the next 2 years and 6% during the next 3 years after that

So, average inflation for the next 3 years = (inflation in 1st year + 2nd year + 3rd year)/3 = (3.5+3.5+6)/3 = 4.33%

similarly, average inflation for the next 5 years = (2*3.5 + 3*6)/5 = 5%

Maturity risk premium = 0%

So, Yield on a 3-year Treasury security = r* + average inflation for 3 year = 2 + 4.33 = 6.33%

So, Yield on a 5-year Treasury security = r* + average inflation for 5 year = 2 + 5 = 7.00%