Suppose you and most other investors expect the inflation rate to be 3.00% next
ID: 2787685 • Letter: S
Question
Suppose you and most other investors expect the inflation rate to be 3.00% next year, 4.00% during the following year, and then to remain at a rate of 5.00% thereafter. Assume that the real risk-free rate will remain at 1.00% and that maturity risk premiums on Treasury securities rise from zero on very short- term securities to a level of 0.10% percentage points for 1-year securities. Furthermore, maturity risk premiums increase 0.10 percentage points for each year to maturity, up to a limit of 1.00 percentage point on 10-year or longer-term T-notes and T-bonds. Calculate the interest rate on a 7-year Treasury securities.
Explanation / Answer
7 year inflation rate = [(1 + 3%) × (1 + 4%) × (1 + 5%) ^ 5] ^ (1 / 7) - 1
= [1.3672 ^ (1 / 7)] - 1
= 1.0457 - 1
= 4.57%
7 year inflation rate is 4.57%.
Maturity risk premium = 0.10% × (10 - 1)
= 0.90%.
Yield on treasury bill = Real risk free rate + Inflation rate + Maturity risk premium
= 1% + 4.57% + 0.90%
= 6.47%
Yield on treasury security is 6.47%.