Suppose you and most other investors expect the inflation rate to be 3.00% next
ID: 2805693 • 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 5-year Treasury securities.Question options:
5.70%
6.30%
5.90%
6.10%
5.70%
6.30%
5.90%
6.10%
Explanation / Answer
Option 5.9% is correct For each of the bonds, we will find the average expected inflation rate over years 1 to N: Inflation is expected to be 3% next year, 4% the following year, and 5% thereafter. IP5= [3% + 4% + 5%(3)] / 5 = 4.40% Step 2 – Find the appropriate maturity risk premium (MRP). For this example, the following equation will be used find a security’s appropriate maturity risk premium Using the given equation: MRP5 = 0.1% x (5) = 0.5% r = r* + IP + DRP + LP + MRP, but for Treasury securities, liquidity premium (LP) and default risk premium (DRP) are 0. Step 3 – Use IP and MRP to calculate the nominal rates. rRF, t = r* + IPt + MRPt We are told to assume real risk-free rate r* = 1%: rRF, 5 = 1% + 4.4% + 0.5% = 5.9%