Question

Problem 6-15
Expectations Theory

Assume that the real risk-free rate is 2.5% and that the maturity risk premium is zero. Also assume that the 1-year Treasury bond yield is 5.8% and a 2-year bond yields 6.4%.

What is the 1-year interest rate that is expected for Year 2? Round your answer to two decimal places.

_______%

What inflation rate is expected during Year 2? Round your answer to two decimal places.

______%

Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2. (select multiplw choice answer)

a.The difference is due to the fact that there is no liquidity risk premium.

b.The difference is due to the inflation rate reflected in the two interest rates. The inflation rate reflected in the interest rate on any security is the average rate of inflation expected over the security's life.

c.The difference is due to the real risk-free rate reflected in the two interest rates. The real risk-free rate reflected in the interest rate on any security is the average real risk-free rate expected over the security's life.

d.The difference is due to the fact that the maturity risk premium is zero.

e.The difference is due to the fact that we are dealing with very short-term bonds. For longer term bonds, you would not expect an interest rate differential.

Answer 1

Q1. Based on Pure Expectations Theory, short term interest rates are indicator of future interest rates. For question, this implies whether you invest in a 2 year bond or you invest in 1 year bond now, and when it matures, again invest in another 1 year bond, youw will earn same yield or return in both cases.

(1 + Spot Yield for 2yr bond)² = (1 + Spot Yield for 1 yr bond) * (1 + Rate on 1 yr bond 1 yr from now)

(1 + 6.4%)² = ( 1 + 5.8%) * (1 + Rate on 1 yr bond 1 yr from now)

Rate on 1 yr bond 1 yr from now = 7.41%

Q2. Based on Fischer relation, Nominal rate = Real Rate + Inflation

Real risk free rate = 2.5%

Nominal Rate for a 1 year bond (1 year from now) = 7.41%

Hence, Inflation = 4.91% --> Answer

Q3. Answer is option b.

As the optiona explains nominal yield accounts for average inflation over the life of bond.

For year 1, inflation is = 3.3%, For year 2, inflation = 4.91%.

2 year bond yeild will take inflation = (3.3% + 4.91%)/2 = 4.105%, whereas the 1 year bon 1 year from now yield will take 4.91% into its nominal calculation.