Question

EXPECTATIONS THEORY Assume that the real risk-free rate is 2% and that the maturity risk premium is zero. If a 1-year Treasury bond yield is %5 and a 2-year Treasury bond yields 7%, what is the 1-year interest rate that is expected for Year 2? Calculate this yield using a geometric average. What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2.

Answer 1

Yield using geometric average:

Let 1 year interest rate that is expected for year 2 be x

(1 + Yield of 2-year Treasury Bond)² = (1 + Yield on 1-year Treasury Bond) * (1 + x)

(1 + 0.07)² = (1 + 0.05) * (1 + x)

x = (1.1449 / 1.05 ) - 1 = 0.09038

x = 9.04%

Expected infaltion in 1-year: Nominal interest = Real interest + Inflation

Hence Inflation (for 1 year) = 5% - 2% = 3%

Expected infaltion in 2-year: Nominal interest = Real interest + Inflation

Hence Inflation (for 2 years) = 7% - 2% = 5%

Inflation for 2 years = ( Inflation 1st year + Inflation 2nd year ) / 2

Substituting values,

5 % = ( 3% + Inflation 2nd year ) / 2

Inflation during year 2 = 7%

Inflation during year 2 is higher than the average interest rate durinng 2 year period indicates that the inflation is expected to increase.