Question

The real short-term risk-free rate is 1.5% and expected to stay constant. The inflation rate is expected to be 1% this year, 2% for each of the following 5 years, and 2.5% thereafter. The maturity risk premium is expected to be 0.0004 * T, where T is the number of years to maturity.

What is the expected yield on a 1-year Treasury bill?

part 2: What is the expected yield on a 3-year Treasury note?

part 3: What is the expected yield on a 30-year Treasury bond?

Answer 1

1)Expected yield on a 1-year Treasury bill = Risk free rate+ Inflation premium

                           = 1.5 + 1

                           = 2.50%

2)Average Inflation for 3 years = [IP1+IP2+IP3]/N

                 =[1+2+2]/3

                 = 5/3

                 = 1.67%

Maturity risk premium = .0004* 3 = .0012

Expected yield on 3 year Treasury note = Risk free rate +Inflation premium +Maturity risk premium

                  = 1.5+1.67+ .0012

                   = 3.1712%

3)Average Inflation for 30 years =[1+ (2*5)+(2.5*24)]/30

             =[1+ 10+ 60]/30

             = 71/30

             = 2.37%

Maturity risk premium = .0004*30 = .012

expected yield on a 30-year Treasury bond =Risk free rate +Inflation premium +Maturity risk premium+Default risk premium +liquidity premium

        = 1.5 +2.37+.012

= 3.882%