Question

The real risk-free rate of interest, is 3%, and it is expected to remain constant over time. Inflation is expected to be 2% per year for the next 3 years and 4% per year for the next 5 years. The maturity risk premium is equal to 0.1 x (t-1) %, where t = the bond’s maturity. The default risk premium for a BBB-rated bond is 1.3%.

If the yield on a 9-year Treasury bond is 7.3%, what does that imply about expected inflation in 9 years?

Answer 1

Yield on 9 year treasury bond = Risk free rate +Average inflation + maturity risk premium

     7.3 = 3 +AI + .8

     7.3 = 3.8 + AI

    AI = 7.3 -3.8

         = 3.5%

Now

Average inflation = [(i1-3 *n)+(i4-8*n) +(i9-n)] Total n

           3.5     = [(2*3)+(4*5)+ (i9*1)]/9

           3.5 =[6 +20 + i9 ]/9

   3.5 *9 = 26 +i9

   31.5 - 26 = i9

   i9= 5.5%

Expected inflation in 9 years = 5.5%

Note:

Default risk premium is a risk of borrower failing to repay the principal amount .This risk premium is a component included in corporate rated bonds as treasury bonds are risk free (government bonds) therefore Default risk premium is not included in interest rate of treasury bond

Maturity risk premium = .1*(9-1)

                  = .1*8

                  =.8%