Question

A recent edition of The Wall Street Journal reported interest rates of 6%, 6.35%, 6.65% and 6.75% for 3-year, 4-year, 5-year and 6-year Treasury notes, respectively.

According to the unbiased expectations hypothesis, what are the expected one-year rates for year 4, 5, and 6 (i.e., what are 4f1, 5f1, and 6f1)?

Answer 1

4F1 = [(1+r4)^4/(1+r3)^3]    -1

       =[(1+.0635)^4/(1+.06)^3]   -1

        = [1.27923/1.19102]   -1

        = 1.0741-1

         = .0741 or 7.41%

5F1= [(1+.0665)^5/(1+.0635)^4]   -1

       = [1.37976/1.27923] -1

       = 1.0786-1

       = .0786 or 7.86%

6F1=[(1+r6)^6/(1+r5)^5 ]   -1

     =[(1+.0675)^6 /(1+.0665)^5 ] -1

      =[1.47981/1.37976]-1

     = 1.0725-1

     = .0725 or 7.25%