Question

A recent edition of The Wall Street Journal reported interest rates of 3.10 percent, 3.45 percent, 3.76 percent, and 3.02 percent for three-year, four-year, five-year, and six-year Treasury notes, respectively. According to the unbiased expectations theory of the term structure of interest rates, what are the expected one-year rates during years 4, 5, and 6?

Answer 1

Expected one year rates in year4 = {[1+i4]^4 /[1+i3]^3} -1

                            = {[1+.0345]^4 /[1+.031]^3 } -1

                            = {1.14531/ 1.09591 } -1

                            = 1.0451-1

                             = .0451 or 4.51%

Expected one year rate in year 5 ={[1+i5]^5 /[1+i4]^4} -1

                                       = {[1+.0376]^5 /[1+.0345]^4} -1

                                       = {1.20268 / 1.14531 } - 1

                                       = 1.0501 - 1

                                       = .0501 or 5.01%

Expected one year rate in year 6 ={[1+i6]^6 /[1+i5]^5} -1

                                          = {[1+.0302]^6 /[1+.0376]^5 1} -1

                                          = {1.19544/1.20268 } - 1

                                          = .99398-1

                                         = - .00602 or - .60%