Question

Suppose that the spot interest rate on a one-year zero-coupon bond is 2% and the spot interest rate on a two-year zero-coupon bond is 3.5%. Based on the pure expectations theory of the term structure of interest rates, what is the expected one-year interest rate starting in one year?

Answer 1

Given ,

One year spot rate ( S1) = 2%

Two year spot rate (S2) = 3.5%

Based on pure expectation theory ,

One year interest rate starting in one year = (1+ S2)^2 / (1+S1) – 1

                                                                   = (1+3.5%)^2 / (1+2%) -1

                                                                   = (1.035^2 /1.02) -1

= (1.071225 / 1.02) -1 = 1.050221 -1 = 5.0221%

Hence, One year interest rate starting one year = 5.0221%