Question

Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e. years 2, 3, and 4, respectively) are as follows: IRI . 0.58, E(2r 1) . 1.51, E(3r1)-9.9%, E(4r1 ) . 10.25% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. (Round your answers to 3 decimal places. (e.g., 32.161) Current (Long-Term) Rates One-year Two-year Three-year Four-year

Answer 1

As per the unbiased expectations theory:

One year = 1.005 =(1+r)^1 = 0.5%

Two year = 1.005*1.015 = (1+r)^2 = r = 0.009987 = 0.999%

Three year = 1.005*1.015*1.099 = (1+r)^3 = r = 0.038827 = 3.883%

Four year = 1.005*1.015*1.099*1.1025 = (1+r)^4 = r = 0.05439199 = 5.439%