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: 1R1 = 0.4%, E(2r 1) = 1.4%, E(3r1) = 1.9%, E(4r1) = 2.25% 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))

Answer 1

1. One year long term rate = one year spot rate = 0.400%

2. Two year long term rate = (1 + 1R1) * (1 + E(2R1) - 1

Two year long term rate = ((1.004) * (1.014)]^1/2) - 1

Two year long term rate = 0.748%

3. 3 year long term rate = [(1 + 1R1) * (1 + E(2R1)) * (1 + E(3R1)]^(1/3) - 1

3 year long term rate = [ 1.004 * 1.014 * 1.019]^(1/3) - 1

3 year long term rate = 1.021%

4. 4 year long term rate = [(1 + 1R1) * (1 + E(2R1)) * (1 + E(3R1) * (1 + E(4R1)]^(1/4) - 1

4 year long term rate = [1.004 * 1.014 * 1.019 * 1.0225]^(1/4) - 1

4 year long term rate = 1.244%