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 = 0.3%, E(2r 1) = 1.3%, E(3r1) = 9.4%, E(4r1) = 9.75%. 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

Answer:

Year 1 long term rate is the same as first year 1 year rate = 0.3%

Year 2

= √[(1 + year 1 rate%) * (1 + year 2 rate%)]  - 1

= √[(1 + 0.3%) * (1 + 1.3%)] - 1

= 0.799%

Year 3

= ³√[(1 + year 1 rate%) * (1 + year 2 rate%) *  (1 + year 3 rate%)]  - 1

= ³√[(1 + 0.3%) * (1 + 1.3%) * (1 * 9.4)] - 1

= 3.588%

Year 4

=  ⁴√[(1 + year 1 rate%) * (1 + year 2 rate%) *  (1 + year 3 rate%) * (1 + 4 year rate)]  - 1

= ⁴√[(1 + 0.3%) * (1 + 1.3%) * (1 * 9.4) * (1 + 9.75%)] - 1

= 5.095%