8. 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:

Question

1R1 = 5 percent, E(2r1) = 6 percent, E(3r1) = 7.5 percent E(4r1) = 6.85 percent

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securiti
es.

Answer 1

1R1 = 6%
1R2 = [(1 + .06)*(1 + .07)] 1/2- 1 = 6.5%
1R3 = [(1 + .06)*(1 + .07)*(1 + .075)] 1/3- 1 = 6.8%
1R4 = [(1 + .06)*(1 + .07)*(1 + .075)*(1 + .0785)] 1/4- 1 = 7.1%