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 = 5%, E(₂r₁) = 6%, E(₃r₁) = 7.5% E(₄r₁) = 6.85%
Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities.

Question

Quizplus · Accepted Answer

The unbiased expectations theory states that the current long-term rate for a given maturity is equal to the average of the expected one-year rates over that maturity. Therefore, the current one-year rate is 5%, the current two-year rate is (5% + 6%) / 2 = 5.50%, the current three-year rate is (5% + 6% + 7.5%) / 3 = 6.16%, and the current four-year rate is (5% + 6% + 7.5% + 6.85%) / 4 = 6.33%.

Suppose That the Current One-Year Rate (One-Year Spot Rate) and Expected