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 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 securities.

Question

Quizplus · Accepted Answer

The unbiased expectations theory suggests that the current long-term rates can be calculated as the average of the current and expected future short-term rates. For a two-year maturity, the average rate is (5% + 6%) / 2 = 5.50%. For a three-year maturity, it's (5% + 6% + 7.5%) / 3 = 6.16%. For a four-year maturity, it's (5% + 6% + 7.5% + 6.85%) / 4 = 6.33%.

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