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) = 7.85 percent
Using the unbiased expectations theory, calculate the current (long-term) rates for three-year- and four-year-maturity Treasury securities.

Question

Quizplus · Accepted Answer

The unbiased expectations theory states that the current long-term rate is the average of the expected future one-year rates. Therefore, the current three-year rate is:(₁R₁ + E(₂r₁) + E(₃r₁))/3 = (5% + 6% + 7.5%)/3 = 6.16%And the current four-year rate is:(₁R₁ + E(₂r₁) + E(₃r₁) + E(₄r₁))/4 = (5% + 6% + 7.5% + 7.85%)/4 = 6.58%

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