Suppose we observe the following rates: ₁R₁ = 6 percent, ₁R₂ = 7.5 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now, E(₂r₁)?

Question

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The unbiased expectations theory suggests that the future interest rate can be derived from the current term structure. Given a 1-year rate of 6% and a 2-year rate of 7.5%, the expected 1-year rate one year from now can be calculated using the formula: $(1 + z_2)^2 = (1 + z_1)(1 + E[z_1])$, where $z_2$ is the 2-year rate, $z_1$ is the 1-year rate, and $E[z_1]$ is the expected 1-year rate one year from now. Solving for $E[z_1]$ gives approximately 9.02%.

Suppose We Observe the Following Rates: 1R1 = 6 Percent

Suppose We Observe the Following Rates: ₁R₁ = 6 Percent