Unbiased Expectations Theory Suppose we observe the three-year Treasury security rate (₁R₃) to be 6 percent, the expected one-year rate next year E(₂r₁) to be 3 percent, and the expected one-year rate the following year E(₃r₁) to be 5 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate, ₁R₁?

Question

Quizplus · Accepted Answer

According to the unbiased expectations theory, the long-term interest rate should be equal to the geometric average of expected future short-term interest rates. Thus, we can calculate the expected yield for the three-year bond as: (1+r)³ = (1+3%) * (1+5%) * (1+x%) where x is the unknown one-year rate. Solving for x, we get: x = 10.13% Therefore, the one-year Treasury security rate should be ₁R₁, which is 10.13%. Answer choice B is correct.

Unbiased Expectations Theory Suppose We Observe the Three-Year Treasury Security