Assume the current interest rate on a one-year Treasury bond (₁R₁) is 5.00 percent, the current rate on a two-year Treasury bond (₁R₂) is 5.75 percent, and the current rate on a three-year Treasury bond (₁R₃) is 6.25 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the one-year interest rate expected on Treasury bills during year 3, ₃f₁?

Question

Quizplus · Accepted Answer

The unbiased expectations theory suggests that the forward rates implied by current long-term interest rates are unbiased predictors of future short-term interest rates. To find the expected one-year interest rate in year 3 ($S_3^1$), we use the given yields to solve for the implied forward rate. The formula to equate the return from investing in a three-year bond to a strategy of rolling over one-year bonds is: $(1 + 5\%) \times (1 + S_2^1) \times (1 + S_3^1) = (1 + 6.25\%)^3$. We already know the rates for the first two years, so we solve for $S_3^1$, which gives us an expected rate of approximately 7.26 percent for the third year.

Assume the Current Interest Rate on a One-Year Treasury Bond