The Wall Street Journal reports that the rate on four-year Treasury securities is 4.75 percent and the rate on five-year Treasury securities is 5.95 percent. According to the unbiased expectations hypotheses, what does the market expect the one-year Treasury rate to be four years from today, E(₅r₁)?

Question

Quizplus · Accepted Answer

The unbiased expectations hypothesis suggests that the future interest rates are reflected in the term structure of interest rates. To find the expected one-year rate four years from now, we can use the formula that equates the return from investing in a five-year security to the return from investing in a four-year security and then rolling over the investment into a one-year security after four years. The formula is: $(1 + r_{5-year})^5 = (1 + r_{4-year})^4 \times (1 + E(r_{1-year, 4 years from now}))$. Plugging in the given rates: $(1 + 0.0595)^5 = (1 + 0.0475)^4 \times (1 + E(r_{1-year, 4 years from now}))$. Solving for $E(r_{1-year, 4 years from now})$ gives approximately 10.89 percent.

The Wall Street Journal Reports That the Rate on Four-Year