If the expected path of one-year interest rates over the next five years is 4
percent, 5 percent, 7 percent, 8 percent, and 6 percent, then the expectations theory predicts that today's interest rate on the five-year bond is

Question

BlackTom AI · Accepted Answer

To tackle this question, I’ll break down what the expectations theory implies and then evaluate each choice.
Option A: 4 percent. If the five-year rate were 4 percent today, that would suggest the market expects each of the next five consecutive one-year rates to average to 4 percent. However, the given expected path includes values above 4 percent (5, 7, 8, and 6), so 4 percent is too low to reflect the expected path.
Option B: 5 percent. Similarly, 5 percent would require the five annual one-year rates to average to 5 percent. But since the sequence includes rates above 5 percent (7, 8, and 6), simply averaging to 5 would undershoot the higher expectations in several years, making 5 percent inconsistent with the stated path.
Option C: 6 percent. The expectations theory states that the current yield on a five-year bond equals the average of the expected one-year rates over the next five years. Compute the average: (4 + 5 + 7 + 8 + 6) / 5 = 30 / 5 = 6. Therefore, 6 percent aligns exactly with the given expected path.
Option D: 7 percent. A 7 percent five-year rate would require the average of the five annual one-year rates to be 7 percent, which contradicts the provided sequence where several years have rates well below 7 (4 and 5). Hence this choice misrepresents the implied average.
In summary, the only option consistent with the expectations theory and the supplied path is the one that yields an average of 6 percent across the five expected one-year rates.

If the expected path of one-year interest rates over the next five years is 4 percent, 5 percent, 7 percent, 8 percent, and 6 percent, then the expectations theory predicts that today's interest rate on the five-year bond is

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