Final Answer:
Assuming the expectations theory is correct, the interest rates in the term structure for maturities of one to four years would be, respectively:
A. 5%
B. 7%
C. 12%
D. 12%
Step-by-step explanation:
In the expectations theory of the term structure, it is posited that the long-term interest rates are an average of current and expected future short-term rates. Therefore, for each maturity, we can use the given paths of one-year interest rates over the next four years to calculate the expected long-term rates. The calculations are straightforward, as each year's rate is taken as is.
For instance, for the maturity of one year (A), the interest rate is simply 5%. For the maturity of two years (B), the interest rate is 7%, and so on. These rates are a direct reflection of the expected one-year rates over the corresponding periods. The yield curve, representing the relationship between interest rates and time to maturity, would thus exhibit an upward-sloping trend in accordance with the expectations theory. Such a curve suggests that investors anticipate higher future short-term interest rates, compensating for increased risk or inflation expectations.
In summary, the calculated interest rates align with the expectations theory, providing a straightforward interpretation of the yield curve under these specific scenarios. The theory's reliance on expectations for future short-term rates helps explain the upward slope of the yield curve in an environment where interest rates are expected to rise over time.