Using the pure expectations approach to the determination of interest rates,calculate the expected (E) rate of interest of a two-year investment that will be available in 12 months' time (₁i₃) ,given the following data:
Current rate of return on a one-year-to-maturity (₀i₁) instrument:7.75% per annum
Current rate of return on a two-year maturity (₀i₂) instrument:8.25% per annum
Current rate of return on a three-year maturity (₀i₃) instrument:8.65% per annum

Question

Quizplus · Accepted Answer

According to the pure expectations theory, expected future interest rates can be calculated using the current rates and the market's expectations of future rates. In this case, we need to calculate the expected interest rate on a two-year investment that will be available in 12 months' time.

Using the current rates, we can calculate the expected one-year rate in 12 months as follows:

Expected one-year rate in 12 months = [(1 + 0.0775) x (1 + 0.0825)]^(1/2) - 1 = 0.0910 or 9.10% per annum

Therefore, the expected rate of interest on a two-year investment that will be available in 12 months' time is 9.10% per annum.

The correct answer is B.

Using the Pure Expectations Approach to the Determination of Interest