Assume investors are indifferent among security maturities. Today, the annualized two-year interest rate is 12 percent, and the one-year interest rate is 9 percent. What is the forward rate according to the pure expectations theory?

Question

Quizplus · Accepted Answer

The pure expectations theory suggests that the forward rate can be calculated in a way that an investor would be indifferent between investing in a two-year security and investing in a one-year security and then reinvesting the proceeds for another year. Given the annualized two-year interest rate is 12 percent and the one-year interest rate is 9 percent, we can use the formula:$$ (1 + r_{2y})^2 = (1 + r_{1y}) \times (1 + r_{f}) $$Where $ r_{2y} $ is the two-year interest rate, $ r_{1y} $ is the one-year interest rate, and $ r_{f} $ is the forward rate for the second year. Plugging in the given rates:$$ (1 + 0.12)^2 = (1 + 0.09) \times (1 + r_{f}) $$$$ 1.2544 = 1.09 \times (1 + r_{f}) $$$$ 1 + r_{f} = \frac{1.2544}{1.09} $$$$ r_{f} = \frac{1.2544}{1.09} - 1 $$$$ r_{f} = 1.1508 - 1 $$$$ r_{f} = 0.1508 $$$$ r_{f} = 15.08\% $$Therefore, the forward rate according to the pure expectations theory is 15.08 percent.

Assume Investors Are Indifferent Among Security Maturities