7. Forecasting interest rates Assume the current interest rate on a one-year Treasury bond (1R1) is 5.50 percent, the current rate on a two-year Treasury bond (1R2) is 5.95 percent, and the current rate on a three-year Treasury bond (1R3) is 8.50 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the one-year interest rate expected on Treasury bills during year 3, 3f1?
According to the unbiased expectations theory of the term structure of interest rates, the expected one-year interest rate on Treasury bills during year 3, denoted as 3f1, can be calculated using the current interest rates on longer-term bonds.
To calculate 3f1, we will use the formula:
3f1 = [(1R3)^3 / (1R2)^2]^(1/3) - 1
Let's substitute the given interest rates into the formula:
1R3 = 8.50% (current rate on a three-year Treasury bond)
1R2 = 5.95% (current rate on a two-year Treasury bond)
Now, we can calculate 3f1:
3f1 = [(8.50%)^3 / (5.95%)^2]^(1/3) - 1
Solving the equation:
3f1 = [(0.7225) / (0.354025)]^(1/3) - 1
3f1 = (2.0416)^(1/3) - 1
3f1 = 1.2655 - 1
3f1 = 0.2655
Therefore, based on the unbiased expectations theory, the expected one-year interest rate on Treasury bills during year 3 (3f1) is 26.55%.