5. Forecasting Interest Rates Assume the current interest rate on a one-year Treasury bond (1R1) is 5.00 percent, the current rate on a two-year Treasury bond (1R2) is 5.75 percent, and the current rate on a three-year Treasury bond (1R3) is 6.25 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 long-term interest rates can be estimated by taking the average of the current and expected short-term interest rates over that period. In this case, the one-year interest rate expected on Treasury bills during year 3, denoted as 3f1, can be calculated using the current and expected short-term interest rates.
To calculate 3f1, we need to consider the following information:
1. Current interest rate on a one-year Treasury bond (1R1) is 5.00%.
2. Current interest rate on a two-year Treasury bond (1R2) is 5.75%.
3. Current interest rate on a three-year Treasury bond (1R3) is 6.25%.
To find 3f1, we will calculate the expected one-year interest rate in the third year by taking the average of the expected one-year interest rates in the first and second years.
Step 1: Calculate the differential between the second and first years:
Differential (2-1) = 1R2 - 1R1 = 5.75% - 5.00% = 0.75%.
Step 2: Calculate the differential between the third and second years:
Differential (3-2) = 1R3 - 1R2 = 6.25% - 5.75% = 0.50%.
Step 3: Calculate the expected one-year interest rate in the third year:
3f1 = 1R2 + Differential (3-2) = 5.75% + 0.50% = 6.25%.
Therefore, based on the unbiased expectations theory, the one-year interest rate expected on Treasury bills during year 3, 3f1, is estimated to be 6.25%.