On March 11, 20XX, the existing or current (spot) 1-, 2-, 3-, and 4-year zero coupon Treasury security rates were as follows:

1R1 = 0.40%, 1R2 = 1.00%, 1R3 = 1.40%, 1R4 = 1.55%
Using the unbiased expectations theory, calculate the 1-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4 as of March 11, 20XX. (Do not round intermediate calculations and round your answers to 2 decimal places.)
Years Forward rates
2. %
3. %
4. %

To calculate the 1-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4, we can use the unbiased expectations theory.

The unbiased expectations theory states that the forward rates should be equal to the market's expectations of future spot rates. In other words, the forward rate for a certain time period is calculated based on the current spot rates and the expected spot rates for that time period.

To calculate the 1-year forward rate for year 2, we need to find the expected spot rate for year 2. According to the unbiased expectations theory, the forward rate for year 2 should be equal to the expected spot rate for year 2.

Using the given spot rates, we have:

Spot rate for year 2: 1R2 = 1.00%

Therefore, the 1-year forward rate for year 2 is 1.00%.

To calculate the 1-year forward rate for year 3, we need to find the expected spot rate for year 3. Again, according to the unbiased expectations theory, the forward rate for year 3 should be equal to the expected spot rate for year 3.

To calculate the expected spot rate for year 3, we can use the current spot rates and the 1-year forward rate for year 2. The expected spot rate for year 3 can be calculated as:

Expected spot rate for year 3 = (1 + 1R2) * (1 + 1-year forward rate for year 2) -1

Plugging in the values, we have:

Expected spot rate for year 3 = (1 + 1.00%) * (1 + 1.00%) - 1 = 2.01%

Therefore, the 1-year forward rate for year 3 is 2.01%.

Similarly, to calculate the 1-year forward rate for year 4, we can use the current spot rates and the 1-year forward rates for years 2 and 3. The expected spot rate for year 4 can be calculated as:

Expected spot rate for year 4 = (1 + 1R3) * (1 + 1-year forward rate for year 3) - 1

Plugging in the values, we have:

Expected spot rate for year 4 = (1 + 1.40%) * (1 + 2.01%) - 1 = 3.42%

Therefore, the 1-year forward rate for year 4 is 3.42%.

In summary, the 1-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4 as of March 11, 20XX, are as follows:

2-year forward rate: 1.00%
3-year forward rate: 2.01%
4-year forward rate: 3.42%