4. Liquidity Premium Hypothesis Suppose we observe the following rates: 1R1 = 8 percent, 1R2 = 10 percent, and E(2r1) = 8 percent. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2, L2?

To calculate the liquidity premium for year 2, L2, according to the liquidity premium hypothesis, we need to use the following formula:

L2 = 1R2 - E(2r1)

Where:
1R2 = the observed interest rate for a two-year bond, in this case, 10 percent.
E(2r1) = the expected one-year interest rate in the second year, in this case, 8 percent.

Now substitute the values into the formula:

L2 = 1R2 - E(2r1)
L2 = 10% - 8%
L2 = 2%

Therefore, the liquidity premium for year 2, L2, is 2%.

To find the liquidity premium for year 2, L2, using the liquidity premium theory of the term structure of interest rates, you can follow these steps:

Step 1: Calculate the expected return for year 2, E(2R2), using the formula:
E(2R2) = 2E(2r1) - 1R1

Here, 2r1 refers to the expected return for year 1, E(2r1), and 1R1 is the observed rate for year 1.
Given that E(2r1) = 8 percent and 1R1 = 8 percent, we can substitute the values into the formula:
E(2R2) = 2(8%) - 8%
E(2R2) = 16% - 8%
E(2R2) = 8%

Step 2: Calculate the expected excess return for year 2, E(2r2), using the formula:
E(2r2) = E(2R2) - 1R2

Here, 1R2 is the observed rate for year 2.
Given that E(2R2) = 8 percent and 1R2 = 10 percent, we can substitute the values into the formula:
E(2r2) = 8% - 10%
E(2r2) = -2%

Step 3: Calculate the liquidity premium for year 2, L2, using the formula:
L2 = E(2r2) - LRP2

Here, LRP2 refers to the liquidity risk premium for year 2.
Since the formula does not provide any specific values to calculate LRP2, we cannot determine a precise value for L2 using the given information.

Therefore, based on the given information, we cannot calculate the liquidity premium, L2.