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?

7.6

The liquidity premium theory suggests that the difference between the interest rate on a long-term bond and a series of short-term bonds should be equal to the expected value of the future short-term interest rates minus the current short-term interest rate. In this case, we are given the following rates:

1R1 = 8% (interest rate for the first year)
1R2 = 10% (interest rate for the second year)
E(2r1) = 8% (expected value of the future short-term interest rates for year 2)

To find the liquidity premium for year 2, L2, we need to calculate the expected value of the future short-term interest rates for year 2 (2r1).

1. First, let's calculate the difference between the interest rates for the two years:
Difference between 1R1 and 1R2 = 1R2 - 1R1 = 10% - 8% = 2%

2. According to the liquidity premium theory, this difference should be equal to the expected value of the future short-term interest rates (2r1) minus the current short-term interest rate (1R1):
Difference = E(2r1) - 1R1

3. Rearranging the equation, we can find the expected value of the future short-term interest rates for year 2 (2r1):
E(2r1) = Difference + 1R1 = 2% + 8% = 10%

4. Now that we have the expected value of the future short-term interest rates for year 2 (2r1), we can find the liquidity premium for year 2 (L2) by subtracting the current short-term interest rate for year 2 (1R2) from the expected value:
L2 = E(2r1) - 1R2 = 10% - 10% = 0%

Therefore, the liquidity premium for year 2 (L2) is 0%.