Question

Suppose we observe the following rates: 1R1 = 10%, 1R2 = 14%, and E(2r1) = 18%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2?

pleas show how to do in excel

Answer 1

Liquidity Premium can be found using excel utility 'solver'

Step 1:

a. Inputs the details of 1R1; 1R2 and E(2r1) given in the question.

b. Assume Liquidity Premium (which is the requirement of the question) to be 0

c. As per Liquidity Premium Theory ,

1R2 = ((1+1R1)*(1+LP+E(2r1))

Using the details given for 1R1, E(2r1) and assuming LP as 0, solve this equation as:

((1+10%)^1*(1+18%+0%))^(1/2)-1 which will return the value as 13.93%

Step 2 :

a. As per the equation, the value calculated of 13.93% should equal 1R2.

b. Hence, compute the difference between 13.93% and 14% as below (which will be 0.07%):

Step 3:

a. Open the 'Solver' excel add-on utility

b. The objective here is to have the difference as 'zero' by changing the value of Liquidity Premium (LP).

c. Click 'Solve'

d. Click 'OK'

Step 4:

Solver would have found the solution returning LP as 0.145% and the difference being 0%.

Thus, the liquidity premium for year 2 is 0.145%