Question

Your client also wants to determine the Liquidity of his investment by using Liquidity Premium Theory. Base on the question 1, it shows the information as follows:

₁R₁ = 1.50%
E(₂r₁) = 2.5%
E(₃r₁) = 3.0%
E(₄r₁) = 3.5%
E(₅r₁) = 4.5%

In addition, you charge a liquidity premium on longer-term securities such that:

L₂ = 0.15%
L₃ = 0.25%
L₄   = 0.35%
L₅ = 0.40%

Instructions:

1] Please using the Liquidity Premium Theory of the Term Structure of Interest Rates.
2] Please provide a clear calculation and brief explanation to support your calculation.

Answer 1

1R1 means the interest rate for the next one year. 2R1 means the future one-year interest rate after one year. L2 means the liquidity premium for the debt terminating after 2 years.

Hence, the spot interest rate after 2 years (without the liquidity premium) will be-

(1+0.015)x(1+0.025) = (1+r)^2

hence, r= 1.998%(=2%)

Now we add the liquidity premium to it and it becomes-

Spot 2-year interest rate = 2.15%

Similarly, we calculate the three-year spot rate-

1.015 x 1.025 x 1.03 = (1+r)^3

r = 2.33%

Adding liquidity premium, we get the 3-year rate = 2.33 + 0.25 = 2.58%

Similarly, we calculate the 4-year rate.

1.015 x 1.025 x 1.03 x 1.035 = (1+r)^4

r= 2.62%; Add liquidity premium, r = 2.62 + 0.35 = 2.97%

5-year rate-

r=2.99% + 0.4% = 3.4%