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:

_{1}R_{1} = 1.50%

*E*(_{2}r_{1}) = 2.5%

*E*(_{3}r_{1}) = 3.0%

*E*(_{4}r_{1}) = 3.5%

*E*(_{5}r_{1}) = 4.5%

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

*L*_{2} = 0.15%

*L*_{3} = 0.25%

*L*_{4 } = 0.35%

*L*_{5} = 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%

Problem 6-11 Liquidity Premium Theory (LG6-7)
Based on economists’ forecasts and analysis, 1-year Treasury
bill rates and liquidity premiums for the next four years are
expected to be as follows:
R1
=
0.55
%
E(2r1)
=
1.70
%
L2
=
0.08
%
E(3r1)
=
1.80
%
L3
=
0.12
%
E(4r1)
=
2.10
%
L4
=
0.14
%
Using the liquidity premium theory, determine the current
(long-term) rates. (Do not round intermediate calculations.
Round your answers to 2 decimal places.)

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows:
1R1
=
.33%
E(2r1)
=
.70%
L2
=
0.06%
E(3r1)
=
.80%
L3
=
0.15%
E(4r1)
=
1.10%
L4
=
0.16%
Identify the four annual rates. (Round your answers to 2
decimal places. (e.g., 32.16))
Annual Rates
Year
1
%
Year
2
%
Year
3
%
Year
4
%

Based on economists’ forecasts and analysis, 1-year Treasury
bill rates and liquidity premiums for the next four years are
expected to be as follows:
R1
=
2.10
%
E(2r1)
=
3.00
%
L2
=
0.07
%
E(3r1)
=
3.40
%
L3
=
0.09
%
E(4r1)
=
3.85
%
L4
=
0.14
%
Using the liquidity premium theory, determine the current
(long-term) rates. (Do not round intermediate calculations.
Round your answers to 2 decimal places.)
YEAR 1
YEAR 2
YEAR 3...

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows:
1R1
=
5.65
%
E(2r1)
=
6.75
%
L2
=
0.05
%
E(3r1)
=
6.85
%
L3
=
0.10
%
E(4r1)
=
7.15
%
L4
=
0.12
%
Calculate the four annual rates. (Round your answers to 2
decimal places. (e.g., 32.16))
Annual Rates
Year 1
%
Year 2
%
Year 3
%
Year 4
%

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows:
1R1
=
.50%
E(2r1)
=
.98%
L2
=
0.09%
E(3r1)
=
1.08%
L3
=
0.14%
E(4r1)
=
1.38%
L4
=
0.16%
Calculate the four annual rates. (Round your answers to 2
decimal places. (e.g., 32.16))
Year 1: 0.50%
Year 2: ____%
Year 3: _____%
Year 4: _____%

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows: 1R1 = .50% E(2r1) = .75% L2 = 0.07% E(3r1) = .85%
L3 = 0.16% E(4r1) = 1.15% L4 = 0.17% Identify the four annual
rates. (Round your answers to 2 decimal places. (e.g., 32.16))
Annual Rates Year 1 .5 % Year 2 % Year 3 % Year 4 %

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