FIN2601 Assignment 2
COMPLETE ANSWERS)
Semester 2 2024
100% GUARANTEED
,FIN2601 Assignment 2 COMPLETE ANSWERS) Semester
2 2024
Question 1 Complete Mark 1.00 out of 1.00 QUIZ The
financial manager of Summer Financial Group is tasked
with evaluating the standard deviation of a proposed
investment project. This analysis aims to provide insights
into the potential risk associated with the project's
expected returns, which are linked to the future
performance of the economy over a specific period as
follows: Economic scenario Probability of occurrence Rate
of return Recession 0,1 20% Normal 0,6 13% Boom 0,3
17% What is the standard deviation of the proposed
investment project? 1. 7,07% 2. 10,45% 3. 15,81% 4.
18,67% −
To calculate the standard deviation of the proposed investment project, we can follow these
steps:
1. Calculate the Expected Rate of Return (E[R]):
E[R]=(P1×R1)+(P2×R2)+(P3×R3)E[R] = (P_1 \times R_1) + (P_2 \times R_2) + (P_3 \
times R_3)E[R]=(P1×R1)+(P2×R2)+(P3×R3)
Where:
o P1,P2,P3P_1, P_2, P_3P1,P2,P3 are the probabilities of the scenarios.
o R1,R2,R3R_1, R_2, R_3R1,R2,R3 are the corresponding rates of return.
E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)E[R] = (0.1 \times 20\%) + (0.6 \times 13\%) +
(0.3 \times 17\%)E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)
E[R]=0.02+0.078+0.051=0.149=14.9%E[R] = 0.02 + 0.078 + 0.051 = 0.149 =
14.9\%E[R]=0.02+0.078+0.051=0.149=14.9%
2. Calculate the Variance (σ²):
σ2=P1×(R1−E[R])2+P2×(R2−E[R])2+P3×(R3−E[R])2\sigma^2 = P_1 \times (R_1 -
E[R])^2 + P_2 \times (R_2 - E[R])^2 + P_3 \times (R_3 - E[R])^2σ2=P1×(R1
−E[R])2+P2×(R2−E[R])2+P3×(R3−E[R])2 σ2=0.1×(20%−14.9%)2+0.6×(13%
−14.9%)2+0.3×(17%−14.9%)2\sigma^2 = 0.1 \times (20\% - 14.9\%)^2 + 0.6 \times
(13\% - 14.9\%)^2 + 0.3 \times (17\% - 14.9\%)^2σ2=0.1×(20%−14.9%)2+0.6×(13%
, −14.9%)2+0.3×(17%−14.9%)2 σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2\sigma^2 =
0.1 \times (5.1\%)^2 + 0.6 \times (-1.9\%)^2 + 0.3 \times
(2.1\%)^2σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2
σ2=0.1×0.002601+0.6×0.000361+0.3×0.000441\sigma^2 = 0.1 \times 0.002601 + 0.6 \
times 0.000361 + 0.3 \times 0.000441σ2=0.1×0.002601+0.6×0.000361+0.3×0.000441
σ2=0.0002601+0.0002166+0.0001323=0.000609\sigma^2 = 0.0002601 + 0.0002166 +
0.0001323 = 0.000609σ2=0.0002601+0.0002166+0.0001323=0.000609
3. Calculate the Standard Deviation (σ):
σ=0.000609≈0.02466=2.47%\sigma = \sqrt{0.000609} \approx 0.02466 =
2.47\%σ=0.000609≈0.02466=2.47%
Since the calculated standard deviation of 2.47% does not match any of the options provided,
there may have been a calculation error. I'll recalculate to ensure accuracy.
Let's compute the variance more carefully.
1. Calculate the Expected Rate of Return:
E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)=0.02+0.078+0.051=14.9%E[R] = (0.1 \times
20\%) + (0.6 \times 13\%) + (0.3 \times 17\%) = 0.02 + 0.078 + 0.051 =
14.9\%E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)=0.02+0.078+0.051=14.9%
2. Calculate the Variance:
σ2=0.1×(20%−14.9%)2+0.6×(13%−14.9%)2+0.3×(17%−14.9%)2\sigma^2 = 0.1 \times
(20\% - 14.9\%)^2 + 0.6 \times (13\% - 14.9\%)^2 + 0.3 \times (17\% -
14.9\%)^2σ2=0.1×(20%−14.9%)2+0.6×(13%−14.9%)2+0.3×(17%−14.9%)2
σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2\sigma^2 = 0.1 \times (5.1\%)^2 + 0.6 \
times (-1.9\%)^2 + 0.3 \times (2.1\%)^2σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2
σ2=0.1×(0.002601)+0.6×(0.000361)+0.3×(0.000441)\sigma^2 = 0.1 \times (0.002601) +
0.6 \times (0.000361) + 0.3 \times
(0.000441)σ2=0.1×(0.002601)+0.6×(0.000361)+0.3×(0.000441)
σ2=0.0002601+0.0002166+0.0001323=0.000609\sigma^2 = 0.0002601 + 0.0002166 +
0.0001323 = 0.000609σ2=0.0002601+0.0002166+0.0001323=0.000609
3. Calculate the Standard Deviation:
σ=0.000609=0.02466=2.47%\sigma = \sqrt{0.000609} = 0.02466 = 2.47\%σ=0.000609
=0.02466=2.47%
It seems there was an error in identifying the correct standard deviation. I will compute this once
more using a different approach.
COMPLETE ANSWERS)
Semester 2 2024
100% GUARANTEED
,FIN2601 Assignment 2 COMPLETE ANSWERS) Semester
2 2024
Question 1 Complete Mark 1.00 out of 1.00 QUIZ The
financial manager of Summer Financial Group is tasked
with evaluating the standard deviation of a proposed
investment project. This analysis aims to provide insights
into the potential risk associated with the project's
expected returns, which are linked to the future
performance of the economy over a specific period as
follows: Economic scenario Probability of occurrence Rate
of return Recession 0,1 20% Normal 0,6 13% Boom 0,3
17% What is the standard deviation of the proposed
investment project? 1. 7,07% 2. 10,45% 3. 15,81% 4.
18,67% −
To calculate the standard deviation of the proposed investment project, we can follow these
steps:
1. Calculate the Expected Rate of Return (E[R]):
E[R]=(P1×R1)+(P2×R2)+(P3×R3)E[R] = (P_1 \times R_1) + (P_2 \times R_2) + (P_3 \
times R_3)E[R]=(P1×R1)+(P2×R2)+(P3×R3)
Where:
o P1,P2,P3P_1, P_2, P_3P1,P2,P3 are the probabilities of the scenarios.
o R1,R2,R3R_1, R_2, R_3R1,R2,R3 are the corresponding rates of return.
E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)E[R] = (0.1 \times 20\%) + (0.6 \times 13\%) +
(0.3 \times 17\%)E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)
E[R]=0.02+0.078+0.051=0.149=14.9%E[R] = 0.02 + 0.078 + 0.051 = 0.149 =
14.9\%E[R]=0.02+0.078+0.051=0.149=14.9%
2. Calculate the Variance (σ²):
σ2=P1×(R1−E[R])2+P2×(R2−E[R])2+P3×(R3−E[R])2\sigma^2 = P_1 \times (R_1 -
E[R])^2 + P_2 \times (R_2 - E[R])^2 + P_3 \times (R_3 - E[R])^2σ2=P1×(R1
−E[R])2+P2×(R2−E[R])2+P3×(R3−E[R])2 σ2=0.1×(20%−14.9%)2+0.6×(13%
−14.9%)2+0.3×(17%−14.9%)2\sigma^2 = 0.1 \times (20\% - 14.9\%)^2 + 0.6 \times
(13\% - 14.9\%)^2 + 0.3 \times (17\% - 14.9\%)^2σ2=0.1×(20%−14.9%)2+0.6×(13%
, −14.9%)2+0.3×(17%−14.9%)2 σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2\sigma^2 =
0.1 \times (5.1\%)^2 + 0.6 \times (-1.9\%)^2 + 0.3 \times
(2.1\%)^2σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2
σ2=0.1×0.002601+0.6×0.000361+0.3×0.000441\sigma^2 = 0.1 \times 0.002601 + 0.6 \
times 0.000361 + 0.3 \times 0.000441σ2=0.1×0.002601+0.6×0.000361+0.3×0.000441
σ2=0.0002601+0.0002166+0.0001323=0.000609\sigma^2 = 0.0002601 + 0.0002166 +
0.0001323 = 0.000609σ2=0.0002601+0.0002166+0.0001323=0.000609
3. Calculate the Standard Deviation (σ):
σ=0.000609≈0.02466=2.47%\sigma = \sqrt{0.000609} \approx 0.02466 =
2.47\%σ=0.000609≈0.02466=2.47%
Since the calculated standard deviation of 2.47% does not match any of the options provided,
there may have been a calculation error. I'll recalculate to ensure accuracy.
Let's compute the variance more carefully.
1. Calculate the Expected Rate of Return:
E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)=0.02+0.078+0.051=14.9%E[R] = (0.1 \times
20\%) + (0.6 \times 13\%) + (0.3 \times 17\%) = 0.02 + 0.078 + 0.051 =
14.9\%E[R]=(0.1×20%)+(0.6×13%)+(0.3×17%)=0.02+0.078+0.051=14.9%
2. Calculate the Variance:
σ2=0.1×(20%−14.9%)2+0.6×(13%−14.9%)2+0.3×(17%−14.9%)2\sigma^2 = 0.1 \times
(20\% - 14.9\%)^2 + 0.6 \times (13\% - 14.9\%)^2 + 0.3 \times (17\% -
14.9\%)^2σ2=0.1×(20%−14.9%)2+0.6×(13%−14.9%)2+0.3×(17%−14.9%)2
σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2\sigma^2 = 0.1 \times (5.1\%)^2 + 0.6 \
times (-1.9\%)^2 + 0.3 \times (2.1\%)^2σ2=0.1×(5.1%)2+0.6×(−1.9%)2+0.3×(2.1%)2
σ2=0.1×(0.002601)+0.6×(0.000361)+0.3×(0.000441)\sigma^2 = 0.1 \times (0.002601) +
0.6 \times (0.000361) + 0.3 \times
(0.000441)σ2=0.1×(0.002601)+0.6×(0.000361)+0.3×(0.000441)
σ2=0.0002601+0.0002166+0.0001323=0.000609\sigma^2 = 0.0002601 + 0.0002166 +
0.0001323 = 0.000609σ2=0.0002601+0.0002166+0.0001323=0.000609
3. Calculate the Standard Deviation:
σ=0.000609=0.02466=2.47%\sigma = \sqrt{0.000609} = 0.02466 = 2.47\%σ=0.000609
=0.02466=2.47%
It seems there was an error in identifying the correct standard deviation. I will compute this once
more using a different approach.
