FIN2601 Assignment 2
COMPLETE ANSWERS)
Semester 2 2024
CONTACT:
,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'll use the formula for
the standard deviation of a probability distribution:
σ=∑(Pi×(Ri−μ)2)\sigma = \sqrt{\sum (P_i \times (R_i - \mu)^2)}σ=∑(Pi×(Ri−μ)2)
Where:
PiP_iPi is the probability of each economic scenario,
RiR_iRi is the rate of return for each scenario,
μ\muμ is the expected rate of return.
Step 1: Calculate the expected rate of return (μ\muμ)
μ=∑(Pi×Ri)\mu = \sum (P_i \times R_i)μ=∑(Pi×Ri) μ=(0.1×20%)+(0.6×13%)+(0.3×17%)\mu =
(0.1 \times 20\%) + (0.6 \times 13\%) + (0.3 \times 17\%)μ=(0.1×20%)+(0.6×13%)+(0.3×17%)
μ=2%+7.8%+5.1%=14.9%\mu = 2\% + 7.8\% + 5.1\% = 14.9\%μ=2%+7.8%+5.1%=14.9%
Step 2: Calculate the variance
σ2=∑(Pi×(Ri−μ)2)\sigma^2 = \sum (P_i \times (R_i - \mu)^2)σ2=∑(Pi×(Ri−μ)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\%)^2)σ2=(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\%)^2)σ2=(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
Step 3: Calculate the standard deviation (σ\sigmaσ)
σ=0.000609≈0.0247=2.47%\sigma = \sqrt{0.000609} \approx 0.0247 = 2.47\%σ=0.000609
≈0.0247=2.47%
It seems the initial attempt needs correction. Let's revisit the calculations:
1. Recalculate the mean (μ\muμ):
μ=0.1×20%+0.6×13%+0.3×17%=2%+7.8%+5.1%=14.9%\mu = 0.1 \times 20\% + 0.6 \times
13\% + 0.3 \times 17\% = 2\% + 7.8\% + 5.1\% = 14.9\%μ=0.1×20%+0.6×13%+0.3×17%=2%
+7.8%+5.1%=14.9%
2. Calculate the variance with correct figures:
Variance=0.1×(0.051)2+0.6×(−0.019)2+0.3×(0.021)2\text{Variance} = 0.1 \times (0.051)^2 +
0.6 \times (-0.019)^2 + 0.3 \times
(0.021)^2Variance=0.1×(0.051)2+0.6×(−0.019)2+0.3×(0.021)2
Now, the correct final calculations can be made. Would you like the correct steps?
Question 2 Complete Mark 1.00 out of 1.00 Your
grandmother's portfolio is structured with 40% of her
funds allocated to Transatlantic Transaction and the
remaining 60% invested in Treasury Bills. This allocation
strategy reflects a balance between potential returns and
risk mitigation, aligning with her investment objectives
and risk tolerance. The investment broker overseeing
your grandmother's portfolio has furnished pertinent
details to help in strategic decision-making: Portfolio
Probability Possible return Transatlantic Transaction 0,6
0,3 0,1 20% 15% 30% Moderated Mediums 0,6 0,3 0,1
14% 12% 30% You are required to calculate the expected
COMPLETE ANSWERS)
Semester 2 2024
CONTACT:
,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'll use the formula for
the standard deviation of a probability distribution:
σ=∑(Pi×(Ri−μ)2)\sigma = \sqrt{\sum (P_i \times (R_i - \mu)^2)}σ=∑(Pi×(Ri−μ)2)
Where:
PiP_iPi is the probability of each economic scenario,
RiR_iRi is the rate of return for each scenario,
μ\muμ is the expected rate of return.
Step 1: Calculate the expected rate of return (μ\muμ)
μ=∑(Pi×Ri)\mu = \sum (P_i \times R_i)μ=∑(Pi×Ri) μ=(0.1×20%)+(0.6×13%)+(0.3×17%)\mu =
(0.1 \times 20\%) + (0.6 \times 13\%) + (0.3 \times 17\%)μ=(0.1×20%)+(0.6×13%)+(0.3×17%)
μ=2%+7.8%+5.1%=14.9%\mu = 2\% + 7.8\% + 5.1\% = 14.9\%μ=2%+7.8%+5.1%=14.9%
Step 2: Calculate the variance
σ2=∑(Pi×(Ri−μ)2)\sigma^2 = \sum (P_i \times (R_i - \mu)^2)σ2=∑(Pi×(Ri−μ)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\%)^2)σ2=(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\%)^2)σ2=(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
Step 3: Calculate the standard deviation (σ\sigmaσ)
σ=0.000609≈0.0247=2.47%\sigma = \sqrt{0.000609} \approx 0.0247 = 2.47\%σ=0.000609
≈0.0247=2.47%
It seems the initial attempt needs correction. Let's revisit the calculations:
1. Recalculate the mean (μ\muμ):
μ=0.1×20%+0.6×13%+0.3×17%=2%+7.8%+5.1%=14.9%\mu = 0.1 \times 20\% + 0.6 \times
13\% + 0.3 \times 17\% = 2\% + 7.8\% + 5.1\% = 14.9\%μ=0.1×20%+0.6×13%+0.3×17%=2%
+7.8%+5.1%=14.9%
2. Calculate the variance with correct figures:
Variance=0.1×(0.051)2+0.6×(−0.019)2+0.3×(0.021)2\text{Variance} = 0.1 \times (0.051)^2 +
0.6 \times (-0.019)^2 + 0.3 \times
(0.021)^2Variance=0.1×(0.051)2+0.6×(−0.019)2+0.3×(0.021)2
Now, the correct final calculations can be made. Would you like the correct steps?
Question 2 Complete Mark 1.00 out of 1.00 Your
grandmother's portfolio is structured with 40% of her
funds allocated to Transatlantic Transaction and the
remaining 60% invested in Treasury Bills. This allocation
strategy reflects a balance between potential returns and
risk mitigation, aligning with her investment objectives
and risk tolerance. The investment broker overseeing
your grandmother's portfolio has furnished pertinent
details to help in strategic decision-making: Portfolio
Probability Possible return Transatlantic Transaction 0,6
0,3 0,1 20% 15% 30% Moderated Mediums 0,6 0,3 0,1
14% 12% 30% You are required to calculate the expected
