Financial Modelling Assessment 1 (2012-13 Semester 2)
The table below shows the expected annual return (%) and standard deviation of the return (%) on the shares of 10 companies:
Company
|
Expected
Return
|
Standard
Deviation
|
A
|
25%
|
84%
|
B
|
8%
|
24%
|
C
|
10%
|
36%
|
D
|
3%
|
27%
|
E
|
15%
|
51%
|
F
|
12%
|
31%
|
G
|
16%
|
37%
|
H
|
4%
|
20%
|
I
|
18%
|
60%
|
J
|
12%
|
28%
|
The returns on the different shares are correlated as follows:
Correlation Matrix
| ||||||||||
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
| |
A
|
1.00
|
0.22
|
0.37
|
-0.20
|
0.51
|
0.30
|
0.38
|
-0.10
|
0.20
|
0.25
|
B
|
0.22
|
1.00
|
0.40
|
-0.29
|
0.27
|
0.40
|
0.33
|
0.00
|
0.25
|
0.30
|
C
|
0.37
|
0.40
|
1.00
|
-0.28
|
0.45
|
0.44
|
0.53
|
0.20
|
0.15
|
0.40
|
D
|
-0.20
|
-0.29
|
-0.28
|
1.00
|
-0.15
|
-0.15
|
-0.23
|
0.30
|
-0.20
|
-0.10
|
E
|
0.51
|
0.27
|
0.45
|
-0.15
|
1.00
|
0.34
|
0.39
|
0.00
|
0.05
|
0.20
|
F
|
0.30
|
0.40
|
0.44
|
-0.15
|
0.34
|
1.00
|
0.46
|
-0.15
|
0.23
|
0.25
|
G
|
0.38
|
0.33
|
0.53
|
-0.23
|
0.39
|
0.46
|
1.00
|
0.20
|
0.15
|
0.30
|
H
|
-0.10
|
0.00
|
0.20
|
0.30
|
0.00
|
-0.15
|
0.20
|
1.00
|
-0.20
|
-0.20
|
I
|
0.20
|
0.25
|
0.15
|
-0.20
|
0.05
|
0.23
|
0.15
|
-0.20
|
1.00
|
0.10
|
J
|
0.25
|
0.30
|
0.40
|
-0.10
|
0.20
|
0.25
|
0.30
|
-0.20
|
0.10
|
1.00
|
You are required to set up a spreadsheet model which can be used to find efficient portfolios of these ten shares, and answer the following:...Click here to get more on this essay.....
1. Identify a portfolio with the minimum risk that gives an expected return of at least 15%. Discuss the relationship between risk and return in the context of share portfolios.
2. Identify a portfolio which gives the maximum return but whose combined risk is lower than the risk for any of the individual shares within the portfolio. Explain how diversification reduces risk.
3. Create a chart showing the efficient frontier.
4. Introduce a risk-free asset into the model and find the optimal portfolio of risky shares. Explain what happens to the optimal portfolio as the risk-free return increases.
5. Introduce a risk aversion factor into the model and discuss its effect upon the optimal complete portfolio.
Write a report explaining each part of the answer, including the mathematical programming formulation (variables, objective, constraints) as well as the results. Credit will be given for a correct explanation and interpretation of the models and the answers. The word limit is 1000 to 1200 words.
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