In this report, an attempt is made to discuss the important topics of optimal portfolio and the systematic risk of the shares of a company. The portfolio that maximizes the return of the investors based on the preference of risk is known as optimal portfolio. The investors prefer an efficient portfolio because the characteristics of risk or reward of the portfolio satisfies the utility function of the investor. It is important to determine the optimal portfolio because it maximizes the return based on the expected risk of the investors. There are two types of risk associated with investment in shares of a company. These two types of risks are systematic risk and unsystematic risk and in this report, the focus is on systematic risk. The systematic risk is an inherent risk for the entire market segment and it is also known as diversifiable risk. It is not possible to completely avoid systematic risk, as it is unpredictable. However, the systematic risk can be reduced by diversification and using proper asset allocation strategy. In most cases beta is used for determining the systematic risk. Therefore, it can be said that is important to determine systematic risk for proper asset allocation and avoid unnecessary risk.
The main aim of this report is to determine the optimal portfolio of two risky assets and one-risk free assets. The report also calculates the systematic risks of two risky assets for period before and after general financial crisis.
The two companies that have been selected from Australian Stock Exchange for investment in risky assets are Adelaide Brighton Limited (ABC.AX) and AMP Limited (AMP.AX). The Adelaide Brighton Limited is engaged in manufacturing and distribution of construction materials in Australia. The operation of the company is divided into two segments. The products of the company are offered to residential or nonresidential construction, alumina production, engineering Construction and for mining. The company headquarter is located in Adelaide Australia and it was founded in the year 1882. The second company that have been selected as risky assets is AMP Limited. This company is engaged an independent Wealth Management mainly in Australia and New Zealand. The company operates through multiple segments like Australian Wealth Management, AMP capital, AMP bank and others. The company manages investments in various sectors and offer various financial products. The company is headquartered in Sydney Australia and was founded in the year 1849.
In this section of the report, the calculation is provided and it is segregated between pre global financial crisis and post global financial crisis era.
Pre Global Financial crisis
|
Pre Global Financial Crisis calculations |
||||
|
|
Adelaide Brighton Limited (ABC) |
AMP Limited (AMP) |
||
|
Date |
Adj Close |
Return % |
Adj Close |
Return % |
|
31-07-08 |
1.88 |
-3% |
3.70 |
1.42% |
|
31-08-08 |
1.60 |
-15% |
3.71 |
0.29% |
|
30-09-08 |
1.21 |
-25% |
2.99 |
-19.48% |
|
31-10-08 |
1.05 |
-13% |
2.97 |
-0.74% |
|
30-11-08 |
1.12 |
6% |
2.99 |
0.93% |
|
31-12-08 |
0.90 |
-19% |
2.91 |
-2.77% |
|
31-01-09 |
0.92 |
1% |
2.67 |
-8.35% |
|
28-02-09 |
1.04 |
13% |
2.60 |
-2.69% |
|
31-03-09 |
1.21 |
16% |
3.02 |
16.43% |
|
30-04-09 |
1.31 |
9% |
2.82 |
-6.74% |
|
31-05-09 |
1.29 |
-2% |
2.84 |
0.83% |
|
30-06-09 |
1.42 |
11% |
3.27 |
15.16% |
|
31-07-09 |
1.57 |
10% |
3.71 |
13.17% |
|
31-08-09 |
1.64 |
5% |
3.80 |
2.52% |
|
30-09-09 |
1.67 |
2% |
3.56 |
-6.22% |
|
31-10-09 |
1.47 |
-12% |
3.70 |
3.87% |
|
30-11-09 |
1.62 |
10% |
4.05 |
9.55% |
|
31-12-09 |
1.46 |
-10% |
3.75 |
-7.53% |
|
31-01-10 |
1.40 |
-4% |
3.56 |
-5.11% |
|
28-02-10 |
1.59 |
14% |
3.87 |
8.72% |
|
31-03-10 |
1.81 |
14% |
3.87 |
0.00% |
|
30-04-10 |
1.68 |
-7% |
3.45 |
-10.70% |
|
31-05-10 |
1.65 |
-2% |
3.22 |
-6.80% |
|
30-06-10 |
1.95 |
18% |
3.27 |
1.73% |
|
31-07-10 |
2.02 |
3% |
3.11 |
-4.91% |
|
31-08-10 |
2.21 |
9% |
3.16 |
1.39% |
|
30-09-10 |
2.30 |
4% |
3.42 |
8.43% |
|
31-10-10 |
1.93 |
-16% |
3.24 |
-5.43% |
|
30-11-10 |
2.12 |
10% |
3.39 |
4.75% |
|
31-12-10 |
2.16 |
2% |
3.43 |
1.13% |
|
31-01-11 |
2.12 |
-1% |
3.40 |
-0.75% |
|
28-02-11 |
2.18 |
3% |
3.60 |
5.91% |
|
31-03-11 |
2.14 |
-2% |
3.64 |
0.92% |
|
30-04-11 |
2.13 |
0% |
3.46 |
-4.93% |
|
31-05-11 |
2.09 |
-2% |
3.25 |
-6.14% |
|
30-06-11 |
1.77 |
-15% |
3.03 |
-6.75% |
|
31-07-11 |
1.89 |
7% |
3.01 |
-0.66% |
|
31-08-11 |
1.86 |
-2% |
2.62 |
-12.80% |
|
30-09-11 |
2.02 |
9% |
2.95 |
12.65% |
|
31-10-11 |
2.04 |
1% |
2.86 |
-3.04% |
|
30-11-11 |
2.03 |
0% |
2.81 |
-1.93% |
|
31-12-11 |
2.09 |
3% |
2.95 |
4.91% |
|
Average |
|
0.69% |
|
-0.23% |
|
Variance |
|
1.013% |
|
0.564% |
|
Standard Deviation |
|
10.06% |
|
7.51% |
|
Covariance |
0.44% |
|
|
|
Table1: Calculations
(Source: Created by Author)
|
Calculation of Optimum weights for risky assets |
|
|
Particulars |
Amount |
|
Expected Return of ABC |
0.69% |
|
Expected Return of AMP |
-0.23% |
|
Standard deviation of ABC |
10.06% |
|
Standard deviation of AMP |
7.51% |
|
Risk free rate |
4.52% |
|
Covariance |
0.44% |
|
Optimum weight for ABC |
0.37 |
|
Optimum weight for AMP |
0.63 |
Table 2: Optimum weightage
(Source: created by Author)
|
Optimum portion of risk and risk free assets |
|
|
Particulars |
Amount |
|
Expected Return of portfolio |
0.11% |
|
Standard deviation |
21% |
|
Optimum portion of risky assets |
-0.19 |
|
Optimum portion of risk free assets |
1.19 |
Table 3: Mean and Standard deviation
(Source: Created by Author)
|
Post Global Financial Crisis calculations |
||||
|
|
Adelaide Brighton Limited |
AMP Limited |
||
|
Date |
Adj Close |
Return % |
Adj Close |
Return % |
|
31-01-12 |
2.11 |
0.99% |
2.77 |
-6.09% |
|
29-02-12 |
2.13 |
0.97% |
3.11 |
12.29% |
|
31-03-12 |
2.24 |
5.17% |
3.07 |
-1.16% |
|
30-04-12 |
2.16 |
-3.61% |
2.79 |
-9.13% |
|
31-05-12 |
2.34 |
8.16% |
2.77 |
-0.77% |
|
30-06-12 |
2.47 |
5.66% |
2.88 |
4.16% |
|
31-07-12 |
2.15 |
-13.10% |
3.21 |
11.22% |
|
31-08-12 |
2.29 |
6.81% |
3.11 |
-2.91% |
|
30-09-12 |
2.41 |
5.32% |
3.42 |
9.81% |
|
31-10-12 |
2.42 |
0.32% |
3.43 |
0.22% |
|
30-11-12 |
2.38 |
-1.89% |
3.58 |
4.57% |
|
31-12-12 |
2.58 |
8.65% |
3.96 |
10.60% |
|
31-01-13 |
2.79 |
7.96% |
4.08 |
3.01% |
|
28-02-13 |
2.69 |
-3.28% |
3.88 |
-4.93% |
|
31-03-13 |
2.68 |
-0.46% |
4.15 |
6.79% |
|
30-04-13 |
2.63 |
-2.06% |
3.98 |
-4.07% |
|
31-05-13 |
2.60 |
-0.90% |
3.26 |
-17.95% |
|
30-06-13 |
2.59 |
-0.61% |
3.47 |
6.35% |
|
31-07-13 |
2.64 |
2.13% |
3.64 |
4.87% |
|
31-08-13 |
3.00 |
13.66% |
3.54 |
-2.74% |
|
30-09-13 |
3.13 |
4.34% |
3.76 |
6.17% |
|
31-10-13 |
3.09 |
-1.56% |
3.69 |
-1.69% |
|
30-11-13 |
2.99 |
-3.17% |
3.48 |
-5.79% |
|
31-12-13 |
3.08 |
3.00% |
3.38 |
-2.73% |
|
31-01-14 |
3.40 |
10.58% |
3.83 |
13.11% |
|
28-02-14 |
3.33 |
-2.05% |
3.95 |
3.11% |
|
31-03-14 |
3.25 |
-2.49% |
4.13 |
4.64% |
|
30-04-14 |
2.80 |
-13.81% |
4.33 |
4.75% |
|
31-05-14 |
2.87 |
2.37% |
4.34 |
0.19% |
|
30-06-14 |
3.04 |
6.09% |
4.49 |
3.58% |
|
31-07-14 |
2.95 |
-3.01% |
4.81 |
7.10% |
|
31-08-14 |
2.67 |
-9.58% |
4.47 |
-7.14% |
|
30-09-14 |
2.88 |
8.02% |
4.92 |
10.20% |
|
31-10-14 |
2.94 |
2.08% |
4.75 |
-3.59% |
|
30-11-14 |
3.06 |
4.08% |
4.63 |
-2.48% |
|
31-12-14 |
3.07 |
0.28% |
4.85 |
4.91% |
|
31-01-15 |
3.67 |
19.55% |
5.64 |
16.12% |
|
28-02-15 |
3.89 |
5.84% |
5.42 |
-3.88% |
|
31-03-15 |
4.00 |
2.85% |
5.57 |
2.80% |
|
30-04-15 |
4.11 |
2.88% |
5.76 |
3.42% |
|
31-05-15 |
3.81 |
-7.31% |
5.21 |
-9.61% |
|
30-06-15 |
4.18 |
9.74% |
5.72 |
9.80% |
|
31-07-15 |
3.99 |
-4.65% |
5.15 |
-9.98% |
|
31-08-15 |
3.85 |
-3.55% |
4.81 |
-6.55% |
|
30-09-15 |
3.85 |
0.22% |
5.12 |
6.48% |
|
31-10-15 |
3.99 |
3.58% |
5.19 |
1.40% |
|
30-11-15 |
4.37 |
9.45% |
5.21 |
0.34% |
|
31-12-15 |
4.35 |
-0.42% |
4.80 |
-7.89% |
|
31-01-16 |
4.55 |
4.65% |
4.75 |
-0.93% |
|
29-02-16 |
4.66 |
2.42% |
5.17 |
8.83% |
|
31-03-16 |
4.91 |
5.19% |
5.45 |
5.40% |
|
30-04-16 |
5.39 |
9.86% |
5.23 |
-4.08% |
|
31-05-16 |
5.29 |
-1.94% |
4.79 |
-8.51% |
|
30-06-16 |
5.61 |
6.10% |
5.39 |
12.60% |
|
31-07-16 |
4.98 |
-11.17% |
4.88 |
-9.47% |
|
31-08-16 |
5.26 |
5.52% |
5.08 |
4.10% |
|
30-09-16 |
5.20 |
-1.18% |
4.40 |
-13.45% |
|
31-10-16 |
4.97 |
-4.30% |
4.52 |
2.84% |
|
30-11-16 |
5.27 |
6.05% |
4.85 |
7.23% |
|
31-12-16 |
4.97 |
-5.75% |
4.81 |
-0.79% |
|
Average |
|
1.78% |
|
1.02% |
|
Variance |
|
0.44% |
|
0.49% |
|
Standard Deviation |
|
6.62% |
|
6.97% |
|
Covariance |
0.23% |
|
|
|
Table 4: Calculation
(Source: created by Author)
|
Calculation of Optimum weights for risky assets |
|
|
Particulars |
Amount |
|
Expected Return of ABC |
1.78% |
|
Expected Return of AMP |
1.02% |
|
Standard deviation of ABC |
6.62% |
|
Standard deviation of AMP |
6.97% |
|
Risk free rate |
2.64% |
|
Covariance |
0.23% |
|
Optimum weight for ABC |
0.35 |
|
Optimum weight for AMP |
0.65 |
Table 5: Optimum weightage
(Source: created by Author)
|
Mean and Standard Deviation of optimum Portfolio |
|
|
Particulars |
Amount |
|
Expected Return of portfolio |
1.28% |
|
Standard deviation |
20% |
|
Optimum portion of risky assets |
-0.07 |
|
Optimum portion of risk free assets |
1.07 |
Table 6: Mean and Standard deviation
(Source: Created by Author)
Analysis
The tables above shows the calculation of the expected return, variance, standard deviation and covariance. The calculation of optimum weight of the portfolio is also provided for the pre and post global financial crisis is calculated. On analyzing the calculation, it can be seen that the optimum weightage has shifted in pre and post global financial crisis period. It can be seen that pre global financial crisis the more weightage was given to AMP in portfolio and after the post-financial crisis, the emphasis further increased. It can be seen that the expected return from the portfolio has increased post financial crisis. On analyzing the calculations, it can be seen that there has been a shift from risk free assets to risky assets from pre global financial crisis to post global financial crisis. The calculation of portfolio allocation came in negative, as the return from risky assets is less than risk free assets. That means the investor will not invest in risky assets, as the rate of return is less.
The calculation of pre and post global financial crisis systematic risk of stock is given below.
|
Calculation of Systematic risk Pre Global Financial crisis |
||||
|
Date |
ADJ close |
Market Return |
ABC |
AMP |
|
31-07-08 |
5215.50 |
3.33% |
-3.44% |
1.42% |
|
31-08-08 |
4631.30 |
-11% |
-14.64% |
0.29% |
|
30-09-08 |
3982.70 |
-14% |
-24.64% |
-19.48% |
|
31-10-08 |
3672.70 |
-8% |
-13.00% |
-0.74% |
|
30-11-08 |
3659.30 |
0% |
6.33% |
0.93% |
|
31-12-08 |
3478.10 |
-5% |
-19.05% |
-2.77% |
|
31-01-09 |
3296.90 |
-5% |
1.47% |
-8.35% |
|
28-02-09 |
3532.30 |
7% |
13.33% |
-2.69% |
|
31-03-09 |
3744.70 |
6% |
16.18% |
16.43% |
|
30-04-09 |
3813.30 |
2% |
8.53% |
-6.74% |
|
31-05-09 |
3947.80 |
4% |
-1.75% |
0.83% |
|
30-06-09 |
4249.50 |
8% |
10.67% |
15.16% |
|
31-07-09 |
4484.10 |
6% |
10.04% |
13.17% |
|
31-08-09 |
4739.30 |
6% |
4.88% |
2.52% |
|
30-09-09 |
4646.90 |
-2% |
1.79% |
-6.22% |
|
31-10-09 |
4715.50 |
1% |
-12.32% |
3.87% |
|
30-11-09 |
4882.70 |
4% |
10.44% |
9.55% |
|
31-12-09 |
4596.90 |
-6% |
-10.18% |
-7.53% |
|
31-01-10 |
4651.10 |
1% |
-4.05% |
-5.11% |
|
28-02-10 |
4893.10 |
5% |
13.91% |
8.72% |
|
31-03-10 |
4833.90 |
-1% |
13.57% |
0.00% |
|
30-04-10 |
4453.60 |
-8% |
-6.83% |
-10.70% |
|
31-05-10 |
4324.80 |
-3% |
-1.83% |
-6.80% |
|
30-06-10 |
4507.40 |
4% |
18.28% |
1.73% |
|
31-07-10 |
4438.80 |
-2% |
3.47% |
-4.91% |
|
31-08-10 |
4636.90 |
4% |
9.45% |
1.39% |
|
30-09-10 |
4733.40 |
2% |
4.07% |
8.43% |
|
31-10-10 |
4676.40 |
-1% |
-16.20% |
-5.43% |
|
30-11-10 |
4846.90 |
4% |
10.00% |
4.75% |
|
31-12-10 |
4850.00 |
0% |
1.52% |
1.13% |
|
31-01-11 |
4923.60 |
2% |
-1.49% |
-0.75% |
|
28-02-11 |
4928.60 |
0% |
2.58% |
5.91% |
|
31-03-11 |
4899.00 |
-1% |
-1.86% |
0.92% |
|
30-04-11 |
4788.90 |
-2% |
-0.32% |
-4.93% |
|
31-05-11 |
4659.80 |
-3% |
-1.90% |
-6.14% |
|
30-06-11 |
4500.50 |
-3% |
-15.21% |
-6.75% |
|
31-07-11 |
4369.90 |
-3% |
6.87% |
-0.66% |
|
31-08-11 |
4070.10 |
-7% |
-1.95% |
-12.80% |
|
30-09-11 |
4360.50 |
7% |
8.71% |
12.65% |
|
31-10-11 |
4184.70 |
-4% |
1.05% |
-3.04% |
|
30-11-11 |
4111.00 |
-2% |
-0.34% |
-1.93% |
|
31-12-11 |
4325.70 |
5% |
2.77% |
4.91% |
|
|
|
|
|
|
|
Variance of Index return |
|
0.26% |
|
|
|
Covariance |
|
|
0.37% |
0.28% |
|
Beta (systematic risk) |
|
|
1.42 |
1.09 |
Table 7: Pre GFC calculation
(Source: Created by Author)
|
Calculation of Systematic risk Post Global Financial crisis |
||||
|
Date |
ADJ close |
Market Return |
ABC |
AMP |
|
31-01-12 |
4388.10 |
1.44% |
0.99% |
-6% |
|
29-02-12 |
4420.00 |
0.73% |
0.97% |
12% |
|
31-03-12 |
4467.20 |
1.07% |
5.17% |
-1% |
|
30-04-12 |
4133.70 |
-7.47% |
-3.61% |
-9% |
|
31-05-12 |
4135.50 |
0.04% |
8.16% |
-1% |
|
30-06-12 |
4289.40 |
3.72% |
5.66% |
4% |
|
31-07-12 |
4339.00 |
1.16% |
-13.10% |
11% |
|
31-08-12 |
4406.30 |
1.55% |
6.81% |
-3% |
|
30-09-12 |
4535.40 |
2.93% |
5.32% |
10% |
|
31-10-12 |
4518.00 |
-0.38% |
0.32% |
0% |
|
30-11-12 |
4664.60 |
3.24% |
-1.89% |
5% |
|
31-12-12 |
4901.00 |
5.07% |
8.65% |
11% |
|
31-01-13 |
5120.40 |
4.48% |
7.96% |
3% |
|
28-02-13 |
4979.90 |
-2.74% |
-3.28% |
-5% |
|
31-03-13 |
5168.60 |
3.79% |
-0.46% |
7% |
|
30-04-13 |
4914.00 |
-4.93% |
-2.06% |
-4% |
|
31-05-13 |
4775.40 |
-2.82% |
-0.90% |
-18% |
|
30-06-13 |
5035.70 |
5.45% |
-0.61% |
6% |
|
31-07-13 |
5125.30 |
1.78% |
2.13% |
5% |
|
31-08-13 |
5217.70 |
1.80% |
13.66% |
-3% |
|
30-09-13 |
5420.30 |
3.88% |
4.34% |
6% |
|
31-10-13 |
5314.30 |
-1.96% |
-1.56% |
-2% |
|
30-11-13 |
5353.10 |
0.73% |
-3.17% |
-6% |
|
31-12-13 |
5205.10 |
-2.76% |
3.00% |
-3% |
|
31-01-14 |
5415.40 |
4.04% |
10.58% |
13% |
|
28-02-14 |
5403.00 |
-0.23% |
-2.05% |
3% |
|
31-03-14 |
5470.80 |
1.25% |
-2.49% |
5% |
|
30-04-14 |
5473.80 |
0.05% |
-13.81% |
5% |
|
31-05-14 |
5382.00 |
-1.68% |
2.37% |
0% |
|
30-06-14 |
5623.10 |
4.48% |
6.09% |
4% |
|
31-07-14 |
5624.60 |
0.03% |
-3.01% |
7% |
|
31-08-14 |
5296.80 |
-5.83% |
-9.58% |
-7% |
|
30-09-14 |
5505.00 |
3.93% |
8.02% |
10% |
|
31-10-14 |
5298.10 |
-3.76% |
2.08% |
-4% |
|
30-11-14 |
5388.60 |
1.71% |
4.08% |
-2% |
|
31-12-14 |
5551.60 |
3.02% |
0.28% |
5% |
|
31-01-15 |
5898.50 |
6.25% |
19.55% |
16% |
|
28-02-15 |
5861.90 |
-0.62% |
5.84% |
-4% |
|
31-03-15 |
5773.70 |
-1.50% |
2.85% |
3% |
|
30-04-15 |
5774.90 |
0.02% |
2.88% |
3% |
|
31-05-15 |
5451.20 |
-5.61% |
-7.31% |
-10% |
|
30-06-15 |
5681.70 |
4.23% |
9.74% |
10% |
|
31-07-15 |
5222.10 |
-8.09% |
-4.65% |
-10% |
|
31-08-15 |
5058.60 |
-3.13% |
-3.55% |
-7% |
|
30-09-15 |
5288.60 |
4.55% |
0.22% |
6% |
|
31-10-15 |
5218.20 |
-1.33% |
3.58% |
1% |
|
30-11-15 |
5344.60 |
2.42% |
9.45% |
0% |
|
31-12-15 |
5056.60 |
-5.39% |
-0.42% |
-8% |
|
31-01-16 |
4947.90 |
-2.15% |
4.65% |
-1% |
|
29-02-16 |
5151.80 |
4.12% |
2.42% |
9% |
|
31-03-16 |
5316.00 |
3.19% |
5.19% |
5% |
|
30-04-16 |
5447.80 |
2.48% |
9.86% |
-4% |
|
31-05-16 |
5310.40 |
-2.52% |
-1.94% |
-9% |
|
30-06-16 |
5644.00 |
6.28% |
6.10% |
13% |
|
31-07-16 |
5529.40 |
-2.03% |
-11.17% |
-9% |
|
31-08-16 |
5525.20 |
-0.08% |
5.52% |
4% |
|
30-09-16 |
5402.40 |
-2.22% |
-1.18% |
-13% |
|
31-10-16 |
5502.40 |
1.85% |
-4.30% |
3% |
|
30-11-16 |
5719.10 |
3.94% |
6.05% |
7% |
|
31-12-16 |
5675.00 |
-0.77% |
-5.75% |
-1% |
|
Variance of Index return |
|
0.12% |
|
|
|
Covariance |
|
|
0.13% |
0.19% |
|
Beta (systematic risk) |
|
|
1.13 |
1.61 |
Table 8: Post Financial crisis
(Source: Created by Author)
Analysis
The calculation above shows the systematic risk of stocks for pre and post-global financial crisis. The beta of the stocks are calculated for determining the systematic risk. On analyzing the calculation, it shows that pre global financial crisis the beta of ABC is more than that of AMP. That means for investments ABC is more risky than AMP. The beta calculation post global financial crisis shows that the beta of AMP is more than that of ABC. This indicates that after the financial crisis the shares of AMP has become more risky than ABC. It is further observed that from the prospective of individual stock the system risk associated with the stock ABC has decreased and the systematic risk associated with the stock AMP has increased.
The above discussion and calculation has helped to analyze the optimum portfolio and systematic risk pre and post global financial crisis. It can be seen that the pre and post-global financial crisis the optimum weight for risky assets have almost remained similar. However, it can be seen that pre global financial crisis the assets allocation for the risk free assets is more than the risky assets. The calculation shows that in the post global financial crisis the assets allocation for the risky assets increased. The report also shows the calculation of systematic risks of two stocks. It can be seen that the systematic risk of AMP Limited is more than ABC post the global financial risk.
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