Stock Analysis
The purpose of this report is to investigate the different methods of constructing a tracking portfolio using the 12 stocks below and the ASX200 index.
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Commonwealth Bank |
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BHP Billiton Limited |
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CSL Limited |
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Westpac Banking Corp |
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ANZ Banking Group Limited |
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National Aust. Bank |
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Wesfarmers Limited |
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Macquarie Group Limited |
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Woolworths Group Limited |
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Telstra Corporation |
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Woodside Petroleum |
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RIO Tinto Limited |
In Chapter 2, the 12 stock prices and index from the sample data are transformed into weekly returns. The data is then analyzed to determine the annualized returns, variance covariance matrix and beta.
In Chapter 3, three portfolios out of the 12 stocks that track the ASX200 index are constructed and compared using three different methods.
In Chapter 4, the performance of the tracker portfolio is analyzed after 12 months to determine how close it follows the index.
The table below shows the weekly returns annualized expected returns, variance and standard deviation for the 12 stocks and ASX200.
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0.0002% |
0.0103% |
3.7387% |
19.3357% |
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-0.0477% |
-2.4797% |
11.2708% |
33.5721% |
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0.4376% |
22.7564% |
3.9468% |
19.8665% |
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0.0015% |
0.0755% |
4.8913% |
22.1163% |
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-0.0189% |
-0.9828% |
5.2796% |
22.9774% |
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0.0384% |
1.9977% |
4.9629% |
22.2777% |
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0.0238% |
1.2355% |
3.0230% |
17.3866% |
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0.2725% |
14.1695% |
5.4349% |
23.3128% |
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-0.1589% |
-8.2626% |
4.4082% |
20.9957% |
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-0.1882% |
-9.7869% |
2.9918% |
17.2969% |
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-0.1701% |
-8.8427% |
5.4856% |
23.4215% |
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0.1457% |
7.5770% |
8.6946% |
29.4866% |
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0.0443% |
2.3019% |
1.8244% |
13.5072% |
The table below shows the covariance variance matrix for the 12 stocks
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3.74% |
2.95% |
1.12% |
3.41% |
3.50% |
3.26% |
1.23% |
2.67% |
1.75% |
1.03% |
2.06% |
1.97% |
2.11% |
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2.95% |
11.27% |
0.82% |
3.97% |
4.09% |
3.91% |
2.23% |
3.06% |
2.82% |
0.68% |
4.66% |
8.35% |
3.15% |
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1.12% |
0.82% |
3.95% |
1.28% |
0.91% |
1.15% |
1.29% |
1.44% |
0.91% |
0.73% |
0.86% |
0.54% |
1.16% |
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3.41% |
3.97% |
1.28% |
4.89% |
4.31% |
4.02% |
1.73% |
2.92% |
2.19% |
0.92% |
2.57% |
2.76% |
2.52% |
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3.50% |
4.09% |
0.91% |
4.31% |
5.28% |
4.29% |
1.39% |
3.02% |
2.19% |
0.65% |
2.64% |
2.98% |
2.52% |
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3.26% |
3.91% |
1.15% |
4.02% |
4.29% |
4.96% |
1.79% |
3.38% |
2.66% |
0.97% |
2.54% |
2.68% |
2.52% |
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1.23% |
2.23% |
1.29% |
1.73% |
1.39% |
1.79% |
3.02% |
1.15% |
2.32% |
1.09% |
1.85% |
1.50% |
1.47% |
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2.67% |
3.06% |
1.44% |
2.92% |
3.02% |
3.38% |
1.15% |
5.43% |
1.92% |
0.55% |
1.92% |
1.54% |
2.10% |
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1.75% |
2.82% |
0.91% |
2.19% |
2.19% |
2.66% |
2.32% |
1.92% |
4.41% |
1.09% |
2.33% |
1.70% |
1.78% |
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1.03% |
0.68% |
0.73% |
0.92% |
0.65% |
0.97% |
1.09% |
0.55% |
1.09% |
2.99% |
0.92% |
0.60% |
0.94% |
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2.06% |
4.66% |
0.86% |
2.57% |
2.64% |
2.54% |
1.85% |
1.92% |
2.33% |
0.92% |
5.49% |
3.11% |
2.08% |
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1.97% |
8.35% |
0.54% |
2.76% |
2.98% |
2.68% |
1.50% |
1.54% |
1.70% |
0.60% |
3.11% |
8.69% |
2.28% |
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2.11% |
3.15% |
1.16% |
2.52% |
2.52% |
2.52% |
1.47% |
2.10% |
1.78% |
0.94% |
2.08% |
2.28% |
1.82% |
The variance of the ASX200 is 1.8244%. Using the ASX200 index as a proxy for the market portfolio, the betas for the 12 stocks can be determined as:
The table below shows the Beta for the 12 stocks
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1.1552 |
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1.7251 |
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0.6333 |
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1.3791 |
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1.3793 |
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1.3806 |
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0.8081 |
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1.1518 |
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0.9740 |
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0.5179 |
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1.1411 |
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1.2494 |
The table below shows the variance of each stock decomposed into its systematic and unsystematic components. Furthermore, it also shows the diversification ratio (R2) for all 12 stocks and ASX200.
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Variance |
Systematic Risk |
Unsystematic Risk |
R2 |
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0.0374 |
0.0243 |
0.0130 |
0.6512 |
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0.1127 |
0.0543 |
0.0584 |
0.4817 |
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0.0395 |
0.0073 |
0.0322 |
0.1854 |
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0.0489 |
0.0347 |
0.0142 |
0.7094 |
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0.0528 |
0.0347 |
0.0181 |
0.6574 |
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0.0496 |
0.0348 |
0.0149 |
0.7007 |
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0.0302 |
0.0119 |
0.0183 |
0.3941 |
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0.0543 |
0.0242 |
0.0301 |
0.4453 |
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0.0441 |
0.0173 |
0.0268 |
0.3926 |
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0.0299 |
0.0049 |
0.0250 |
0.1635 |
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0.0549 |
0.0238 |
0.0311 |
0.4331 |
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0.0869 |
0.0285 |
0.0585 |
0.3275 |
Assuming the risk free rate is 2%, the graph below shows the capital market line with positions of the 12 stocks and index.
The graph below shows the security market line with positions of the 12 stocks and ASX200 index.
From the graph above, we observe the following:
- The CSL, RIO and MQG stocks are undervalued as they appear above the SML.
- TLS, WES, WOW, WPL, CBA, NAB, WBC, ANZ and BHP stocks are overvalued as they appear below the SML.
In this section, three portfolios that track the ASX200 index were constructed out of the 12 stocks using 3 methods as defined below.
In this method, excel solver in the data analysis tool pack was used to determine the weights that satisfy the following conditions:
- Minimizes the portfolio variance (the portfolio variance is determined as the product of the weights and covariance variance matrix for the 12 stocks).
- Sum of weights equals must equal one i.e. =
- Exposure to Beta is one i.e. =
The table below shows the weights which satisfy the conditions above. Based on these weights, the portfolio’s minimized variance is 1.94%.
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11.92% |
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1.03% |
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11.16% |
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5.52% |
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11.23% |
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1.22% |
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13.59% |
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10.24% |
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4.33% |
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14.82% |
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6.77% |
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8.17% |
In this method, excel solver in the data analysis tool pack was used to determine the weights that satisfy the following conditions.
- Minimizes the portfolio variance which is the difference between the portfolio return and the index.
- Sum of weights equals must equal one
The table below shows the weights which satisfy the conditions above. Based on these weights, the portfolio’s minimized variance is 2.08%.
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Weights |
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11.97% |
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3.74% |
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10.82% |
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7.36% |
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10.54% |
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3.37% |
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12.67% |
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9.70% |
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3.92% |
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12.85% |
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6.50% |
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6.55% |
In this method, the top 6 stocks from method 2 are chosen to construct the portfolio. Based on these stocks, the portfolio’s minimized RMSE is 0.857%. Hence removal of less risky assets from portfolio reduces the portfolio’s variance.
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11.97% |
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10.82% |
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10.54% |
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12.67% |
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9.70% |
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12.85% |
The table below summarizes the expected return, variance, beta and R2 for the three portfolios above.
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0.0227 |
0.0221 |
0.0263 |
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1.94% |
2.08% |
0.86% |
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0.9406 |
0.9493 |
0.8524 |
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1.0000 |
1.0398 |
0.6329 |
Based on the above, we recommend that the tracker portfolio that mininmizes the RMSE should be used to track the index because it has the highest R2.
The graph below plots the tracker portfolio and index from September 22, 2017 to September 14 2018. The values have been normalized to base 100 for comparison.
The simple annualized returns for the tracker portfolio and ASX200 index are 9.4085% and 7.7145% respectively.
The table below summarizes the beta, R2 and RMSE for the tracker portfolio over the investment period.
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1.059% |
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0.00213% |
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0.90308 |
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1.08502 |
In summary, the tracker portfolio did not perfectly track the index, because it is impossible to achieve this objective unless the portfolio is rebalanced regularly.
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