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Due to the complexity of today ’ s financial market, it is normally difficult for investors to choose high-quality investment targets. However, professional calculation and analysis can effectively evaluate the risk and the performance of each stock. Hence, the investors can choose a more suitable portfolio according to their own risk preferences. In this report, eight stocks in Australian markets are selected, which are ANZ, NST, WOW, QAN, TLS, AGL, CBA and SYD. By calculating the various data for the recent 2 years from 2016 to 2018 of these stocks, four effective investment portfolios are obtained. The purpose of this research is to provide samples and methods for investors to analyze and it can help investors to choose more suitable portfolios for themselves. In this report, Excel software is used to calculate specific data and draw the curve of the portfolio opportunity set and CAL line. Besides, Capital Asset Pricing Model is used to analyze as well.

This report selects eight Australian companies’ stocks, and obtains the basic data of eight stocks through Yahoo Finance (2018) and Australian security (2018) exchange website and calculation. The data from 2016 to 2018 are collected and calculated in this report. The Excel software Solver is used to calculate and draw the charts. Through these specific data, the performance and value of these stocks can be analyzed. Different fund managers have different investment ideas and preferences, which will form different investment strategies, and then evolve into different investment style, which will lead to different investment performance. Therefore, investment style is an important influencing factor of fund performance, which should be classified and evaluated on the basis of appropriate classification of investment styles ( Su, 2018). As a result, this report has combined four portfolios from these eight stocks. These combinations have different characteristics. Investors can choose their own portfolio according to their own risk preferences. In this report, first of all, it is necessary to calculate the expected return, standard deviation, correlation matrix and covariance matrix. Then, portfolio opportunity set can be obtained, and use risk-free assets and CAL to analyze these portfolio structures to find a suitable portfolio. Finally, the risk and performance of different stocks and portfolios can be analyzed by calculating alpha and beta.

The evaluation of investment value is a multi-level problem, which is a continuous process for decision-makers to face a variety of needs, requirements and values. Therefore, all investments and portfolios should be evaluated, selected and prioritized, taking into account not only capital, but also reliability, sustainability and other aspects, so as to form the best portfolio ( Räikkönen et al., 2020). In 1952, Markovitz established the famous optimized portfolio model, which is mean-variance model. The model solves the problem of how to allocate fixed assets to different risk assets. It helps investors to minimize the risk in the case of a given expected return, and maximum expected return when risk is given ( Liu, 2019). But Black and Litterman (1991) pointed that the tiny change of the expected return will have great effect on the asset allocation. Capital asset pricing model (CAPM) is considered to be the first consistent model to describe the relationship between return on equity investment, investment risk and cost of equity. As a technical tool, it is widely used in the pricing of high-risk securities. It provides a rough estimate of the relationship between their expected return and the systemic risk caused by the use of capital expenditure ( Alhabeeb, 2020). Muller (1993) pointed that according to the experience, risk models always tend to underestimate the risk of the optimal portfolio.

In this section, the original data is collected from Yahoo Finance (2018) and Aus- tralian security (2018) exchange website. Expected return is calculated through monthly return. Expected return equals to the average of monthly return. Monthly return is calculated by adj close form the second month minus the first month and then divided by first monthly adj close. From

The standard deviation can describe the statistical distribution degree in the statistics. In stock area, firstly, if standard deviation is very large, it means that this stock has high risks. Secondly, if standard deviation is very small, it means this stock has low risk and stable return. From

The Correlation Matrix is always use correlation between two variables. In general, Correlation Matrix will between −1 and 1. According to the

Expected Return | Standard Deviation | |
---|---|---|

ANZ | 1.56% | 4.93% |

NST | 2.14% | 10.74% |

WOW | 1.06% | 3.85% |

QAN | 1.98% | 9.24% |

TLS | −1.32% | 4.57% |

AGL | 1.04% | 5.15% |

CBA | 0.81% | 4.90% |

SYD | 0.49% | 5.62% |

ASX & P200 | 0.875 | 2.41% |

ANZ | NST | WOW | QAN | TLS | AGL | CBA | SYD | ASX & P200 | |
---|---|---|---|---|---|---|---|---|---|

ANZ | 1 | ||||||||

NST | −0.00823 | 1 | |||||||

WOW | 0.3892806 | 0.03766044 | 1 | ||||||

QAN | −0.138642 | −0.1512646 | 0.01148 | 1 | |||||

TLS | −0.022662 | 0.16877601 | −0.0305 | −0.267586 | 1 | ||||

AGL | 0.166683 | 0.23075705 | 0.16094 | 0.091451 | 0.370559 | 1 | |||

CBA | 0.557905 | −0.2265356 | 0.21141 | −0.058059 | 0.398078 | 0.540709919 | 1 | ||

SYD | −0.06633 | 0.22998867 | 0.247503 | 0.247503 | 0.088365 | 0.401731566 | 0.004743932 | 1 | |

ASX&P200 | 0.6208904 | 0.07567481 | −0.063139 | −0.063139 | 0.38973 | 0.544069876 | 0.672520234 | 0.468736 | 1 |

But some stocks have high risks and low return. These kinds of stocks are not recommended investment. In addition, Covariance Matrix can measure the stock. Different stocks should has low Covariance Matrix. According to this table, it is clearly shows that there are 7 stocks has positive Covariance Matrix with ASX except QAN. Among them, CBA has the highest Covariance Matrix with ASX (0.0008). NST has the lowest Covariance Matrix with ASX (0.0002). in fact, between different stocks also has Covariance Matrix. For example, NST has a high Covariance Matrix with SYD (0.017), and has a negative Covariance Matrix with CBA (−0.003). It means that SYD and CBA can be a portfolio, because the Covariance Matrix between them is negative.

The portfolio opportunity set can be described by a curve, which is drawn by the Excel software. The 8 stocks shows in the

ANZ | NST | WOW | QAN | TLS | AGL | CBA | SYD | ASX & P200 | |
---|---|---|---|---|---|---|---|---|---|

ANZ | 0.002325 | −0.0011625 | 0.00071 | −0.000605 | −4.9E−05 | 0.00040518 | 0.00128 | −0.00018 | 0.000707109 |

NST | −0.00116 | 0.01106047 | 0.00015 | −0.001439 | 0.000795 | 0.00122339 | −0.0011 | 0.001735 | 0.000187964 |

WOW | 0.000707 | 0.00014386 | 0.00142 | 3.91E−05 | −5.1E−05 | 0.00030566 | 0.00038 | 0.000149 | 0.000466258 |

QAN | −0.00060 | −0.0014386 | 3.9E−05 | 0.008178 | −0.00108 | 0.00041690 | −0.0002 | 0.001231 | −0.00013485 |

TLS | −4.89E−05 | 0.00079477 | −5.1E−05 | −0.00108 | 0.002005 | 0.00083642 | 0.00085 | 0.000218 | 0.000412139 |

AGL | 0.000405 | 0.00122339 | 0.00031 | 0.000417 | 0.000836 | 0.00254124 | 0.00130 | 0.001114 | 0.000647761 |

CBA | 0.001289 | −0.001142 | 0.00038 | −0.000252 | 0.000854 | 0.00130660 | 0.00229 | 1.25E−05 | 0.000761372 |

SYD | −0.00017 | 0.00173467 | 0.00015 | 0.001231 | 0.000218 | 0.00111386 | 1.25074E | 0.002298 | 0.000608889 |

ASX & P200 | 0.0007071 | 0.00018796 | 0.00047 | −0.000135 | 0.000412 | 0.000647761 | 0.0007613 | 0.000609 | 0.000557793 |

frontier. Efficient frontier is a slanting curve, and it Satisfy the high return and high risk principles. Following with high return, the risk will be high. Minimum Variance Portfolio is MVP. According to the curve, just QAN and NST are higher than the portfolio opportunity curve, and other 6 stocks are below than the portfolio opportunity curve. These 6 stocks mean that they may be have the high risk but low return. In addition, NST has the highest return and it can be a portfolio with NST which can be invest advance.

The minimum variance portfolio and the recommended portfolios A and B are listed in

According to the tabular data, the expected yield of the minimum variance portfolio is 0.54% with a standard deviation of 2.25%. The minimum variance portfolio is the portfolio with the lowest effective boundary risk. As the chart shown in section two, all points on the opportunity curve below the minimum variance portfolio has a lower expected return and a higher standard deviation than the minimum variance portfolio.

It is clear that portfolio A has the monthly expected rate of return (0.65%) is higher than the minimum variance portfolio. However, the standard deviation of portfolio A is only 2.26%, only a little higher than it of minimum variance portfolio. In addition, due to the much higher monthly expected return of Portfolio B (1.83%), which is almost four times the minimum variance portfolio, it is recommended as well. Nevertheless, Portfolio B is more risky than Portfolio A because of its standard deviation which is the highest among three portfolios (3.51%). It is advisable that the directors and investors balance the return and

Min Variance Portfolio | Portfolio A | Portfolio B | ||||
---|---|---|---|---|---|---|

Expected Return | 0.54% | 0.65% | 1.83% | |||

Standard Deviation | 2.25% | 2.26% | 3.51% | |||

Weight | Amount | Weight | Amount | Weight | Amount | |

ANZ | 20.48% | $ 20,478,689 | 22.71% | $ 22,705,498 | 46.31% | $ 46,309,440 |

NST | 4.02% | $ 4,024,301 | 5.24% | $ 5,241,487 | 26.25% | $ 26,246,485 |

WOW | 24.85% | $ 24,849,672 | 24.85% | $ 24,847,320 | 0.00% | $ 0 |

QAN | 10.64% | $ 10,638,695 | 11.35% | $ 11,345,768 | 27.44% | $ 27,444,075 |

TLS | 29.49% | $ 29,494,971 | 26.23% | $ 26,225,475 | 0.00% | $ 0 |

AGL | 0% | $ 0 | 0% | $ 0 | 0.00% | $ 0 |

CBA | 0% | $ 0 | 0% | $ 0 | 0.00% | $ 0 |

SYD | 10.51% | $ 10,513,672 | 9.63% | $ 9,634,452 | 0.00% | $ 0 |

risks before choosing from portfolio A and portfolio B.

It can be seen that the

method, which is calculated by Excel Solver. It can be seen that A and C maintain the same expected return of 0.65%, while the same B and D maintain the expected return of 1.68%. According to the rules, the portfolio can short risky assets but each asset weight does not exceed 5%. From the above table, it can be concluded that the new portfolio C has standard deviation that is half the lower than Portfolio A, with the expected return being the same. Portfolios B and D share the same situation. This conclusion means that it is effective to reduce the risk of portfolios A and B by rebuilding risk and risk-free assets as portfolios C and D, while can still maintain the expected return equal. Therefore, C and D are more worthy of recommendation than portfolios A or B.

Beta indicates the risk of securities or portfolio systems. It is a mathematical tool to measure the systematic undiversifiable market risk ( Alhabeeb, 2020). It repre- sents a direct relationship between securities or portfolio returns and market trends. Based on Beta, the expected return can be calculated by using the Capital Asset Pricing Model (CAPM). Alpha refers to the return of more than expected returns in the CAPM model. In this section, all Betas are calculated based on the standard deviation of stocks, portfolios, and market indices, as well as covariance and correlation coefficients. Among them, Alpha is the difference between the actual return of the portfolio and the expected return of the CAPM model. In addition, in general, the risk increases with the increase of Beta.

The alpha and beta values for the four selected stocks and the four portfolios are depicted in the chart above. In the analysis of the portfolio, a higher Beta means higher risk.

Portfolio A | Portfolio C | Portfolio B | Portfolio D | |
---|---|---|---|---|

Expected Return | 0.65% | 0.65% | 1.83% | 1.83% |

Standard Deviation | 2.26% | 1.08% | 3.51% | 2.93% |

Weight | ||||

ANZ | 22.71% | 14.19% | 46.31% | 45.86% |

NST | 5.24% | 7.02% | 26.25% | 19.69% |

WOW | 24.85% | 5.22% | 0.00% | 16.07% |

QAN | 11.35% | 6.86% | 27.44% | 20.81% |

TLS | 26.23% | −5% | 0.00% | −5% |

AGL | 0% | 3.09% | 0.00% | 3.38% |

CBA | 0% | 2.23% | 0.00% | 3.98% |

SYD | 9.63% | −5% | 0.00% | −5% |

Risk Free Asset | 22.71% | 71.39% | 0.00% | 00.21% |

Beta | Alpha | |
---|---|---|

ANZ | 1.544042 | 0.0147 |

NST | 0.410437 | 0.0037 |

WOW | 1.01812 | 0.0095 |

QAN | −0.00146 | 0.0024 |

Portfolio A | 0.702703 | 0.0072 |

Portfolio B | 1.254802 | 0.0101 |

Portfolio C | 0.502703 | 0.0046 |

Portfolio D | 2.297297 | 0.0106 |

portfolio, portfolio D has the highest risk factor. In terms of alpha, ANZ and B have the highest alpha, and higher alpha can bring higher returns. It should be noted that investment assets with higher alpha prefer to have higher beta coefficient, which means that high returns always have high risks. Overall, portfolio C is a good choice for risk-averse investors, and portfolio D is attractive for risk lovers.

In summary, the report analyzes the portfolio of eight stocks and Treasury bills. The report shows opportunities for risky assets in graphical and tabular form, and finds the optimal portfolio, the portfolios with riskfree assets through Solver and the effective set. This report separately calculates the min variance portfolio and the weights of portfolios A and B. The risk of portfolio B is higher than portfolio A. It is recommended to balance the benefits and risks when customers choose A or B. Then it shows the CAL line, using risk and risk-free assets as portfolios C and D to rebuild portfolios A and B while still maintaining the expected return equal. The expected return on portfolio C is relatively low, so the risk is also lower than portfolio D, which represents a safer management of such a large portfolio of funds. Portfolio D has higher returns and higher risks.

However, the analysis in this report is limited. For example, the data in this report are from 2016 to January 2018. This report will be more accurate if there is more data to support the analysis.

The author declares no conflicts of interest regarding the publication of this paper.

Lyu, K. (2021). Portfolio Management of 8 Australian Com- panies’ Stocks. Open Journal of Social Sci- ences, 9, 438-446. https://doi.org/10.4236/jss.2021.91032