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Investment Management

Executive summary

Portfolio management is very important from the point of view of investment and to take the benefits of steady and regular Returns. Everyone has to decide the portfolio according to their financial objectives and their capability of taking the risks. The portfolio design for the risk aversive the people will be different and for the risk-tolerant people is different. Generally, people do not want to take much rest and they want to balance the risk in such a way that higher returns on their investment can be achieved. It is important to understand various estimates related to average Returns, risk indexes, portfolio weights, etc. before selecting a Portfolio. This report is prepared to design an investment portfolio in the listed equities of three ASX 200 companies and financial modeling is used to evaluate this portfolio from the different aspects. Under the financial modelling, statistical analysis related to the compounded monthly Returns, average monthly Returns and annualized returns are calculated. The diagram depicting portfolio opportunity sets, unconstrained minimum variance sets, the capital market line will be prepared and Portfolio weights are also calculated. Security market line and beta are also estimated using various index models. Based on dis quantitative analysis, recommendation is provided and the investment portfolio is evaluated keeping in mind the risk and return aspects.


Executive summary. 2

Introduction and Asset Selection. 4

Reasons for the Asset Selection. 4

Financial theory related to selection. 5

Findings and discussions. 5

Part 1. 5

Basic statistical analysis. 5

Continuous compounded monthly returns. 7

Average monthly returns and Standard Deviation. 7

Annual average returns and variance-covariance matrix. 8

Part 2. 8

Portfolio opportunity lines. 8

Minimum Variance Set and Minimum variance portfolio. 11

Capital Market line. 12

Portfolio weights. 14

Part 3. 15

Beta Estimation. 15

SML equations and Plotting of SML’s. 16

Comments. 19

Conclusion and recommendations. 19

References. 21

 Introduction and Asset Selection

This business report is prepared for the purpose of investment management for which different companies are selected for the purpose of investing in shares and a proper portfolio is designed for the client by keeping in view the risk and return perspective of the investment. Three companies, namely, ANZ Banking Group, Rio Tinto Limited, and Woolworths Limited are selected for the purpose of portfolio designing, and these companies are listed in Australian securities exchange 200 lists(Morningstar, 2020). The shares of these three companies will be analyzed in order to guide the client for the investment. Which of the company belongs to a different global industry classification standard or GICS because of the Sectors and industries to which these companies belong are different. The GICS sector for Woolworths Limited is consumer staples and the GICS industry to which it belongs is Food & Staples Retailing. Rio Tinto Limited belongs to GICS sector materials and the industry is also materials (Morningstar, Inc. , 2020). ANZ Banking Group belongs to sector financials under GICS and the industry is banking (Morningstar Inc., 2020).

Reasons for the Asset Selection

For the purpose of the investment portfolio, these companies are selected because of the following reasons:

  • All of these companies belong to large-cap funds which ensure regular and more predictable Returns.
  • These companies are well established which reduces the risk because the companies are doing really well and continue working on their improvement by making modifications according to the changing needs of the environment.
  • These companies are likely to provide more stable and regular Returns because these have already set a benchmark in the capital market and it is easy to check the Trends of these companies and accordingly investment portfolio can be decided.
  • Another reason for selecting these companies is diversification of risk because all of these companies belong to a different sector and industry. By doing so, there is a possibility to minimize the risk and to enhance the returns. Generally, not all sectors perform badly at the same time, which helps to diversify the risk. The bad Returns from one sector can be compensated from the growing returns from the other sector and overall, it can be better managed. Also, all of these companies belong to growing sectors of the economy, such as the financial sector, the mining sector, and the consumer staples and retail sector.
  • Even at the time of risk and turbulence, these companies a strong enough to deal with such uncertainties, and in the long run, steady Returns are being promised by these companies.

Financial theory related to selection

There is a famous portfolio theory which talks about the general nature of the investors. According to this theory, most of the investors want to increase their wealth and Returns in comparison to the portfolio risk. This is also known as modern portfolio theory or MPT. By keeping in mind this theory, the shares from above large-cap funds belonging to different sectors are selected in order to maximize the possibilities of Return and to reduce the portfolio risk (Mangram, 2013).


Findings and discussions

Part 1

Basic statistical analysis

The closing prices for all three companies for the year July 2002 to 30th June 2020 are being analyzed and after doing a basic statistical analysis of the data, some outliers are being found outliers are the sudden drop or increase in the closing prices from the data.In order to find the outliers, for calculating the lower and upper limit is used to identify the outliers. The items where “true” has popped up because of the formula are selected to remove because of the outliers and a clean data is created after removing all of these outliers. It was important to remove the outliers because these variations were unfavorable and beyond the upper and lower limit. In order to make more effective analysis, this action is being taken. For Rio Tinto Limited, 4 outliers are identified and removed the. 5 outliers are removed from the Woolworths Limited and maximum outliers give the quantity 13 are being identified and removed for the ANZ Banking Group in order to get a clean data. On this clean data, statistical analysis in order to find out Arithmetic mean, compounded Returns, variance, standard deviation, etc. is calculated.

28-Feb-2007 0.65% 13.56% -1.31% Remove
31-Jan-2008 -5.42% -16.57% -8.53% Remove
29-Feb-2008 -16.74% 0.66% 10.78% Remove
30-Jun-2008 -14.68% -12.55% -1.83% Remove
31-Jul-2008 -14.15% 3.02% -7.75% Remove
30-Sep-2008 12.12% -4.18% -41.14% Remove
30-Nov-2008 -15.95% -3.66% -51.00% Remove
31-Jan-2009 -14.17% 3.79% 10.36% Remove
31-Mar-2009 16.83% -4.42% 18.00% Remove
31-Aug-2009 13.88% 2.79% -7.37% Remove
30-Sep-2011 -3.87% -1.44% -16.00% Remove
31-May-2012 -13.45% 1.91% -15.44% Remove
31-May-2013 -14.51% -9.83% -1.12% Remove
30-Nov-2014 -4.83% -14.57% -2.19% Remove
31-Aug-2015 -15.71% -8.00% -4.98% Remove
31-Jan-2016 -14.42% -0.90% -13.33% Remove
31-May-2017 -15.66% -3.14% 3.85% Remove
31-Jan-2020 4.45% 14.59% -1.64% Remove
31-Mar-2020 -38.12% -10.02% -3.14% Remove

(Singh & Upadhyaya, 2012)

Continuous compounded monthly returns

In this case, the return is calculated at compounded rate on continuous period and a formula is used for this purpose. In case of the continuous compounding return, each and every moment is considered for the purpose of compounding and compounding occurs continuously which give more precise view about the returns. For the purpose of calculating this, clean data with the outliers removed is being used.This gives a more accurate view about the investments and investor can understand and predict the performance of a stock did the use of this measure. The calculations related to continuous compounding monthly rate of return is done in the Excel worksheet.

Average monthly returns and Standard Deviation

The Arithmetic average return on the monthly basis and the variance is calculated for this. In order to calculate the average return, all the compounded returns calculated in the previous step what different companies are added and then the sum is divided by the number of entries in order to calculate the monthly average return. It gives a simple statistic for the investor to understand the return on the monthly basis and accordingly investment decisions become easier. Even a layman can understand the average return. On the other hand, the variance helps to understand the deviations from the returns. In other words, it describes the level of risk not receiving the estimated Returns and it has to be considered while making investment decisions and portfolio. This variance is further used to calculate the standard deviation which again means the degree at which there is a possibility that the variation can occur with respect to the mean value.

Average monthly returns 0.83% 0.82% 1.38%
Variance 0.22% 0.18% 0.49%
Standard deviation 4.65% 4.22% 7.04%


RIO giving the maximum average monthly returns and also so the chances of variance which means the possibility of the actual returns to deviate from the average return is also maximum in the case of RIO (Ali & Bhaskar, 2016).

Annual average returns and variance-covariance matrix

Average annual returns are calculated in order to give a view to the investors about the annual earnings which we can expect from their portfolio. An investor generally invests for the long term and because of this, they need to understand the annual returns which we can expect from their investment. For this purpose, formula in Excel is being used and the monthly average return is converted to the annual average return. The variance and covariance matrix are also prepared using appropriate formulas in the Excel sheet. It helps to understand the errors which are likely to take place and all the possible pairs of these errors and deviations from the point of view of the portfolio depicted by the matrix.The figures are converted into percentages in order to make them more comprehensible both for the annualized Arithmetic average return and for the variance and covariance matrix.Again, the average returns are maximum in the case of Rio Tinto limited.

Annualised arithmetic average returns 10.38% 10.25% 17.89%


Annualised variance-covariance matrix
ANZ 0.22% 0.05% 0.06%
WOW 0.05% 0.18% 0.02%
RIO 0.06% 0.02% 0.49%


(Xu et al., 2007)

Part 2

Portfolio opportunity lines

The portfolio opportunities set that helps to understand the number of possible risks associated with the combination of different portfolios, according to which an investor can decide the portfolio and manage it in a better manner so that the level of risk can be reduced and the estimated returns can be increased. According to the level of risk tolerance for an investor did that can be used. For an investor who is ready to take high risk, a Portfolio with higher returns and higher risk can be decided based on the combination lines produced by the portfolio opportunity set and for the investor who is not ready to take a risk, the minimum variance is selected.Considering the short sale constraint, the possibility of the combination lines according to the risk factor involved for the two companies is created. Accordingly, 3 different combinations of sets are created in order to understand their relationship of the risk and return between two companies. From the diagram below, the standard deviation is found in the combination of the line of RIO and WOW, and also the returns are higher in this combination. It is being observed that in the combination set there RIO is present, estimated returns are more in comparison to the other portfolio of it and also the degree of risk is higher (Sanchez & Robert, 2008).

Diagram 1: Portfolio Opportunity sets for ANZ and WOW

Diagram 2: Portfolio Opportunity sets for RIO and WOW

Diagram 3: Portfolio Opportunity sets for RIO and ANZ


Minimum Variance Set and Minimum variance portfolio

The minimum variance set is a function which helps to identify the possible portfolio after considering the risk factor. It is an effort to develop such a portfolio which will result in the most efficient portfolio consisting of various shares of different companies. It is an effort to reduce the overall risk of the portfolio by mix and match the different shares.

Portfolio  1 Weights
ANZ 0.10
WOW 0.10
RIO 0.80
 Expected Return of the portfolio 1 16%
Variance of portfolio 1 0.0033
Standard Deviation of portfolio 1 6%



portfolio 2 Weight Portfolio 2
ANZ 28.00% Expected return 12.94%
WOW 30.00% Variance 0.14%
RIO 42.00% Standard deviation 3.84%
total 100.00%


portfolio 3 Weight Portfolio 3
ANZ 20.00% Expected return 14.55%
WOW 15.00% Variance 0.24%
RIO 65.00% Standard deviation 4.94%
total 100.00%


The data above is showing the MVS for the MVP. Different sets of portfolios are selected keeping in view the risk factors and it is seen that the variance and standard deviation which means the possibility of the deviations from the expected returns or the risk involved gets higher as the investment in the Rio Tinto is increased and this investment comes up with more returns. The portfolio 1 is giving maximum returns because 80% of the capital is invested in Rio Tinto, Portfolio 3 is giving comparatively less returns because 65% is invested in Rio and the portfolio 2 is giving the minimum returns. However, the risk involved in portfolio 2 and 3 is almost same whereas the returns are higher in case of portfolio 3. Therefore, the MVS helps to understand the MVP and accordingly, investors are able to take prudent decisions. From the investor to investor it differs. A risk tolerant investor is ready to take higher risk in order to increase the chances of earning more retunes. On the other hand, a risk aversive investor is not ready to take higher risk rather, he wants to reduce the risk to the minimum possible limit. Thus, the Minimum variance set helps the investor to consider the risk factor and calculation of the suitable possible portfolio set which will produce the minimum variance is possible through this test (Maillet et al., 2013).

Capital Market line

Capital market line equation considers the risk-free return which means the investment in such securities where the minimum return is ensured. In this case the capital market line is drawn from the point of risk-free rate. For this portfolio, a risk-free rate of 1.40% is identified and if the investor finds the portfolio, giving returns more than this rate, then the investment is worth making. It considers the opportunity cost of investment and alternatives are considered. A capital market equation is used to assess the portfolio. 

 Capital market line equation
Rp= Return of portfolio
Rf= Risk free return
Rt= market return
SD(t)= Standard deviation of market return
SD(p)= Standard deviation of portfolio return

For the purpose of drawing the capital market line, a treasury rate for the risk-free return is decided in this case which is 1.4% and accordingly the investment decisions have to be taken. Therefore, as discussed in the previous step, the most efficient portfolio set will be one where there is proper tradeoff between the risk and return and risks are minimum and the returns are maximum (Lee, 2014).

Portfolio weights

According to the discussion done above for the different set of portfolios, the efficient portfolio will be the one which will give minimum variance or risk and provide better returns. For a risk aversive investor, the tendency of risk is less and he is not ready to undertake the risks. Therefore, a risk and return tradeoff has to be done for such as investor. Out of the three portfolios mentioned above, the portfolio 3rd will suit the risk aversive investor the most because the variance and standard deviation is less in this case and the diversification of risk is done properly while keeping the returns in mind. If the investment in the RIO will be reduced further from 65%, it will reduce the returns more. Therefore, for an investor who does not want to take much risk, the portfolio consisting of 65% investment in the shares of the Rio Tinto, 20% in the ANZ group and remaining 15% in the Wools worth group is recommended.

Portfolio 1
ANZ 10.00%
WOW 10.00%
RIO 80.00%
 Total 100.00%
Portfolio Expected Return 15.60%
Variance 0.32%
Standard Deviation 5.66%

Utility score is a measure which can be considered to understand the appropriate portfolio for the risk aversive investor.

Utility score = E(r) – 0.5 x A x σ2

Here, E(r)= expected returns of the portfolio

σ2= Square of the variance which represents portfolio risk

A= Risk aversion coefficient

The minus sign represents the negative attitude of the investor towards the risks associated with the portfolio.

Utility score = E(r) – 0.5 x A x σ2
Expected return (Er) 15.60%
Coefficient (A) 3
 σ2 (variance) 0.32%
U (utility Score) 15.12%


Therefore, the utility score represents that the portfolio is beneficial for the investor because it is giving more returns than the risk-free rate which is assumed to be 1.4% (Lee, 2014).


Part 3

Beta Estimation

  1. a) The first pass regression line helps to understand the presence of systematic risk which is also known as a beta in the portfolio. This type of risk is unavoidable because it is already present in the market and it is also very difficult to predict the systematic risk. Even the portfolio diversification can also not help to avoid the Systematic. It means, beta is always present in the portfolio and more focus should be on the unsystematic risk which is controllable and also can be avoided through proper diversification of the portfolio. The beta informs to be zero in this case which means there does not exist any systematic risk in the market because the expected return is equal to the actual return or the market return.First-pass regression is used in order to calculate the Beta or the systematic risk between the two companies.

r   –   Rf   =   beta x (Km – Rf) +   alpha



  1. b) The portfolio selected is going to give an average return of 15.60% with the standard deviation of 5.66%.


SML equations and Plotting of SML’s

SML is a security market line used to present a Capital Asset pricing model and the equation is used under this case. The equation represents the calculation of the required rate of return. For the purpose of calculating the required rate of, the security market line uses the risk-free rate also considers the systematic risk which is beta for the calculation of market return.

The equation for the second pass regression line will be:

r1-r1=y0+y1b1+y202(e1), which will give the result of Y0=0; y1= rm-rf y2 = 0


The diagrams below show the plotting of the beta or the systematic risk on the security market line which is scattered and shows that the risk is very volatile and because of which it is unpredictable.






About this question helps understand the possibility of risk or the volatility of the expected Returns. The volatility, which is not controllable or cannot be protected while deciding the portfolio is also considered a above. The regression analysis is used to understand the systematic risk, for which first pass regression index and second pass regression index equations are used (Naveenan, 2019). The slope of the regression also considers the systematic risk and this is that risk which master cannot ignore. For example, the systematic risk can be the risk related to the enforcing situations such as the risk of covid-19 because of which suddenly the stock started performing badly. The market return is considered for the purpose of calculating beta of the portfolio. The ordinary indices are used for the calculation of market return. All these risks are considered in the beta analysis and in the analysis of security market line. It is being observed that the volatility is more in Rio Tinto but also the chances of having Returns are more in this case. It helps to understand and manage the portfolio in a better manner. Therefore, it is important that the security market line, the involvement of Beta to the regression analysis, has to be considered before making the investment decisions (Khan & Faisal, 2018).


Conclusion and recommendations

The above discussion shows that there is a direct link between the returns and risk. If an investor wants to increase the returns, the investor has to increase the tolerance power for the risk. It has been observed that the stocks of Rio Tinto are volatile because the change in the monthly closing prices fluctuate more and also this stock gives a lot of Returns. While comparing the monthly returns or the annual returns of the three stocks, it can be seen that Rio Tinto is having maximum Returns in comparison to the other two stocks. Therefore, there is a need to find a trade-off between the risk and return in such a way that the risk can be minimized and the return can be maximized. For this purpose, the diversification of risk is needed. Three portfolios are suggested to the investor for the investment purpose. In the first portfolio, percent of the capital is invested in Rio Tinto, which is going to give almost a 16 % estimated return, but the level of variance is higher in this case in comparison to the other two portfolios. In the next portfolio, 42% is invested in Rio Tinto, the remaining 28%, and 30% is invested in ANZ and WOW respectively. The return expected from this portfolio that has decreased to 12.94%, but the risk factor of the deviations has also shown a decrease, but the decrease in the deviations is not much in comparison to the decrease in the return. Therefore, the third option for the portfolio set is the most suitable where 65% of the capital is invested in high performing asset RIO and 20% is invested in ANZ and the remaining 15% in the WOW. The portfolio set is providing a return of 14.55% with a standard deviation of 4.7%.

Keeping in mind the situation of covid-19, it is recommended that the investor should invest for the long-term purpose liquidate investments in a short period because the present period is very volatile. This time is also good for the investment purpose because the prices of the stocks have reduced as the market is bear at this time. There are huge chances that the stocks will perform better in the coming times when the situation will go back to normal. Therefore, the invested is recommended to diversify the portfolio in such a way that the risk and return are balanced and after analyzing the Trends of previous market prices of the stocks, more than 50% should be invested in RIO Tinto and the remaining should be diversified between the other two companies. This will help to balance the rest profile. Holding the stocks for a long period of time will help to manage the systematic risk which has occurred due to the covid-19.




Ali, Z. & Bhaskar, S., 2016. Basic statistical tools in research and data analysis. Indian journal of anaesthesia, 60(9).

Khan, A. & Faisal, S., 2018. Estimating Beta (β) Values of Stocks in the Creation of Diversified Portfolio – A Detailed Study. 5(3).

Lee, M., 2014. Capital market line based on efficient frontier of portfolio with borrowing and lending rate.

Maillet, B., Tokpavi, S. & Vaucher, B., 2013. Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach.

Mangram, M., 2013. A Simplified Perspective of the Markowitz Portfolio Theory. Global Journal of Business Research.

Morningstar Inc., 2020. Australia & New Zealand Banking Group Ltd ANZ. [Online] Available at:

Morningstar, Inc. , 2020. Rio Tinto Limited RIO price chart. [Online] Available at:

Morningstar, 2020. Woolworths Group Limited WOW price chart. [Online] Available at:

Naveenan, R., 2019. Risk and Return Analysis of Portfolio Management Services of Reliance Nippon Asset Management Limited (RNAM).

Sanchez, H. & Robert, B., 2008. A Project Portfolio Risk-Opportunity Identification Framework. Project Management Journal, 39(3), pp.97 – 109.

Singh, K. & Upadhyaya, S., 2012. Outlier Detection: Applications And Techniques. International Journal of Computer Science Issues, 9(3).

Xu, P., Liu, Y., Shen, Y. & Fukuda, y., 2007. Estimability analysis of variance and covariance components. Journal of Geodesy, 274(3).


Executive Summary

This assignment is a compilation of the case analysis of the demise of the company world as a result of the accounting scandal in June 2002. A risk-based auditing approach has been implemented to study the significance of the organisation operating as a going concern and choosing to go for administration or its liquidation. All these cases of the operational performance are analysed with the help of the Australian accounting standards and auditing concepts to arrive at the conclusions related to the reasons that resulted in the collapse of this organisation and recommendations are provided to the people practicing accountancy and auditing as well as the organisation on how to ensure that they do not face the same fate. Creative accounting was not a technique that was new in the market and there are a number of organisations that have been reported to make use of them to ensure that they are pure more profitable or they are easily able to attract the resources and investors. World was also involved in the creative accounting practices by capitalising the cost improperly. On June 2002, it was revealed that the organisation was practising fraudulent reporting and the accounting reports of the organisation were full of made up figures that indicated that the organisation had an annual profit of $3 billion when in fact LDDS was registering a loss of $500 million for that year. This was followed by a detailed investigation of the reports and operations of the company that revealed total misstatement by the company of about $11 billion till the year 2002.


This assignment is a compilation of the case analysis of the demise of the company WorldCom as a result of the accounting scandal in June 2002. A risk-based auditing approach has been implemented to study the significance of the organisation operating as a going concern and choosing to go for administration or its liquidation. All these cases of the operational performance are analysed with the help of the Australian accounting standards and auditing concepts to arrive at the conclusions related to the reasons that resulted in the collapse of this organisation and recommendations are provided to the people practicing accountancy and auditing as well as the organisation on how to ensure that they do not face the same fate .

WorldCom was an organisation providing long distance telephone services two individuals and organisations. It had its humble beginnings in the United States of America as the Long Distance Discount Services (LDDS) providing organisation that slowly and gradually went on to become one of the largest telecommunication service providing organisations in the United States. The Organisation was established in the year 1983 and Bernie Ebbers was appointed the CEO of the organisation in the year 1985. LDDS decided to go public in the year 1989 and your organisation went on to become a company having $30 billion as their annual revenue after acquiring other telecom organisation operating in the country. Ebbers became one of the richest people in America and his net worth was attributed to be close to $1.4 billion in the year 1999 and he further continued with the acquisition strategy and served as an extremely strong leader making the organisation rise in the industry. However, on June 2002, it was revealed that the organisation was practising fraudulent reporting and the accounting reports of the organisation were full of made up figures that indicated that the organisation had an annual profit of $3 billion when in fact LDDS was registering a loss of $500 million for that year. This was followed by a detailed investigation of the reports and operations of the company that revealed total misstatement by the company of about $11 billion till the year 2002 .

This research includes an analysis of this case to understand why this fraud happened and what were the constituent and the reasons for it. It is not only important to study this case to ensure better accounting practices but this case will also provide the auditors with the methods to analyse and identify any threats to the organisational performance and their ability to operate as a Going Concern in the near future.

Research methodology

The research methodology for a study is defined as the approach adopted for conducting the study and for analysing the data collected for the research to reach the desired conclusions. This is a desk research which follows the exploratory research design. It involves the exploration of the case of WorldCom and how the accounting fraud by the organisation resulted in its demise and impacted not only the organisation but also the entire business world. This is a research that is completely based on the secondary data that is gathered from the previously published electronic and non-electronic sources of information. These include the research journals, articles, research papers, government reports, business reports, newspapers, magazines and other scholarly paper. A combination of qualitative and quantitative information is used in this study in order to effectively carry out the analysis of the given case and find out the reason that led to the fraudulent reporting, the characteristics of the fraud detected by the reporting organisations and the consequences of this incident for all the stakeholders involved . The implications of the findings from this research will be analysed with regard to the going concern, administration and liquidation of the organisation. Wild qualitative data adds to the description and the detailed attributes and properties of the case, the quantitative information will help in objectively carrying out the comparison and analysing the case by measuring and quantifying the information.

It is important to note that being an academic research, this study is limited in its scope. Due to the limited availability of time and resources, the findings of this research are only limited to the case of WorldCom and how the fraudulent reporting by the organisation has impacted the stakeholders of the company. The findings from the study cannot be generalized for any other organisation or case.