Assignment Problem:
The assignment has three main sections: Preliminary Work, Optimisation Models and Report.
Assignment Assurance: This assignment assesses following:
Assignment Outcomes:
A) Discipline-specific knowledge and capabilities: appropriate to the level of study related to a discipline or profession.
B) Problem solving: creating solutions to authentic (real world and ill-defined) problems.
C) Critical thinking: evaluating information using critical and analytical thinking and judgment.
Unit Learning Outcomes:
A) Conceptualise, formulate and represent a business problem as a decision model.
B) Develop and solve business problems using advanced decision modelling techniques such as optimisation, stochastic modelling and risk analysis in spreadsheets.
C) Interpret and analyze the results; investigate the assumptions of the decision model.
Assignment Details: This assignment is designed to let you explore and evaluate a number of approaches to investment portfolio optimisation, using live real-world data. The relevant URL for finding stock prices is: Australia yahoo finance under the "Quote lookup" search.
In this assignment you will use asset return data for a period of 3 years to identify the optimum portfolio using a variety of different optimisation methods.
Assignment Section 1: Preliminary Work (Data acquisition + Classifications)
Choose five investments listed on the Australian Stock Exchange, one from each of the categories given in the following table, to complete a set of 10 investments:
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Basic materials
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Consumer goods and media
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Financial
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Healthcare
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Industrial
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1. Rio Tinto Limited (RIO.AX)
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2. Coca-Cola Amatil Limited (CCL.AX)
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3. Westpac Banking Corporation (WBC.AX)
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4. Cochlear Limited (COH.AX)
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5. Qantas Airways Limited (QAN.AX)
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6. Your choice
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7. Your choice
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8. Your choice
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9. Your choice
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10. Your choice
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To access the assets, click Industries on the ribbon menu, and select a category. Click on the symbol for the asset you want to include in your portfolio. Click Historical data on the ribbon menu, set Time period to 1 November 2016 - 1 November 2019 and Frequency to Monthly, then click the Apply button, and download the data. Delete any rows showing dividend. We are only interested in the opening price, listed in the column headed Open. Discard the rest of the data.
The chosen assets must satisfy the following general requirements:
Each must have 37 consecutive months of opening prices, up to and including 1 November 2019.
They should be selected from the five industry categories listed in the table, namely Basic materials, Consumer goods and media, Financial, Healthcare, and Industrial. You must choose only one asset from each of these five categories.
They should span a reasonable range of volatilities/risk. For this reason you might try several assets in a category before settling on one.
Classify each of the ten assets into one of three risk groups R1, R2, and R3, where R1 < R2 < R3. It is up to you to determine the basis for the classification, but you must have at least three assets in each risk group.
Each asset must belong to one of the five industry categories and one of the three risk categories.
Assignment Section 2: Optimisation Models
For your portfolio optimisations, you should use all of the data to undertake parts 1, 2, 3a, 3b, and 3c.
The assignment requires you to consider three different approaches to portfolio optimisation:
A) Choosing according to asset class restrictions, and individual asset risk appetite.
B) Choosing according to portfolio size restrictions and risk appetite.
C) Choosing according to portfolio risk and return requirements.
These three approaches allow exploration of three different optimisation techniques: linear programming (LP), integer linear programming (ILP) and non-linear programming (NLP):
1. LP model (Mathematical Model + Solver and results + Sensitivity Analysis worksheet): In this approach, the aim is to achieve the maximum overall return, subject to specified requirements on risk mix (percentages in R1 to R3) and category mix (percentages in C1 to C5). These requirements may be simple - such as "no more than 10% in R1, or more complex such as "there should be as much invested in R1 as there is in R3" or "Investment in high risk assets shouldn't exceed the 30% of the portfolio". Other restrictions might be of the form - "at least 25% should be in the Financial category, and no more than 20% in the Industrial category". It is up to you to determine the restrictions that you wish to impose. These should be "sensible", respecting a sense of diversity in the portfolio, and a defendable risk acceptance approach. The only requirement is that they should respect the learning aims of this assignment and therefore they should not in any way trivialise the problem. There should be realistic range requirements for each of R1 to R3, and C1 to C5. For example, requiring all assets in the portfolio to be in risk category R1 would trivialise the problem.
2. ILP model (Model + Solver and results): In this approach, we assume that a balanced portfolio of exactly 8 stocks is to be chosen. The 5 asset categories have to be included. In addition, at most 2 of the assets can be in the riskiest group R3, and at least 1 must be in the least risky group R1. The goal is to achieve the maximum overall return, subject to these requirements.
3. NLP model: In this approach, the aim is to optimise without imposing any category or risk group constraints. Instead the overall portfolio risk/return profile is optimised. There are three sub-problems here:
a) Achieve the maximum overall return, subject to an upper limit on portfolio risk (your choice of limit).
b) Achieve the minimum portfolio risk, subject to a requirement to achieve at least a specified return (your choice of required return).
c) Semi-variance is an alternative measure of risk that is used to estimate the potential downside risk of an investment portfolio. To calculate semi-variance, you add up the squares of the differences between the sample mean and each observation that falls below the mean, and then divide the result by the number of such observations.
Repeat parts (a) and (b) using this alternative measure.
Assignment Section 3: Report
The PowerPoint document should present all your results in a coherent and compelling manner. Each model should be accompanied by the following:
- A conceptual diagram of the model
- An algebraic formulation of the model
- The optimal solution
- Interpretation of sensitivity analysis output for part 1 of section 2 (Use Solver's sensitivity analysis report for part 1 to comment on how changes to risk and category constraints might affect the optimum portfolio.)
Then, based on your assessment of the various approaches, briefly explain which strategy you might prefer to use for portfolio optimisation, and why. Include a summary table listing the details of each optimal portfolio with percentages of assets, portfolio return and risk based on the 3 years of data.
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