Investment Portfolio Optimization Decision Analytics Assignment Sample

Optimization Models For Australian Stock Portfolio Decisions

Section 1

1.1 Introduction

This report analyses a “portfolio of 10 stocks” selected from the “Australian Stock Exchange, which represents five different industry categories. The selected stocks are Rinto.Tinto Limited, CSL Limited, Westpac Banking Corporation, Computershare Limited, Quantas Airways Limited, Orocobre Limited, Sonic Healthcare Limited, Medibank Private Limited, Technology One Limited, and SEEK Limited.

1.2 Stock (Asset) Selection

The selection of the stocks is done to represent a diverse range of industries and profiles of risk (Dong et al. 2021). Every stock has 37 consecutive months of opening prices up to February 1, 2024. Monthly returns were determined for every stock, with the average returns and standard deviations for the risk assessment.

1.3 Risk Group Classifications

The classification of the stocks is done into four risk groups, which are based on their standard deviation of returns. In this regard, R1 (safe) is less than 6% of the standard deviation, R2 (Low risk is greater than 6% and less than or equal to the 7% standard deviation, R3 (medium to high risk) is greater than 7% and less than or equal to the 8% standard deviation, and R4 (high risk) is greater than the 8% standard deviation (Mills et al. 2020). This classification ensures at least two stocks in every risk group while providing a reasonable range of volatilities.

1.4 Summary Table(S)/Numerical Summaries

Stock	Industry	Risk Group	Average Return	Standard Deviation
CSL	C2	R1	0.41%	5.16%
SHL	C2	R1	0.06%	6.83%
MPL	C3	R2	0.91%	5.45%
CPU	C4	R2	1.86%	6.65%
ORA	C1	R3	0.76%	7.29%
WBC	C3	R3	0.64%	7.03%
TNE	C4	R3	1.98%	7.96%
QAN	C5	R3	0.88%	7.74%
RIO	C1	R4	0.87%	8.43%
SEK	C5	R4	0.09%	9.25%.

Table 1: Summary table(s)/numerical summaries

(Source: Self-created in MS Excel)

The above classification and selection in the image provide a well-balanced portfolio throughout different industries and levels of risk, setting the foundation for the models' optimisation in the sections.

Section 2

2.1 LP Model

2.1.1 Formulation Algebraic

Figure 1: Investment weight

(Source: Self-created in MS Excel)

In the image above, the algebraic formulation of the LP model is demonstrated. In this regard, it is demonstrated that the objective function and constraints, including the requirement that weights sum to 1 and meet the specific risk group and industry category allocations.

2.1.2 Optimal Solution

Figure 2: Optimal solution of LP Model

(Source: Self-created in MS Excel)

The optimal solution is presented in the image above, which demonstrates the weights for every stock.

2.1.3 Sensitivity Report

Figure 3: Sensitivity Analysis

(Source: Self-created in MS Excel)

The sensitivity report is presented above, which is important for understanding the way in which constraint changes might affect the optimal solution (Tian et al. 2021)

2.1.4 Interpretation

The optimal solution allocates 30% to CPU, 25% to MPL, 30% to TNE, and 15% to CSL.

2.2 ILP Model

The binary decision variables are introduced in the ILP model for the selection of exactly 8 stocks for an equally weighted portfolio.

2.2.1 Conceptual Diagram

Figure 4: Conceptual framework

(Source: Self-created in draw.io)

In the image above, the conceptual diagram is presented, through which the structure of the model and constraints are represented. Through this diagram regarding the model’s logic, understanding is enhanced.

2.2.2 Algebraic Formulation

Figure 5: Investment Weight

(Source: Self-created in MS Excel)

In the image above, the algebraic formulation is presented, which shows the constraints and objective functions, which include the binary variables for the selection of stock.

2.2.3 Optimal Solution

Figure 6: Optimal Solution of IPL model

(Source: Self-created in MS Excel)

In the image above, the optimal solution is demonstrated regarding the ILP model.

2.2.4 Interpretation

The model selects an equally weighted portfolio regarding 8 stocks, which are RIO, CSL, WBC, CPU, QAN, QRA, MPL, and TNE.

2.3 NLP Models

2.3 (a) Overall Return Maximization

1. Formulation Algebraic

Figure 7: Decision investment

(Source: Self-created in MS Excel)

The algebraic formulation is provided in the image above. The solution demonstrates the selected weights for every stock and the resulting portfolio risk and return (Karthiga et al. 2024).

2. Optimal Solution

Figure 8: Maximize overall return subject to an upper limit on portfolio risk

(Source: Self-created in MS Excel)

The optimal solution is provided in the image above. The solution demonstrates the selected weights for every stock and the resulting portfolio risk and return. 

3. Interpretation

This model allocates majorly to higher-return stocks, where CPU is 43.7% and TNE is 36.3%, while including small allocations to lower-risk stocks, where CSL is 13.7% and MPL is 6.3%, to stay within the specific risk limit (Molineaux et al. 2024).

2.3 (b) Portfolio Risk Minimization

1. Formulation Algebraic

Figure 9: Investment portfolio

(Source: Self-created in MS Excel)

The algebraic formulation is provided in the image above (Hambly et al. 2023). It demonstrates the way the portfolio is constructed for minimising risk while achieving a particular return. 

2. Optimal Solution

Figure 10: Optimal Solution Minimize Portfolio Risk

(Source: Self-created in MS Excel)

The optimal solution is provided in the image above. It demonstrates the way the portfolio is constructed to minimise risk while achieving a particular return.

3. Interpretation

The solution diversifies throughout more stocks, with major allocations to lower-risk assets, where CSL is present at 29.8% and MPL is present at 24.5%, while including higher-return stocks, where CPU is present at 19.7% and TNE is present at 15.9%, to meet the requirement of return.

2.3(c) Maximum Of Risk-Adjusted Return

1. Algebraic Formulation

Figure 11: Algebra of Maximum of risk-adjusted return

(Source: Self-created)

The algebraic formulation is provided in the image above. This model aims to maximise the risk-adjusted returns.

2. Optimal Solution

Figure 12: Maximum of risk-adjusted return

(Source: Self-created)

The optimal solution is provided in the image above. It demonstrates that the portfolio offers the best trade-off between return and risk according to this measure.

3. Interpretation

The optimal portfolio balances return and risk, allocating throughout many stocks with CPU at 31.9% and TNE at 24.7%, and these have the largest weights.

Results Optimization And Strategy Of Recommendation

Summary Table (S) Of Results For All Models

The optimal portfolio allocation of LP is present at 30, 25, 30, and 15%, respectively. For ILP, the equal weights are present at 12.5%. For the first NLP, the optimal portfolio allocations are 43.7%, 36.3%, 13.7%, and 6.3%. For the second NLP, the optimal portfolio allocations are 29.8%, 24.5%, 19.7%, and 15.9% and others are less than 5%. For the third NLP, the optimal portfolio allocations are present at 31.9% and 24.7%.

Preferred Strategy

The strategy that is preferred is the NLP model, which minimises portfolio risk, which is subject to achieving a particular return.

Rationale

The NLP model offers the best balance between management of risk and potential of return.