Fuzzy Chance-Constrained Integer Programming Models for Portfolio Investment Selection and Optimization Under Uncertainty

Fuzzy Chance-Constrained Integer Programming Models for Portfolio Investment Selection and Optimization Under Uncertainty

Shayarath Srizongkhram, Kittitath Manitayakul, Pisacha Suthamanondh, Navee Chiadamrong
Copyright: © 2020 |Pages: 26
DOI: 10.4018/IJKSS.2020070103
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Portfolio investment optimization is the process of selecting the best portfolio out of the set of all projects being considered. A high financial return is not the only concern since minimization of associated risk is as important. Its objective should be set to maximize the expected return and minimize the risk in the investment as most data need to be justified based on vagueness and future values. Thus, the portfolio investment optimization problem under a fuzzy environment is studied here by incorporating a classical mathematical optimization model with the fuzzy theory. It is solved with the fuzzy chance-constrained integer programming model by linear programming under predetermined conditions and limitations. This study also uses both the credibility index and credibilistic risk index for measuring the investment return and investment risk. A numerical example is illustrated to demonstrate the effectiveness and benefits of the proposed algorithm.
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1. Introduction

Project Portfolio Management (PPM) is a set of procedures. These procedures are used to assist an organization in handling a combination of projects, which best fit the organization’s various needs (Archer et al., 1999). The set of processes consists of the project selection, established from the organization activities, and portfolio project management. PPM also considers a regular evaluation, to verify that the mix of the processes could benefit the organization (Ross et al., 2006).

To obtain efficient portfolios, investors are faced with a trade-off between a higher risk and a higher expected return by taking on more risk. Financial return, risk, or credibility are the most important criteria for investors to make a financial decision on investments under uncertainty. The financial problem related to project portfolio selection is how to maximize profits when distributing the available investment capital to the selected combination of projects. Several heuristic methods were proposed to deduce the financial feasibility of projects. For instance, Brigham (1975) used Discounted Cash Flow (DCF) analysis to establish the Net Present Value (NPV) and Rate of Return (IRR), and the Present Value Index (PVI) was reviewed by Boer (1999). In the DCF method, investment criteria, like cash inflows and outflows and available investment capital are regarded as definite real numbers. Nevertheless, these variables are perceived to be fuzzy and imprecise in reality.

A study by Beaujon et al. (2001) identified risk as a major problem underlying the choice of methodology for evaluating the value of a project (or a portfolio of projects). In the most basic case, if the value of each project is independent of the value of any other project, the major issue is to correctly identify the risk of each project, according to the selection of a portfolio. Furthermore, there are a number of proposed methodologies for valuing projects including some that explicitly account for risk. In this study, the risk is evaluated by the credibilistic risk index to evaluate the deviation of the result from the expected most-likely outcome as in the study by Zhang et al. (2011), and the credibility index that is evaluated by the possibility to occur that was introduced by Huang (2007).

This study also presents the optimal choice of portfolio investment under uncertain environments that satisfies all financial and risk constraints. The main contribution is to propose the portfolio investment optimization algorithm with uncertain parameters under a specified confidence level. The decision-makers decide what projects and when to invest under a limited budget by considering the credibility index and credibilistic risk index and the optimal logical relationships among invested projects. To our knowledge, judging the optimal portfolio by considering both the credibility index and credibilistic risk index has not been considered. Considering both risk terms is of importance as both results can contribute to each other, in terms of determining the acceptable amount of risk. This would help decision-makers to evaluate the financial return and inherent risk, simultaneously.

The rest of this paper is organized as follows. Section 2 is a literature review that includes relevant research in the field of portfolio optimization and optimization under uncertainty. Section 3 explains the problem formulation of integrating the objective functions by minimizing the credibilistic risk index of the project portfolio and maximizing the expected direct benefits. Moreover, this section also presents a numerical example of project portfolio optimization. Section 4 shows and compares the results. Finally, Section 5 concludes the findings and describes the limitations and suggestions for future research.

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