Multi-objective Portfolio Selection Research Articles

Robust, extended goal programming with uncertainty sets: an application to a multi-objective portfolio selection problem leveraging DEA

AbstractThis study presents a two-phase approach of Data Envelopment Analysis (DEA) and Goal Programming (GP) for portfolio selection, representing a pioneering attempt at combining these techniques within the context of portfolio selection. The approach expands on the conventional risk and return framework by incorporating additional financial factors and addressing data uncertainty, which allows for a thorough examination of portfolio outcomes while accommodating investor preferences and conservatism levels. The initial phase employs a super-efficiency DEA model to streamline asset selection by identifying suitable investment candidates based on efficiency scores, setting the stage for subsequent portfolio optimization. The second phase leverages the Extended GP (EGP) framework, which facilitates the comprehensive incorporation of investor preferences to determine the optimal weights of the efficient assets previously identified within the portfolio. Each goal is tailored to reflect specific financial factors spanning both technical and fundamental aspects. To tackle data uncertainty, robust optimization is applied. The research contributes to the robust GP (RGP) literature by analyzing new RGP variants, overcoming limitations of traditional and other uncertain GP models by incorporating uncertainty sets. Robust counterparts of the EGP models are accordingly developed using polyhedral and combined interval and polyhedral uncertainty sets, providing a flexible representation of uncertainty in financial markets. Empirical results, based on real data from the Tehran Stock Exchange comprising 779 assets, demonstrate the superiority of the proposed approach over traditional portfolio selection methods across various uncertainty settings. Additionally, a comprehensive sensitivity analysis investigates the impact of uncertainty levels on the robust EGP models. The proposed framework offers guidance to investors and fund managers through a pragmatic approach, enabling informed and robust portfolio decisions by considering efficiency, uncertainty, and extended financial factors.

An analytical derivation of properly efficient sets in multi-objective portfolio selection

An analytical derivation of properly efficient sets in multi-objective portfolio selection

A two-stage sustainable uncertain multi-objective portfolio selection and scheduling considering conflicting criteria

This article presents a pioneering approach to project portfolio selection and scheduling, addressing the complexities of contemporary decision-making environments characterized by uncertainty, conflicting criteria, and sustainability imperatives. The proposed framework integrates multiple-attribute and multiple-objective decision-making methods, offering a two-stage solution incorporating fuzzy-robust-stochastic (FRS) optimization techniques. Notably, our work introduces a novel heuristics algorithm designed to optimize conflicting criteria related to sustainability, time-dependency, resources, budget constraints, and human resource capabilities. In the first stage, the framework employs advanced multiple-attribute decision-making methods to comprehensively evaluate project portfolios under the influence of diverse and conflicting criteria. Subsequently, the second stage employs sophisticated multiple-objective decision-making methods to refine the portfolio selection by considering fuzzy, robust, and stochastic optimization elements. The introduced heuristics algorithm plays a pivotal role in enhancing the efficiency and effectiveness of the decision-making process, providing a robust solution to the intricate challenges posed by sustainability concerns, temporal dependencies, resource constraints, budget limitations, and human resource capabilities. The innovation lies in the integration of these disparate elements into a cohesive, two-stage framework, which not only ensures the optimal selection of portfolios but also holistically addresses the intricacies of scheduling. Applying FRS optimization in tandem with the novel heuristics algorithm sets this work apart, offering a versatile and comprehensive solution to decision-makers facing the multifaceted challenges of contemporary project management. Finally, different sensitivity analyses on the proposed model and evaluations of the solution algorithm in various test problems highlight the flexibility of the model against uncertainty and optimality of our solutions to address the given complex criteria. The results showed that more benefits could be obtained by dividing the projects. Despite the increase in total profit, it can increase the risks associated with the completion of the project. In addition, the scheduling of unallocated projects in some periods faces limited resources. On the other hand, sensitivity analysis on Robustness and penalty costs showed that the FRS model could cover the weaknesses of the proposed model in the deterministic model.

Multi-objective portfolio selection considering expected and total utility

To address the challenge of risk minimization associated with investors’ irrational investment decisions in the face of wealth fluctuations, this article integrates prospect theory and disappointment theory into the framework of multi-objective portfolio selection. By concurrently incorporating prospect theory and disappointment theory, this conceptual framework not only considers emotional factors but also offers a comprehensive depiction of individuals’ decision-making processes amidst uncertainty. The proposed portfolio selection model aims to balance return and risk by maximizing both expected and total utility. The effectiveness of the proposed model is validated through comparisons with three other methods.

Solution of Extended Multi-Objective Portfolio Selection Problem in Uncertain Environment Using Weighted Tchebycheff Method

In this paper, a mathematical model for an extended multi-objective portfolio selection (EMOPS) problem is explored with liquidity considered as another objective function besides the risk and return. The model is mathematically formulated in an uncertain environment. The concerned uncertainty is dealt with by employing the fuzzy numbers in the risk matrix and return. While the fuzzy EMOPS model is converted into the corresponding deterministic case based on the α—level sets of the fuzzy numbers, a weighted Tchebycheff method is implemented by defining relative weights and ideal targets. The merit of the suggested method is the applicability in many real-world situations. At the end, some numerical illustration is exhibited for the utility of the suggested EMOPS problem. Finally, it is concluded that the suggested method is simple to learn and to implement in real-life situations for the decision maker.

A novel approach to incorporate investor’s preference in fuzzy multi-objective portfolio selection problem using credibility measure

Investment decision making is usually a multi-objective optimization problem in an uncertain environment. In a real-life scenario, an investor aims to choose a portfolio based on his/her preferences for each objective. Credibility theory has been attributed as one of the most effective ways to model uncertain portfolio attributes. LR fuzzy numbers based credibilistic moments have been used successfully in the recent past to model portfolio selection problems in uncertain environments. Traditionally, the preferences on portfolio attributes are reflected as user defined threshold values. This work proposes a novel way to integrate the investor’s preferences in the portfolio selection model. Investor’s preferences are specified as LR fuzzy numbers corresponding to the portfolio’s expected return and illiquidity distributions. The portfolio models formulated in this study attempt to attain them to the best possible extent. Four new models are presented considering uncertain portfolio attributes, namely, fuzzy return and fuzzy illiquidity. The models are solved using the MIBEX-SM Genetic Algorithm (GA) and ECE methodology. In order to demonstrate the efficient working of the proposed models, practical applications of portfolio selection problem using historical time series data of National Stock Exchange (NSE) is presented. Credibilistic Sharpe Ratio (CSR) has been used to compare the efficiency of models among themselves as well as with the Nifty−50 index.

An integrated generalized TODIM model for portfolio selection based on financial performance of firms

Multi-criteria decision-making (MCDM) models are well-suited for solving portfolio selection problems. Diversified financial indices and complex subjective preferences are important factors affecting investment decisions within the MCDM framework. Therefore, this study adopts a well-known behavioral MCDM model called generalized TODIM (TOmada de Decisão Iterativa Multicritério) for portfolio selection based on the financial performance of firms. First, a multidimensional financial evaluation index system is proposed for financial performance evaluation, which is the most appropriate approach for stock investment within a long-term horizon. Second, features are selected from the financial ratios using affinity propagation clustering (APC). Through the APC algorithm, financial ratios with a strong influence on stock evaluation can be obtained. Third, a generalized TODIM method with entropy weight is used to calculate the dominance relation between stocks and reflect investors’ bounded rational behaviors. Fourth, an extended mean–variance multi-objective portfolio selection model that considers financial and stock market performance is constructed. The compromise solution is used when solving the multi-objective optimization programming. Finally, a case study on medical stock investment in the Chinese stock market is examined to recommend the optimal portfolio allocation for investors. Sensitivity and comparative analyses are performed to demonstrate the robustness, effectiveness, and superiority of the proposed methodology.

A hybrid AHPSort II and multi-objective portfolio selection method to support quality control in the automotive industry

There are several manufacturing errors of different criticality, severity, and occurrence. Correcting all of them is difficult and costly. In this paper, we propose a new hybrid approach to classifying manufacturing errors in an automotive plant and, consequently, to selecting the portfolio of processes that require more attention from the management of the company. Our approach consists of two steps. Firstly, we classify the errors in terms of priority, based on a set of criteria agreed with the management, using the multi-criteria decision-aiding method AHPSort II. The errors belonging to the highest priority class are the most urgent and critical for the company. Secondly, we define a multi-objective portfolio problem, selecting a set of the most critical processes based on the number of errors in each of these processes and on their priority. We adopted an interactive method for finding the most preferred portfolio of processes according to the stakeholder preferences. We applied this approach to a case study of the largest automotive company in Italy, Fiat Chrysler Automobiles, showing how classical quality control tools can benefit from the integration of multi-criteria decision-aiding techniques.

A multi-objective portfolio selection problem with parameters as interval type fuzzy set.

A multi-objective portfolio selection problem with parameters as interval type fuzzy set.

Multi-objective Portfolio Selection Based on Skew-Normal Uncertainty Distribution and Asymmetric Entropy

Seyyed Hamed Abtahi, Gholamhossein Yari, Farhad Hosseinzadeh Lotfi, and Rahman Farnoosh. International Journal of Fuzzy Logic and Intelligent Systems 2021;21:38-48. https://doi.org/10.5391/IJFIS.2021.21.1.38

A cloud theory-based multi-objective portfolio selection model with variable risk appetite

This study proposes a cloud theory-based multi-objective portfolio selection model with variable risk appetite, which incorporates four objectives of mean, variance, skewness, and liquidity constrained by several realistic constraints. Cloud model theory is employed to characterize the return rates and liquidity of assets due to the superiority of simultaneously capturing the ambiguity and randomness of information. The crisp numerical characteristics of the cloud model are defined to obtain the crisp form of the proposed model. To highlight and portray the investors’ risk (averse-neutral-seeking) appetites, the generalized acceptance and rejection functions are modeled by using the extreme values of each objective and introducing a variable risk appetite parameter. Thus the corresponding model is transformed with the objective functions of maximizing acceptance and minimizing rejection, which is solved through the compromise programming approach. The extended model provides investors with an opportunity to adjust risk parameters according to current market status. Moreover, the preference ratio vector is introduced when optimizing, which provides investors with overall control over the preferences regarding all objectives, so that investors can derive optimal portfolios well compatible with their expectations through customized weighting schemes. A real-world empirical application is presented to demonstrate the effectiveness of the proposed model

Pareto efficient buy and hold investment strategies under order book linked constraints

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and “level II order book data”, i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the order book information makes our study much more realistic, since it is more closely related to the real behavior of many financial markets. Besides, ambiguity may be incorporated, which allows us to overcome the model-risk, since a potential discrepancy between the real (and maybe unknown) probabilities and the estimated ones is taken into account. Though the portfolio choice problem is not at all linear, its dual problem becomes a linear goal programming problem, and, consequently, the absence of duality gap allows us to solve the portfolio choice problem in an easy way. Furthermore, the double dual problem is linear too, and its solution also leads to the Pareto-efficient frontier. Lastly, we explore the influence on the Pareto-efficient frontier of the existence of “golden strategies”, i.e., investment strategies whose tail (or downside) risk is strictly lower than their price. Numerical experiments involving all the findings are implemented in a derivative market where both future contracts and call/put options may be traded.

Regret theory-based fuzzy multi-objective portfolio selection model involving DEA cross-efficiency and higher moments

This paper deals with fuzzy portfolio selection problems under the framework of bounded rationality, in which the higher moments and DEA cross-efficiency are taken into consideration. To this end, a regret cross-efficiency (RCE) evaluation model is first proposed to evaluate cross-efficiency scores of all assets by integrating several important financial information: return on equity, earnings per share, current ratio, price/earnings ratio, price/book ratio, and beta value. Then, by incorporating cross-efficiency into the mean–variance–skewness framework, a regret theory-based multi-objective portfolio selection model is developed. The model aims to maximize investor’s perceived utility (composed of utility, regret, and rejoice functions) with respect to the four objectives, namely mean–variance–skewness-efficiency, bounded by several realistic constraints. Additionally, considering the inherent uncertainty in data, the criteria related to RCE evaluation as well as asset returns are characterized as fuzzy variables. The current study not only empowers investors with an overall control over the preferences regarding all portfolio objectives, but also gives investors an opportunity to tweak their intrinsic behavioral tendencies from the perspective of regret aversion and rejoice preference, thus achieving the results that are compatible with the actual preferences of investors. A real-world empirical application is presented to demonstrate the effectiveness of the proposed model.

A minimax regret approach for robust multi-objective portfolio selection problems with ellipsoidal uncertainty sets

Since security return cannot be accurately estimated using past data, in this paper it is assumed to take values in a given ellipsoidal uncertainty set. This paper aims to discuss a robust multi-objective portfolio selection problem based on the minimax regret criterion under an ellipsoidal uncertainty sets, in which the two objective functions are the portfolio return to be maximized and the mean absolute deviation as a risk measure to be minimized. The robust counterpart formulation for the proposed model is firstly presented, then an algorithm based on the relaxation procedure is designed to solve the robust counterpart formulation with second-order cone constraints and infinite constraints. Finally, a practical example based on real market data is presented to illustrate the effectiveness of the proposed model and the algorithm. Compared with the traditional robust portfolio model based on minimax robustness, the robust minimax regret optimal solutions proposed in this paper have better performance on several evaluation criteria.

Parallel Designs for Metaheuristics that Solve Portfolio Selection Problems Using Fuzzy Outranking Relations

In decision-making, the multiobjective portfolio selection problem (MPSP) consists of the selection of alternatives based on preferences of a particular decision-maker (DM). In real-world applications, MPSP has several conflicting criteria that DMs must consider to determine an appropriate solution. So far, only fuzzy outranking relations have been used in a relational system of preferences to guide the search process of genetic algorithms (NOSGAII), and ant colony optimization (NOACO) to approximate the region of interest (RoI) of MPSP involving DM’s preferences. The NOSGAII and NOACO strategies are sequential, and they face a real challenge when solving high-dimensional instances which is a decrement in the computational efficiency due to the increment in the number of objectives. The present research proposes to use parallelism to tackle the efficiency situation in metaheuristics. The study first identifies which approach approximates better the RoI, and then, it analyzes the effect of parallelism in the performance. The results showed that NOACO found more best compromises in almost all the instances than NOSGAII. Hence, it can be concluded that NOACO approximates better the RoI. Also, the results showed a better average speedup with coarse-grained parallelism in NOACO than with data-flow parallelism, suggesting the conclusion that ants independently working are faster than ants working collaboratively. Finally, the main contributions are (1) the analysis of the performance of the two approaches for MPSP, (2) the five parallel designs for NOACO, and (3) the parallel NOACO that speedups up to 2× the sequential version when solving MPSP.

损失厌恶下的多期多目标不确定投资组合模型及算法

损失厌恶下的多期多目标不确定投资组合模型及算法

Robust multi-period and multi-objective portfolio selection

<p style='text-indent:20px;'>In this paper, a multi-period multi-objective portfolio selection problem with uncertainty is studied. Under the assumption that the uncertainty set is ellipsoidal, the robust counterpart of the proposed problem can be transformed into a standard multi-objective optimization problem. A weighted-sum approach is then introduced to obtain Pareto front of the problem. Numerical examples will be presented to illustrate the proposed method and validate the effectiveness and efficiency of the model developed.

DEaf-MOPS/D: An Improved Differential Evolution Algorithm for Solving Complex Multi-objective Portfolio Selection Problems Based on Decomposition

DEaf-MOPS/D: An Improved Differential Evolution Algorithm for Solving Complex Multi-objective Portfolio Selection Problems Based on Decomposition

A Multi-Objective Portfolio Selection Model With Fuzzy Value-at-Risk Ratio

Considering nonstatistical uncertainties and/or insufficient historical data in security return forecasts, fuzzy set theory has been applied in the past decades to build portfolio selection models. Meanwhile, various risk measurements such as variance, entropy, and Value-at-Risk have been proposed in fuzzy environments to evaluate investment risks from different perspectives. Sharpe ratio, also known as the reward-to-variability ratio, which measures the risk premium per unit of the nonsystematic risk (asset deviation), has received great attention in modern portfolio theory. In this study, the Sharpe ratio in fuzzy environments is introduced, whereafter, a fuzzy Value-at-Risk ratio is proposed. Compared with Sharpe ratio, Value-at-Risk ratio is an index with dimensional knowledge that reflects the risk premium per unit of the systematic risk (the greatest loss under a given confidence level). On the basis of the two ratios, a multi-objective model is built to evaluate their joint impact on portfolio selection. Then, the proposed model is solved by a fuzzy simulation based multi-objective particle swarm optimization algorithm, where the global best of each iteration is determined by an improved dominance times based method. Finally, the algorithm superiority is justified via comparing with existing solvers on benchmark problems, and the model effectiveness is exemplified by using three case studies on portfolio selection.

A comprehensive model for fuzzy multi-objective portfolio selection based on DEA cross-efficiency model

In this paper, we discuss the fuzzy portfolio selection problems in multi-objective frameworks. A comprehensive model for multi-objective portfolio selection in fuzzy environment is proposed by incorporating mean-semivariance model and data envelopment analysis cross-efficiency model. In the proposed model, the cross-efficiency model is formulated within the framework of Sharpe ratio; bounds on holdings, and cardinality constraints are also considered. The nonlinear constrained multi-objective portfolio optimization problem cannot be efficiently solved by using traditional approaches. Thus, a multi-objective firefly algorithm is developed to solve the relevant model. Finally, an example verifies the validity of the proposed approaches.