Multi-objective Portfolio Selection Model Research Articles

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 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

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.

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

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.

Fuzzy multi-objective portfolio model based on semi-variance–semi-absolute deviation risk measures

The risk measure plays an important role for portfolio selection problem. The lower partial risk (downside risk) measures have been considered to be more in line with investor’s attitude toward risk. The purpose of this paper is to construct a portfolio selection model in the lower partial risk framework. First, semi-variance and semi-absolute deviation risk measures are used as double-risk measures simultaneously, which can overcome the shortcomings of both semi-variance risk measure and semi-absolute deviation risk measure and can provide additional strengths and flexibility. Second, to address a real portfolio selection problem, by considering the transaction cost and liquidity of portfolio, and regarding the returns of risk assets as LR-type fuzzy variables, we present a fuzzy multi-objective portfolio selection model. Third, in order to limit the proportion of the portfolio invested in assets with common characteristics and to avoid very small holdings, the quantity and class constraints are introduced into the model. Finally, to solve the proposed model efficiently, a new multi-objective evolutionary algorithm is designed. Furthermore, some experiments are conducted by using the data of Shanghai Stock Exchange, and the results indicate the efficiency and effectiveness of the proposed model and algorithm.

Data envelopment analysis based fuzzy multi-objective portfolio selection model involving higher moments

We study the portfolio selection problem from the perspective of incorporating more information about the non-normality of asset returns by considering the mean-variance-skewness-kurtosis framework. Using additional criteria (namely asset turnover, earnings per share, earnings per share growth rate, leverage ratio, price/earnings ratio, and beta (β) value), we employ data envelopment analysis technique to construct a benefit criterion from the efficiency scores of the assets. To incorporate the uncertainty and vagueness of real financial markets, the input data (with respect of all criteria) are assumed as (λ, ρ) interval-valued fuzzy numbers constructed using the historical data. Marginal impacts of the assets on higher moments of the portfolio are used to formulate a fuzzy multi-objective linear programming model. The constraints of the proposed model include the bounds on investment in individual assets, full utilization of the investment capital, and no short selling of assets. The signed distance ranking method is used to obtain a numeric optimization model, which is solved through a weighted max-min approach (in order to incorporate the investor’s preferences regarding investment criteria). A case of real financial market portfolio selection is presented to demonstrate the efficiency of both the proposed model and the solution method.

Multiobjective Efficient Portfolio Selection with Bounded Parameters

In this paper, a multiobjective portfolio selection model is studied, wherein all parameters like return, risk, etc., as well as decision variables are varying in intervals. A methodology is developed using interval analysis to derive an acceptable efficient portfolio. The theoretical developments are justified by assigning the degree of acceptability to every feasible portfolio as well as assigning goals to each objective function. This theoretical development is illustrated in a portfolio selection model with data from Bombay Stock Exchange, India, which justifies that the results obtained by the proposed method are close enough to the existing result.

Fuzzy multi-period portfolio selection model with discounted transaction costs

In this paper, we discuss a multi-period portfolio selection with discounted transaction costs in a fuzzy uncertain investment environment, which has not been given much attention before. We assume that an investor’s motivation is to find the portfolio with maximizing terminal wealth and the cumulative skewness on portfolios, and minimizing the cumulative risk on portfolios. We consider the major criteria including wealth, risk, skewness, transaction costs, proportion entropy, transaction lots, the maximum holding number of assets in the portfolio and budge constraint. We propose a possbilistic mean-semivariance-skewness model with discounted transaction costs for multi-period fuzzy portfolio selection. To solve the multi-objective portfolio selection model, we first introduce a weighted max–min fuzzy goal programming approach to take investor’s different investment preferences into account and transform it into a single-objective programming problem and then design a dynamic differential evolution algorithm for solution. Finally, we provide an empirical study with the sample data from Chinese stock market to analyze the application of the model and the performance of the solution algorithm.

A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios

Abstract Due to the important effect of the higher order moments to portfolio returns, the aim of this paper is to make use of the third and fourth moments for fuzzy multi-objective portfolio selection model. Firstly, in order to overcome the low diversity of the obtained solution set and lead to corner solutions for the conventional higher moment portfolio selection models, a new entropy function based on Minkowski measure is proposed as a new objective function and a novel fuzzy multi-objective weighted possibilistic higher order moment portfolio model is presented. Secondly, to solve the proposed model efficiently, a new multi-objective evolutionary algorithm is designed. Thirdly, several portfolio performance evaluation techniques are used to evaluate the performance of the portfolio models. Finally, some experiments are conducted by using the data of Shanghai Stock Exchange and the results indicate the efficiency and effectiveness of the proposed model and algorithm.

Solving multi-objective portfolio optimization problem using invasive weed optimization

Portfolio optimization is one of the important issues for effective and economic investment. There is plenty of research in the literature addressing this issue. Most of these pieces of research attempt to make the Markowitz’s primary portfolio selection model more realistic or seek to solve the model for obtaining fairly optimum portfolios. In this paper, P/E criterion and Experts’ Recommendations on Market Sectors have been added to the primary Markowitz mean-variance model as two objectives. The P/E ratio is one of the important criteria for investment in the stock market, which captures the current expectations of the market activists about different companies. Experts’ Recommendations for different Market Sectors, on the other hand, captures the experts’ predictions about the future of the stock market. There are many solving methods for the portfolio optimization problem, but almost none of them investigates Invasive Weed Optimization algorithm (IWO). In this research, the proposed multi-objective portfolio selection model has been transformed into a single-objective programming model using fuzzy normalization and uniform design method. Some guidelines are given for parameter setting in the proposed IWO algorithm. The model is then applied to monthly data of top 50 companies of Tehran Stock Exchange Market in 2013. The proposed model is then solved by three methods: (1) the proposed IWO algorithm, (2) the Particle Swarm Optimization algorithm (PSO), and (3) the Reduced Gradient Method (RGM). The non-dominated solutions of these algorithms are compared with each other using Data Envelopment Analysis (DEA). According to the comparisons, it can be concluded that IWO and PSO algorithms have the same performance in most important criteria, but IWO algorithm has better solving time than PSO algorithm and better performance in dominating inefficient solutions, and PSO algorithm has better results in total violation of constraints.

A Fuzzy Multi-Objective Portfolio Selection Model with Piecewise Linear Transaction Costs

A Fuzzy Multi-Objective Portfolio Selection Model with Piecewise Linear Transaction Costs

Multi-objective portfolio selection model with fuzzy random returns and a compromise approach-based genetic algorithm

This paper addresses the multi-objective portfolio selection model with fuzzy random returns for investors by studying three criteria: return, risk and liquidity. In addition, securities historical data, experts’ opinions and judgements and investors’ different attitudes are considered in the portfolio selection process, such that the investor’s individual preference is reflected by an optimistic–pessimistic parameter λ. To avoid the difficulty of evaluating a large set of efficient solutions and to ensure the selection of the best solution, a compromise approach-based genetic algorithm has been designed to solve the proposed model. In addition, a numerical example is presented to illustrate the proposed algorithm.

A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment

This paper deals with a class of chance constrained portfolio selection problems in the fuzzy random decision making system. An integrated fuzzy random portfolio selection model with a chance constraint is proposed on the basis of the mean-variance model and the safety-first model. According to different definitions of chance, we consider two types of fuzzy random portfolio selection models: one is for the optimistic investors and the other is for the pessimistic investors. In order to deal with the fuzzy random models, we develop a few theorems on the variances of fuzzy random returns and the equivalent partitions of two types of chance constraints. We then transform the fuzzy random portfolio selection models into their equivalent crisp models. We further employ the e-constraint method to obtain the efficient frontier. Finally, we apply the proposed models and approaches to the Chinese stock market as an illustration.