Fuzzy Portfolio Selection Model Research Articles

Hesitant fuzzy portfolio selection model with score and novel hesitant semi-variance

Because of the effectiveness in describing uncertain information, the hesitant fuzzy set (HFS) has been well applied in decision making and portfolio selection. Although there have been some risk measures based on the HFS, most of them consider all the membership degrees in the calculation. In fact, investors usually think that only the low membership degrees are undesirable, but this fact is ignored by some researchers in the existing hesitant fuzzy portfolio selection models. Therefore, to better capture investors’ risk attitudes, we extend the downside risk from stochastic environment to hesitant fuzzy environment and define a new hesitant semi-variance (HSV). Then, the corresponding theoretical analysis on the novel definitions is given by strictly mathematical deduction. Moreover, two new score-HSV portfolio selection models are proposed, in which the portfolio return is measured by the score, whereas the risk is measured by the HSV instead of deviation. The two new models can avoid neglecting the portfolios with distinctly high membership degrees, which are desirable for investors in practice. Finally, a case study is provided to illustrate the effectiveness of these models. Sensitivity analysis implies that results of the models are consistent with investors’ preferences for assets.

Multiobjective Fuzzy Portfolio Performance Evaluation Using Data Envelopment Analysis Under Credibilistic Framework

In this article, two different multiobjective fuzzy portfolio selection models are presented. The significant criteria considered for portfolio selection are risk (variance or conditional value at risk), return, liquidity, and entropy. Here, the return of the portfolio is considered to be satisfied by a minimum return threshold constraint. Also, to introduce some degree of diversification in the model, a lower and upper bound constraint on investment in an asset is used along with the capital budget and no short selling constraints. Trapezoidal fuzzy returns are considered to incorporate the inherent uncertainty of the stock market, which is handled by using the credibility theory. The weighted sum approach is used to aggregate the objectives and characterize different investor attitudes. Random sample portfolios with progressively increasing sample sizes are generated that obey the constraints of the portfolio models. These random sample portfolios with multiple inputs (risk and entropy) and multiple outputs (return and liquidity) are evaluated in terms of their performance by using data envelopment analysis. Furthermore, a frontier improvement technique existing in the literature is used to rebalance the inefficient random sample portfolios to make them efficient, so that an investor may have more avenues to select efficient portfolios. A detailed numerical illustration with a simulation study using different sample sizes is presented to substantiate the proposed study.

A novel probabilistic hesitant fuzzy portfolio selection model with value-at-risk and safety level of score

Purpose This paper aims to propose two portfolio selection models with hesitant value-at-risk (HVaR) – HVaR fuzzy portfolio selection model (HVaR-FPSM) and HVaR-score fuzzy portfolio selection model (HVaR-S-FPSM) – to help investors solve the problem that how bad a portfolio can be under probabilistic hesitant fuzzy environment. Design/methodology/approach It is strictly proved that the higher the probability threshold, the higher the HVaR in HVaR-S-FPSM. Numerical examples and a case study are used to illustrate the steps of building the proposed models and the importance of the HVaR and score constraint. In case study, the authors conduct a sensitivity analysis and compare the proposed models with decision-making models and hesitant fuzzy portfolio models. Findings The score constraint can make sure that the portfolio selected is profitable, but will not cause the HVaR to decrease dramatically. The investment proportions of stocks are mainly affected by their HVaRs, which is consistent with the fact that the stock having good performance is usually desirable in portfolio selection. The HVaR-S-FPSM can find portfolios with higher HVaR than each single stock and has little sacrifice of extreme returns. Originality/value This paper fulfills a need to construct portfolio selection models with HVaR under probabilistic hesitant fuzzy environment. As a downside risk, the HVaR is more consistent with investors’ intuitions about risks. Moreover, the score constraint makes sure that undesirable portfolios will not be selected.

Fuzzy multi-period portfolio selection model with time-varying loss aversion

This paper deals with multi-period portfolio selection problem in a fuzzy environment, in which the effects of investors’ time-varying asymmetric attitudes to losses and gains on portfolio selection are taken into consideration. In the paper, a definition of time-varying loss aversion is presented to describe the aforementioned time-varying asymmetric attitudes to losses and gains. A fuzzy multi-period portfolio selection model based on this new definition of time-varying loss aversion is formulated. Then, an improved co-evolutionary particle swarm optimization (ICPSO) algorithm is designed to solve the proposed model. The comparison analysis between the proposed model and the fixed-parameter loss aversion model is provided to demonstrate the fact that the proposed model can significantly affect the performance of portfolio selection. Finally, a numerical example is given to illustrate the application of the proposed model and the efficiency of the designed algorithm.

Multi-parameter Portfolio Selection Model with Some Novel Score-Deviation Under Dual Hesitant Fuzzy Environment

In risk investment, investors have to rely on uncertain information when it is difficult to obtain enough precise data. Dual hesitant fuzzy set (DHFS) is more applicable to deal with uncertain information because it involves membership degrees and non-membership degrees, which can validly describe positive and negative information, respectively. Although there has been research on decision-making based on the DHFS, the focus still remains on ranking the alternatives and choosing the best one, which cannot help investors to find the optimal portfolios. Therefore, to solve this problem, we mainly propose two novel portfolio selection models based on the DHFS in this paper. Firstly, we propose a Max-score dual hesitant fuzzy portfolio selection model with information preference (Model 3) for investors focusing on returns regardless of risks. Secondly, to consider the risks of portfolios, we improve Model 3 and develop a score-deviation dual hesitant fuzzy portfolio selection model with information preference and risk appetite (Model 5). Finally, a case study is conducted to highlight the effectiveness of the proposed models. A detailed sensitivity analysis and an efficient frontier analysis show that Model 5 can validly capture investors’ information preferences and risk appetites. Furthermore, compared with the hesitant fuzzy portfolio model, Model 5 can offer more options to the investors with different information preferences.

A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns

This paper proposes a data envelopment analysis (DEA)-based portfolio efficiency evaluation approach integrated with a rebalancing method to help investors acquire efficient portfolios. Two fuzzy portfolio selection models with value at risk (VaR) and conditional value at risk (CVaR) as objectives are proposed under the credibilistic framework. The models are constrained by realistic constraints of short selling/no short selling, capital budget, bounds on investment in an asset, and minimum return desired by the investor. These models are used to compute the benchmark portfolios, which constitute the portfolio efficient frontier. Furthermore, random sample portfolios are generated individually for each model in compliance with their constraints. These random sample portfolios are evaluated in terms of their relative efficiency with risk (VaR or CVaR) as an input and return as an output using DEA. Bearing in mind the volatile nature of the investment market, negative returns are also considered for portfolio efficiency evaluation using the range directional model. Moreover, an efficiency frontier improvement algorithm is used to rebalance the inefficient random portfolios to make them efficient. The proposed approach provides an alternative to the investors to acquire benchmark portfolios using the traditional portfolio selection models. A detailed numerical illustration and an out of sample analysis with the Nifty 50 index from the National Stock Exchange, India, are presented to substantiate the proposed approach.

Fuzzy hidden Markov-switching portfolio selection with capital gain tax

A fuzzy portfolio selection model is considered with a view to incorporating ambiguity about model and data structure. The model features the uncertainty about the exit time of each risky asset within a pre-specified investment horizon and also the presence of transaction costs. However, departing from the traditional paradigm where the transaction costs are often assumed to be unrelated to holding periods, we introduce the capital gain tax of which the realized tax rate is decreasing with respect to the holding periods with a view to encouraging the long-term investment. Meanwhile, the regime switching property of the market state is introduced to fuzzy portfolio selection, where fuzzy random variables are employed to model uncertain returns of risky assets in a Markov-regime switching market. An adjusted L−R fuzzy number is introduced and some of its mathematical properties are studied. In addition, a bi-objective mean-variance model is formulated, and a time varying numerical integral-based particle swarm optimization algorithm (TVNIPSO) is designed to obtain the efficient frontier of the portfolio in the sense of Pareto dominance. Finally, some numerical experiments are provided to validate the effectiveness of the model and the TVNIPSO.

A polynomial goal programming approach for intuitionistic fuzzy portfolio optimization using entropy and higher moments

Although there are myriad works that deal with fuzzy portfolio optimization, there is a dearth of research that deals with the problem in an intuitionistic fuzzy environment. So, taking the route less travelled, we propose two intuitionistic fuzzy portfolio selection models for optimistic and pessimistic scenarios, respectively. For this purpose, we take into account four objectives, namely return, variance, skewness and entropy, along with some realistic constraints such as a cardinality constraint, a contingent constraint, and complete capital utilization. Also, short selling is prohibited. Another popular constraint, the “floor and ceiling” constraint, is presented and employed in the form of a flexible constraint by considering the confidence interval in the model. The membership and non-membership of the objectives are modelled using the extreme values of the four objectives. The proposed approach provides avenues for the inclusion and minimization of the hesitation degree into the decision making, thereby, resulting in a significantly better portfolio. The proposed model enables the decision makers to obtain a variety of results through the use of several schemes that can be postulated (customized) according to the decision makers’ preferences, and from which, results best suited to their preferences, can be chosen. A numerical illustration with eight different schemes is presented to demonstrate the virtues of the proposed model.

Several Extended Mean-variance Fuzzy Portfolio Selection Models Based on Possibility Theory

Classical Mean-Variance model pioneered by Markowitz 1952 has proposed the model to be one of the most important researches in modern finance. However the classical Markowitz’s Mean-Variance method does not match to represent the practicality of the uncertainties in stock market problem in portfolios. Seven types of extended mean-variance method of portfolio selection model based on the possibilitic return and possibilistic risk is presented in this paper. The returns of assets obey trapezoidal and pentagonal fuzzy numbers. The objective of this paper is to compare the optimal portfolio composition and performance using trapezoidal, pentagonal fuzzy numbers by considering whether the data is assumed normal, using real distribution and follow the trading day situations. A numerical example is presented to illustrate the usability of the model. The result will provide on how the investors could improve on their investment strategy.

Fuzzy Portfolio Optimization for Power Generation Assets

Fuzzy sets theory is proposed as an alternative to the probabilistic approach for assessing portfolios of power plants, in order to capture the complex reality of decision-making processes. This paper presents different fuzzy portfolio selection models, where the rate of returns as well as the investor's aspiration levels of portfolio return and risk are regarded as fuzzy variables. Furthermore, portfolio risk is defined as a downside risk, which is why a semi-mean-absolute deviation portfolio selection model is introduced. Finally, as an illustration, the models presented are applied to a selection of power generation mixes. The efficient portfolio results show that the fuzzy portfolio selection models with different definitions of membership functions as well as the semi-mean-absolute deviation model perform better than the standard mean-variance approach. Moreover, introducing membership functions for the description of investors' aspiration levels for the expected return and risk shows how the knowledge of experts, and investors' subjective opinions, can be better integrated in the decision-making process than with probabilistic approaches.

Fuzzy Portfolio Optimization of Power Generation Assets

Fuzzy theory is proposed as an alternative to the probabilistic approach for assessing portfolios of power plants, in order to capture the complex reality of decision-making processes. This paper presents different fuzzy portfolio selection models, where the rate of returns as well as the investor’s aspiration levels of portfolio return and risk are regarded as fuzzy variables. Furthermore, portfolio risk is defined as a downside risk, which is why a semi-mean-absolute deviation portfolio selection model is introduced. Finally, as an illustration, the models presented are applied to a selection of power generation mixes. The efficient portfolio results show that the fuzzy portfolio selection models with different definitions of membership functions as well as the semi-mean-absolute deviation model perform better than the standard mean-variance approach. Moreover, introducing membership functions for the description of investors’ aspiration levels for the expected return and risk shows how the knowledge of experts, and investors’ subjective opinions, can be better integrated in the decision-making process than with probabilistic approaches.

Algorithm research based on multi period fuzzy portfolio optimization model

Because the investment market in real life is complex and mobile, there are many other factors to consider when meeting the risk and income equilibrium, such as transaction cost, diversification degree and so on. To simulate the real transactions in financial market, multiple decision criteria in portfolio selection should be considered to provide investors with additional choices. This paper discusses a multi-objective portfolio optimization problem for practical portfolio selection in fuzzy environment, in which the return rates and the turnover rates are characterized by fuzzy variables. Under the premise of meeting the two wishes level of investors’ maximum and minimum risk, we assume that the rate of return is a fuzzy variable, and get the corresponding fuzzy portfolio optimization model. What’s more, we apply a particle swarm optimization algorithm to solve the proposed multi-period fuzzy portfolio selection models. To reflect investor’s aspiration levels for the two objectives, a fuzzy decision technique is employed to transform the proposed model into a single objective mixed-integer nonlinear programming problem. Finally, a numerical example is given to illustrate the application of our models. Comparative results show that the designed algorithm is effective for solving the proposed models.

A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms

In this paper, a new bi-objective fuzzy portfolio selection model is proposed, for which Sharp ratio (SR) and Value at Risk ratio (VR) of a portfolio are chosen as objectives. SR is an important nonsystematic risk measurement that examines the investment risk by aspiring the diversification of the capital allocation. On the other hand, VR measures the systematic risk, which reduces the largest loss of an investment at a given confidence level. The proposed fuzzy portfolio model assumes both SR and VR as maximization objectives for which the associated fuzzy parameters are considered as triangular fuzzy numbers. The proposed model is solved using multi-objective genetic algorithms, namely multi-objective cellular genetic algorithm (MOCell), archive-based hybrid scatter search (AbYSS), and nondominated sorting genetic algorithm II (NSGA-II). We have used a data set from the Shenzhen Stock Exchange to illustrate the performance of the proposed model and algorithms. Finally, a comparative study in terms of five standard performance metrics is presented, among the MOCell, AbYSS, and NSGA-II algorithms that are mentioned extensively in various research articles to exhibit the best suitable algorithm.

Fuzzy portfolio selection model with real features and different decision behaviors

In the ever changing financial markets, investor’s decision behaviors may change from time to time. In this paper, we consider the effect of investor’s different decision behaviors on portfolio selection in fuzzy environment. We present a possibilistic mean-semivariance model for fuzzy portfolio selection by considering some real investment features including proportional transaction cost, fixed transaction cost, cardinality constraint, investment threshold constraints, decision dependency constraints and minimum transaction lots. To describe investor’s different decision behaviors, we characterize the return rates on securities by LR fuzzy numbers with different shape parameters in the left- and right-hand reference functions. Then, we design a novel hybrid differential evolution algorithm to solve the proposed model. Finally, we provide a numerical example to illustrate the application of our model and the effectiveness of the designed algorithm.

Investor-friendly and robust portfolio selection model integrating forecasts for financial tendency and risk-averse

This paper proposes an investor-friendly random fuzzy portfolio selection model considering both robustness and adjustment of future asset returns derived from investor’s forecasts for financial tendency using a fuzzy inference method. It is important to predict the price or the return of each asset appropriately considering current market trends in portfolio optimization. In this paper, a standard multi-factor model, namely Arbitrage Pricing Theory (APT), is introduced as an asset pricing model. In addition, in order to extend standard APT by integrating important rules of current markets trends derived from technical analysis and fundamental analysis, each factor of APT is assumed to be a random fuzzy variable whose mean is adjusted by the fuzzy reasoning method, particularly product–sum-gravity method. Furthermore, it is also important for the investor to reduce the worst case of the total loss in terms of risk-averse. Therefore, worst-case conditional Value-at-Risk, which is a robust programming approach without assuming some specific random distribution, is considered. Since the proposed model is formulated as a biobjective programming problem both minimizing the value of worst-case conditional Value-at-Risk and maximizing the total expected return, it is equivalently transformed into the deterministic nonlinear programming problem using the satisficing trade-off method, and the efficient algorithm to obtain the optimal portfolio is developed. By solving our proposed model, the investor can obtain the risk-averse optimal portfolio with the large total return complying with current market trends.

Multi-Period Mean-Absolute Deviation Fuzzy Portfolio Selection Model with Entropy Constraints

AbstractThis paper considers a multi-period fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control, in which the returns of assets are characterized by fuzzy numbers. A fuzzy absolute deviation is originally defined as the risk control of portfolio. Entropy constraints and borrowing constraints are added in the portfolio selection model. Based on the theories of possibility measures, a new multi-period portfolio optimization model with transaction costs is proposed. And then, the proposed model is transformed into a crisp nonlinear programming problem by using fuzzy programming approach. Because of the transaction costs, the multi-period portfolio selection is the dynamic optimization problem with path dependence. Through changing the cost function into a variable, the multi-period portfolio selection is approximately turned into the dynamic programming. Furthermore, the discrete approximate iteration method is designed to obtain the optimal portfolio strategy. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

Forecasting portfolio returns using weighted fuzzy time series methods

We propose using weighted fuzzy time series (FTS) methods to forecast the future performance of returns on portfolios. We model the uncertain parameters of the fuzzy portfolio selection models using a possibilistic interval-valued mean approach, and approximate the uncertain future return on a given portfolio by means of a trapezoidal fuzzy number. Introducing some modifications into the classical models of fuzzy time series, based on weighted operators, enables us to generate trapezoidal numbers as forecasts of the future performance of the portfolio returns. This fuzzy forecast makes it possible to approximate both the expected return and the risk of the investment through the value and ambiguity of a fuzzy number.We incorporate our proposals into classical fuzzy time series methods and analyze their effectiveness compared with classical weighted fuzzy time series models, using historical returns on assets from the Spanish stock market. When our weighted FTS proposals are used to point-wise forecast portfolio returns the one-step ahead accuracy is improved, also with respect to non-fuzzy forecasting methods.

Fuzzy Portfolio Selection Including Cardinality Constraints and Integer Conditions

This paper is concerned with a fuzzy version of the portfolio selection problem, which includes diversification conditions and incorporates investor's subjective preferences. The inclusion of diversification conditions leads to mixed-integer models, which are computationally demanding. On the other hand, the consideration of integer conditions makes the solution very sensitive to investor's subjective preferences with regard to the trade-off between risk and expected return. These preferences are imprecise by their very nature. In this paper, we overcome these issues by proposing a solution method for a fuzzy quadratic portfolio selection model with integer conditions. The suitability of the proposed method is illustrated by means of two numerical examples.

A novel portfolio selection model based on fuzzy goal programming with different importance and priorities

Despite the risk–return tradeoff is main concern of financial theory; the rational investment decisions requires considering many criteria simultaneously. In addition to determining a certain importance and priority among these criteria, modeling the investor behaviors in accordance with market trends provides much more realistic approach. However, the researchers mostly overlook to evaluate these concepts simultaneously. This article introduces a novel fuzzy portfolio selection model that takes into accounts the risk preferences in accordance with the market moving trends as well as the risk–return tradeoff, and allows the decision makers to define a certain importance and priority among their objectives. To construct this model, firstly the portfolio return, risk and beta coefficient are assumed as main objectives including the possibilistic uncertainties. To define possibilistic uncertainty, the specific fuzzy membership functions are constituted for these objectives with respect to the risk preferences of investors and market moving trends. By means of the fuzzy goal programming techniques, a novel portfolio selection model is developed using these specific fuzzy membership functions. In the application section, three investment terms are examined in the Istanbul Stock Exchange National 30 Index. While ISE30 index has the upward (bullish) and the downward (bearish) moving trends in the first two implementations, the third implementation includes a scenario in which the investors desire to chase the ISE30 index. In the analyses, the proposed model is compared with the classical Mean–Variance, Mean-Absolute-Deviation and Maxmin models in terms of their portfolio returns based on the selling prices in the test periods. As a result, the proposed model gives superior performance than the classical models because it takes into account the investor preferences in accordance with market moving trend.

A fuzzy portfolio selection model with background risk

In financial markets, the presence of background risk may affect investors’ investments. This article develops a fuzzy portfolio selection model with background risk, based on the definitions of the possibilistic return and possibilistic risk. For the returns of assets obey LR-type possibility distribution, we propose a specific portfolio selection model with background risk. Then, a numerical study is carried out by using the data concerning some stocks. Based on the data, we obtain the efficient frontier of the possibilistic portfolio with background risk, and compare it with the efficient frontier of the portfolio without background risk. Finally, we conclude that the background risk can better reflect the investment risk of the real economy environment which make the investors choose a more suitable portfolio to them.