Multi-objective Portfolio Selection Problem 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.

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.

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.

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.

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.

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.

A Fuzzy Goal Programming Model for Efficient Portfolio Selection.

This paper considers a multi-objective portfolio selection problem imposed by gaining of portfolio, divided yield and risk control in an ambiguous investment environment, in which the return and risk are characterized by probabilistic numbers. Based on the theory of possibility, a new multi-objective portfolio optimization model with gaining of portfolio, divided yield and risk control is proposed and then the proposed model is solved as a fuzzy goal programming model to fulfill aspiration level of each objective. Furthermore, numerical example of efficient portfolio selection is provided to illustrate that proposed model is versatile enough to be applicable to various unexpected conditions. This paper considers a multi-objective portfolio selection problem imposed by gaining of portfolio, divided yield and risk control in an ambiguous investment environment, in which the return and risk are characterized by probabilistic numbers. Based on the theory of possibility, a new multi-objective portfolio optimization model with gaining of portfolio, divided yield and risk control is proposed and then the proposed model is solved as a fuzzy goal programming model to fulfill aspiration level of each objective. Furthermore, numerical example of efficient portfolio selection is provided to illustrate that proposed model is versatile enough to be applicable to various unexpected conditions.

Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework

In this paper we attempt to automate the process of fitting the uncertain parameters of a multi-objective portfolio selection problem by generating L-R fuzzy numbers that belong to power reference function family. Such an approach is advantageous when the fuzzy parameters of the portfolio are best represented as general functional forms. We also propose four new portfolio selection models in a multi-criteria credibilistic framework. The key financial criteria considered are return, illiquidity (antagonistic to liquidity) and risk. In the absence of joint possibility distribution of these parameters, the return and illiquidity of the entire portfolio are considered as historical data set instead of return and illiquidity of the individual assets. In the process of fitting the most appropriate L-R fuzzy number, the vagueness within the information and deviation of the L-R fuzzy number from historical data is measured using entropy and cross-entropy respectively. These principles are embedded into the modelling process of proposed portfolio selection problems. One of the key contribution of this study is that we propose and design a sub-algorithm namely “Entropy-Cross Entropy (ECE) Algorithm” that is appended within an “MIBEX-SM” genetic algorithm and is used to solve the proposed portfolio optimization problems. This proposed solution methodology results in an automated system that is intelligent enough to extract information required for fitting of L-R fuzzy number from the historical data and does not need any human intervention in terms of stating the parameters of the problem. We also conduct an empirical study to demonstrate the impact of the solution approach and applicability of the proposed models in practical applications of portfolio selection. For this purpose we collected historical data from National Stock Exchange (NSE), Mumbai, India. The data for a period of 2008–2013 is first used to train the models. Then the data sets of one-year period of 2013−2014 and two-year period of 2013−2015 are used to test the performance of the models. We introduce a decision support system strategy of comparing the performance of models by proposing a modified version of Sharpe ratio in fuzzy context, named as “Credibilistic Sharpe Ratio (CrSR)”.

Risk-Controlled Multiobjective Portfolio Selection Problem Using a Principle of Compromise

This paper proposes a multiobjective portfolio selection problem with most probable random distribution derived from current market data and other random distributions of boom and recession under the risk-controlled parameters determined by an investor. The current market data and information include not only historical data but also interpretations of economists’ oral and linguistic information, and hence, the boom and recession are often caused by these nonnumeric data. Therefore, investors need to consider several situations from most probable condition to boom and recession and to avoid the risk less than the target return in each situation. Furthermore, it is generally difficult to set random distributions of these cases exactly. Therefore, a robust-based approach for portfolio selection problems using the only mean values and variances of securities is proposed as a multiobjective programming problem. In addition, an exact algorithm is developed to obtain an explicit optimal portfolio using a principle of compromise.

A fuzzy goal programming approach for solving stochastic portfolio selection problem in a group decision-making context

Earlier works on goal programming models for portfolio selection problem under uncertainty did not utilise the mixture of the different types of uncertainty for a given problem and they only assumed the existence of stochastic or fuzzy uncertainty. These models may be too restrictive in modelling of real life decision making problems where randomness and fuzziness are often mixed up together. In this paper, we develop a novel fuzzy goal programming model for solving a stochastic multi-objective portfolio selection problem by considering multiple future market scenarios. Most important decisions in stock market are made by groups of managers or experts whose preferences are often vague and cannot be estimated in exact numerical values. This paper proposes a new method which allocates different weights for decision maker group members to use linguistic terms in order to express their fuzzy preferences for individual judgments.

Robust goal programming for multi-objective portfolio selection problem

This paper proposes a robust optimization model for the portfolio selection problem that uses a goal programming (GP) approach. In GP, decision makers can achieve more than one objective function. Some uncertain coefficients exist in both single and multi-objective models of the portfolio selection problem, which affects the feasibility and optimality of solutions. Robust optimization is an approach that deals with the uncertainty parameters in mathematical models, and guarantees the feasibility of the solutions. This paper tries to address the uncertainty parameters with robust optimization approach. This paper presents GP for the portfolio selection problem and addresses the uncertainty of the parameters by use of robust optimization approach. The approach is illustrated by a numerical example.

Multiobjective particle swarm optimization for a novel fuzzy portfolio selection problem

AbstractOn the basis of the portfolio selection theory, this paper proposes a novel fuzzy multiobjective model that can evaluate investment risk properly and increase the probability of obtaining an expected return. In building this model, fuzzy value‐at‐risk (VaR) is used to evaluate the exact future risk in terms of loss. The VaR can directly reflect the greatest loss of a selection case under a given confidence level. Conversely, variance, the measure of the spread of a distribution around its expected value, is utilized to make the selection more stable. This model can provide investors with more significant information for decision making. To solve this model, an improved Pareto‐optimal‐set‐based multiobjective particle swarm optimization (IMOPSO) algorithm is designed to obtain better solutions in the Pareto front. The proposed model and algorithm are exemplified by specific numerical examples. Furthermore, comparisons are made between IMOPSO and other existing approaches. Experiments show that the model and algorithm are effective in solving the multiobjective portfolio selection problem. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints

In this paper, we propose a multiobjective credibilistic model with fuzzy chance constraints of the portfolio selection problem. The key financial criteria used are short-term return, long-term return, risk and liquidity. The model generates portfolios which are optimal to the extent of achieving the highest credibility values for the objective functions. The problem is solved using a hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm. The approach adopted here has advantage of handling the multiobjective portfolio selection problem where fuzzy parameters are characterized by general functional forms. Numerical examples are provided to demonstrate effectiveness of the solution approach and efficiency of the model.

On the optimality of hedge fund investment strategies: A Bayesian skew t distribution model

This paper presents a forward looking model for selection of hedge fund investment strategies. Given excess skewness observed in hedge funds’ return distributions, we assume that the historical returns have a skew student t distribution. We implement a Bayesian framework to derive the parameters of the posterior return distribution. The predictive return distribution is easily obtained once the posterior parameters are estimated by assuming that the unknown future expected returns are equal to the posterior distribution multiplied by the likelihood of the unknown future expected returns conditional on available posterior parameters. We derive the predictive mean, predictive variance and predictive skewness from the predictive distribution after twenty-one thousand simulations, and solve a multi-objective portfolio selection problem using a data set of monthly returns of investment strategy indices published by the Hedge Fund Research group. Our results show that the methodology presented in this paper provides the highest rate of return (16.79%) with a risk of 2.62% compared to the mean-variance method, which provides 0.8% rate of return with 1.41% risk, respectively. Key words: Predictive distribution, skew t distribution, posterior distribution, prior distribution, MCMC simulations, Gibbs sampler.

CONSTRAINT ROBUST PORTFOLIO SELECTION BY MULTIOBJECTIVE EVOLUTIONARY GENETIC ALGORITHM

The problem of portfolio selection is a very challenging problem in computational finance and has received a lot of attention in last few decades. Selecting an asset and optimal weighting of it from a set of available assets is a critical issue for which the decision maker takes several aspects into consideration. Different constraints like cardinality constraints, minimum buy in thresholds and maximum limit constraint are associated with assets selection. Financial returns associated are often strongly non-Gaussian in character, and exhibit multivariate outliers. Taking these constraints into consideration and with the presence of these outliers we consider a multi-objective problem where the percentage of each available asset is so selected that the total profit of the portfolio is maximized while total risk is minimized. Nondominated Sorting Genetic Algorithm-II is used for solving this multiobjective portfolio selection problem. Performance of the proposed algorithm is carried out by performing different numerical experiments using real-world data.