Constrained Portfolio Optimization Problem Research Articles

Prospect theory-based formulation of chance constrained portfolio optimization problem using loan

Prospect theory-based formulation of chance constrained portfolio optimization problem using loan

Quantum-inspired meta-heuristic approaches for a constrained portfolio optimization problem

Quantum-inspired meta-heuristic approaches for a constrained portfolio optimization problem

A multi-population evolutionary algorithm for multi-objective constrained portfolio optimization problem

A multi-population evolutionary algorithm for multi-objective constrained portfolio optimization problem

Utilizing dependence among variables in evolutionary algorithms for mixed-integer programming: A case study on multi-objective constrained portfolio optimization

Mixed-Integer Non-Linear Programming (MINLP) is not rare in real-world applications such as portfolio investment. It has brought great challenges to optimization methods due to the complicated search space that has both continuous and discrete variables. This paper considers the multi-objective constrained portfolio optimization problems that can be formulated as MINLP problems. Since each continuous variable is dependent to a discrete variable, we propose a Compressed Coding Scheme (CCS), which encodes the dependent variables into a continuous one. In this manner, we can reuse some existing search operators and the dependence among variables will be utilized while the algorithm is optimizing the compressed variables. CCS actually bridges the gap between the portfolio optimization problems and the existing optimizers, such as Multi-Objective Evolutionary Algorithms (MOEAs). The new approach is applied to two benchmark suites, involving the number of assets from 31 to 2235. The experimental results indicate that CCS is not only efficient but also robust for dealing with the multi-objective constrained portfolio optimization problems.

Quantum beetle antennae search: a novel technique for the constrained portfolio optimization problem

Quantum beetle antennae search: a novel technique for the constrained portfolio optimization problem

A multiobjective credibilistic portfolio selection model. Empirical study in the Latin American integrated market

This paper extends the stochastic mean-semivariance model to a fuzzy multiobjective model, where apart from return and risk, also liquidity is considered to measure the performance of a portfolio. Uncertainty of future return and liquidity of each asset are modeled using L-R type fuzzy numbers that belong to the power reference function family. The decision process of this novel approach takes into account not only the multidimensional nature of the portfolio selection problem but also realistic constraints by investors. Particularly, it optimizes the expected return, the semivariance and the expected liquidity of a given portfolio, considering cardinality constraint and upper and lower bound constraints. The constrained portfolio optimization problem resulting is solved using the algorithm NSGA-II. As a novelty, in order to select the optimal portfolio, this study defines the credibilistic Sortino ratio as the ratio between the credibilistic risk premium and the credibilistic semivariance. An empirical study is included to show the effectiveness and efficiency of the model in practical applications using a data set of assets from the Latin American Integrated Market.

Cardinality constrained portfolio optimization with a hybrid scheme combining a Genetic Algorithm and Sonar Inspired Optimization

The constraints and the vast solution space of operational research optimization problems make them hard to cope with. However, Computational Intelligence, and especially Nature-Inspired Algorithms, has been a useful tool to tackle hard and large space optimization problems. In this paper, a very consistent and effective hybrid optimization scheme to tackle cardinality constrained portfolio optimization problems is presented. This scheme consists of two nature-inspired algorithms, i.e. Sonar Inspired Optimization algorithm and Genetic Algorithm. Also, the incorporation of heuristic information, i.e. an expert’s knowledge, etc., to the overall performance of the hybrid scheme is tested and compared to previous studies. More specifically, under the framework of a financial portfolio optimization problem, the heuristic information-enhanced hybrid scheme manages to reach a new optimal solution. Additionally, a comparison of the proposed hybrid scheme with other hybrid schemes applied to the same problem with the same data is performed.

Explicit Solution for Constrained Scalar-State Stochastic Linear-Quadratic Control With Multiplicative Noise

We study in this paper, a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems.

A CREDIBILISTIC MEAN-SEMIVARIANCE-PER PORTFOLIO SELECTION MODEL FOR LATIN AMERICA

Many real-world problems in the financial sector have to consider different objectives which are conflicting, for example portfolio selection. Markowitz proposed an approach to determine the optimal composition of a portfolio analysing the trade-off between return and risk. Nevertheless, this approach has been criticized for unrealistic assumptions and several changes have been proposed to incorporate investors’ constraints and more realistic risk measures. In this line of research, our proposal extends the mean-semivariance portfolio selection model to a multiobjective credibilistic model that besides risk and return, also considers the price-to-earnings ratio to measure portfolio performance. Uncertain future returns and PER ratio of each asset are approximated using L-R power fuzzy numbers. Furthermore, we consider budget, bound and cardinality constraints. To solve the constrained portfolio optimization problem, we use the algorithm NSGA-II. We assess the proposed approach generating a portfolio with shares included in the Latin American Integrated Market. Results show that this new approach is a good alternative to solve the portfolio selection problem when multiple objectives are considered.

An iterative method for solving a bi-objective constrained portfolio optimization problem

In this work, we consider the problem of portfolio optimization under cardinality and quantity constraints. We use the standard model of mean-variance in its bi-objective form which is presented here as a bi-objective quadratic programming problem under cardinality and quantity constraints. This problem is NP-hard, which is why the majority of methods proposed in the literature use metaheuristics for its resolution. In this paper, we propose an iterative method for solving constrained portfolio optimization problems. Experiments are performed with major market indices, such as the Hang Seng, DAX, FTSE, S&P 100, Nikkei, S&P 500 and Nasdaq using real-world datasets involving up to 2196 assets. Comparisons with two exact methods and a metaheuristic are performed. These results show that the new method allows to find efficient portfolio fronts in reasonable time.

Examining the effect of different configuration issues of the multiobjective evolutionary algorithms on the efficient frontier formulation for the constrained portfolio optimization problem

This article examines the effect of different configuration issues of the Multiobjective Evolutionary Algorithms on the efficient frontier formulation for the constrained portfolio optimization problem. We present the most popular techniques for dealing with the complexities of the constrained portfolio optimization problem and experimentally analyse their strengths and weaknesses. In particular, we examine the efficient incorporation of complex real world constraints into the Multiobjective Evolutionary Algorithms and their corresponding effect on the efficient frontier formulation for the portfolio optimization problem. Moreover, we examine various constraint-handling approaches for the constrained portfolio optimization problem such as penalty functions and reparation operators and we draw conclusions about the efficacy of the examined approaches. We also examine the effect on the efficient frontier formulation by the application of different genetic operators and the relevant results are analysed. Finally, we address issues related with the various performance metrics that are applied for the evaluation of the derived solutions.

Robust and Reliable Portfolio Optimization Formulation of a Chance Constrained Problem

Abstract We solve a linear chance constrained portfolio optimization problem using Robust Optimization (RO) method wherein financial script/asset loss return distributions are considered as extreme valued. The objective function is a convex combination of portfolio’s CVaR and expected value of loss return, subject to a set of randomly perturbed chance constraints with specified probability values. The robust deterministic counterpart of the model takes the form of Second Order Cone Programming (SOCP) problem. Results from extensive simulation runs show the efficacy of our proposed models, as it helps the investor to (i) utilize extensive simulation studies to draw insights into the effect of randomness in portfolio decision making process, (ii) incorporate different risk appetite scenarios to find the optimal solutions for the financial portfolio allocation problem and (iii) compare the risk and return profiles of the investments made in both deterministic as well as in uncertain and highly volatile financial markets.

Metaheuristic Optimization of Constrained Large Portfolios using Hybrid Particle Swarm Optimization

Classical Particle Swarm Optimization (PSO) that has been attempted for the solution of complex constrained portfolio optimization problem in finance, despite its noteworthy track record, suffers from the perils of getting trapped in local optima yielding inferior solutions and unrealistic time estimates for diversification even in medium level portfolio sets. In this work the authors present the solution of the problem using a hybrid PSO strategy. The global best particle position arrived at by the hybrid PSO now acts as the initial point to the Sequential Quadratic Programming (SQP) algorithm which efficiently obtains the optimal solution for even large portfolio sets. The experimental results of the hybrid PSO-SQP model have been demonstrated over Bombay Stock Exchange, India (BSE200 index, Period: July 2001-July 2006) and Tokyo Stock Exchange, Japan (Nikkei225 index, Period: March 2002-March 2007) data sets, and compared with those obtained by Evolutionary Strategy, which belongs to a different genre.

Prediction based mean-variance model for constrained portfolio assets selection using multiobjective evolutionary algorithms

Abstract In this paper, a novel prediction based mean-variance (PBMV) model has been proposed, as an alternative to the conventional Markowitz mean-variance model, to solve the constrained portfolio optimization problem. In the Markowitz mean-variance model, the expected future return is taken as the mean of the past returns, which is incorrect. In the proposed model, first the expected future returns are predicted, using a low complexity heuristic functional link artificial neural network (HFLANN) model and the portfolio optimization task is carried out by using multi-objective evolutionary algorithms (MOEAs). In this paper, swarm intelligence based, multiobjective optimization algorithm, namely self-regulating multiobjective particle swarm optimization (SR-MOPSO) has also been proposed and employed efficiently to solve this important problem. The Pareto solutions obtained by applying two other competitive MOEAs and using the proposed PBMV models and Markowitz mean-variance model have been compared, considering six performance metrics and the Pareto fronts. Moreover, in the present study, the nonparametric statistical analysis using the Sign test and Wilcoxon rank test are also carried out, to compare the performance of the algorithms pair wise. It is observed that, the proposed PBMV model based approach provides better Pareto solutions, maintaining adequate diversity, and also quite comparable to the Markowitz model. From the simulation result, it is observed that the self regulating multiobjective particle swarm optimization (SR-MOPSO) algorithm based on PBMV model, provides the best Pareto solutions amongst those offered by other MOEAs.

A GRASP based solution approach to solve cardinality constrained portfolio optimization problems

In the current work, a solution methodology which combines a meta-heuristic algorithm with an exact solution approach is presented to solve cardinality constrained portfolio optimization (CCPO) problem. The proposed method is comprised of two levels, namely, stock selection and proportion determination. In stock selection level, a greedy randomized adaptive search procedure (GRASP) is developed. Once the stocks are selected the problem reduces to a quadratic programming problem. As GRASP ensures cardinality constraints by selecting predetermined number of stocks and quadratic programming model ensures the remaining problem constraints, no further constraint handling procedures are required. On the other hand, as the problem is decomposed into two sub-problems, total computational burden on the algorithm is considerably reduced. Furthermore, the performance of the proposed algorithm is evaluated by using benchmark data sets available in the OR Library. Computational results reveal that the proposed algorithm is competitive with the state of the art algorithms in the related literature.

Efficient Portfolio Construction with the Use of Multiobjective Evolutionary Algorithms: Best Practices and Performance Metrics

This paper provides a systematic study of the technologies and algorithms associated with the implementation of multiobjective evolutionary algorithms (MOEAs) for the solution of the portfolio optimization problem. Based on the examination of the state-of-the art we provide the best practices for dealing with the complexities of the constrained portfolio optimization problem (CPOP). In particular, rigorous algorithmic and technical treatment is provided for the efficient incorporation of a wide range of real-world constraints into the MOEAs. Moreover, we address special configuration issues related to the application of MOEAs for solving the CPOP. Finally, by examining the state-of-the-art we identify the most appropriate performance metrics for the evaluation of the relevant results from the implementation of the MOEAs to the solution of the CPOP.

A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization

Portfolio optimization involves the optimal assignment of limited capital to different available financial assets to achieve a reasonable trade-off between profit and risk objectives. In this paper, we studied the extended Markowitz's mean-variance portfolio optimization model. We considered the cardinality, quantity, pre-assignment and round lot constraints in the extended model. These four real-world constraints limit the number of assets in a portfolio, restrict the minimum and maximum proportions of assets held in the portfolio, require some specific assets to be included in the portfolio and require to invest the assets in units of a certain size respectively. An efficient learning-guided hybrid multi-objective evolutionary algorithm is proposed to solve the constrained portfolio optimization problem in the extended mean-variance framework. A learning-guided solution generation strategy is incorporated into the multi-objective optimization process to promote the efficient convergence by guiding the evolutionary search towards the promising regions of the search space. The proposed algorithm is compared against four existing state-of-the-art multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA-2), Pareto Envelope-based Selection Algorithm (PESA-II) and Pareto Archived Evolution Strategy (PAES). Computational results are reported for publicly available OR-library datasets from seven market indices involving up to 1318 assets. Experimental results on the constrained portfolio optimization problem demonstrate that the proposed algorithm significantly outperforms the four well-known multi-objective evolutionary algorithms with respect to the quality of obtained efficient frontier in the conducted experiments.

Diversified minimum-variance portfolios

We build on a one parameter family of weighting schemes arising from \(L^2\)-constrained portfolio optimization problems. The parameter allows to fine tune the trade-off between the volatility and the diversification of the portfolio. We propose two criteria in order to determine two unique portfolios: the first criterion requires that no weights be negative while the second one imposes a target diversification which is median between full concentration and full diversification. Both portfolios are empirically compared to classical benchmarks. The first one behaves very much like other popular Long-Only weighting schemes while the second displays a more aggressive profile, while generating moderate turnover. We also discuss implementation issues, as well as estimation related problems.

Robustness of optimal portfolios under risk and stochastic dominance constraints

Solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation, estimation and incomplete information. The obtained results, recommendations for the risk and portfolio manager, should be then carefully analyzed. We shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity-based global contamination bounds. Results obtained in our paper [Dupačová, J., & Kopa, M. (2012). Robustness in stochastic programs with risk constraints. Annals of Operations Research, 200, 55–74.] were derived for the risk and second order stochastic dominance constraints under suitable smoothness and/or convexity assumptions that are fulfilled, e.g. for the Markowitz mean–variance model. In this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints. Local bounds for problems of a special structure are obtained. Under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test.

Решение задачи оптимального портфельного инвестирования с ограничением на кардинальность методами эвристического поиска

Решение задачи оптимального портфельного инвестирования с ограничением на кардинальность методами эвристического поиска