Improved Constrained Portfolio Selection Model using Particle Swarm Optimization

Objective: The main objective of this study is to improve the extended Markowitz mean-variance portfolio selection model by introducing a new constraint known as expert opinion practicable for portfolio selection in real-life situation. Methods: This new extended model consists of four constraints namely: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. The first three constraints have been presented in other researches in literature. The fourth constraint introduced in this study is an essential parameter in making and guiding a realistic portfolio selection. To solve this new extended model an efficient heuristic method of Particle Swarm Optimization (PSO) was engaged with existing benchmark data in the literature. Results: The outcome of the computational results obtained in this study with the new extended Markowitz mean-variance portfolio selection model proposed in this study and solved with PSO showed an improved performance over existing algorithm in particular GA in different instances of the data set used. Conclusion: The study evolves a new extended portfolio selection model and the findings

Particle Swarm Optimization with non-smooth penalty reformulation for a complex portfolio selection problem

In the classical model for portfolio selection the risk is measured by the variance of returns. It is well known that, if returns are not elliptically distributed, this may cause inaccurate investment decisions. To address this issue, several alternative measures of risk have been proposed. In this contribution we focus on a class of measures that uses information contained both in lower and in upper tail of the distribution of the returns. We consider a nonlinear mixed-integer portfolio selection model which takes into account several constraints used in fund management practice. The latter problem is NP-hard in general, and exact algorithms for its minimization, which are both effective and efficient, are still sought at present. Thus, to approximately solve this model we experience the heuristics Particle Swarm Optimization (PSO). Since PSO was originally conceived for unconstrained global optimization problems, we apply it to a novel reformulation of our mixed-integer model, where a standard exact penalty function is introduced.Portfolio selection, coherent risk measure, fund management constraints, NP-hard mathematical programming problem, PSO, exact penalty method, SP100 index's assets.

Portfolio Selection Problem Using Generalized Differential Evolution 3

This Portfolio selection Problem (PSP) remains an intractable research problem in finance and economics and often regarded as NP-hard problem in optimization and computational intelligence. This paper solved the extended Markowitz mean- variance portfolio selection model with an efficient Metaheuristics method of Generalized Differential Evolution 3 (GDE3). The extended Markowitz mean- variance portfolio selection model consists of four constraints: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. There is no research in literature that had ever engaged the set of four constraints with GDE3 to solve PSP. This paper is the first to conduct the study in this direction. The first three sets of constraints have been presented in other researches in literatures. This paper introduced expert opinion constraint to existing portfolio selection models and solved with GDE3. The computational results obtained in this research study show improved performance when compared with other Metaheuristics methods of Genetic algorithm (GA), Simulated Annealing (SA), Tabu Search (TS) and Particle Swarm Optimization (PSO)

A survey on financial applications of metaheuristics

Modern heuristics or metaheuristics are optimization algorithms that have been increasingly used during the last decades to support complex decision-making in a number of fields, such as logistics and transportation, telecommunication networks, bioinformatics, finance, and the like. The continuous increase in computing power, together with advancements in metaheuristics frameworks and parallelization strategies, are empowering these types of algorithms as one of the best alternatives to solve rich and real-life combinatorial optimization problems that arise in a number of financial and banking activities. This article reviews some of the works related to the use of metaheuristics in solving both classical and emergent problems in the finance arena. A non-exhaustive list of examples includes rich portfolio optimization, index tracking, enhanced indexation, credit risk, stock investments, financial project scheduling, option pricing, feature selection, bankruptcy and financial distress prediction, and credit risk assessment. This article also discusses some open opportunities for researchers in the field, and forecast the evolution of metaheuristics to include real-life uncertainty conditions into the optimization problems being considered.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (TRA2013-48180-C3-P, TRA2015-71883-REDT), FEDER, and the Universitat Jaume I mobility program (E-2015-36)

Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective

The problem of portfolio management relates to the selection of optimal stocks, which results in a maximum return to the investor while minimizing the loss. Traditional approaches usually model the portfolio selection as a convex optimization problem and require the calculation of gradient. Note that gradient-based methods can stuck at local optimum for complex problems and the simplification of portfolio optimization to convex, and further solved using gradient-based methods, is at a high cost of solution accuracy. In this paper, we formulate a nonconvex model for the portfolio selection problem, which considers the transaction cost and cardinality constraint, thus better reflecting the decisive factor affecting the selection of portfolio in the real-world. Additionally, constraints are put into the objective function as penalty terms to enforce the restriction. Note that this reformulated problem cannot be readily solved by traditional methods based on gradient search due to its nonconvexity. Then, we apply the Beetle Antennae Search (BAS), a nature-inspired metaheuristic optimization algorithm capable of efficient global optimization, to solve the problem. We used a large real-world dataset containing historical stock prices to demonstrate the efficiency of the proposed algorithm in practical scenarios. Extensive experimental results are presented to further demonstrate the efficacy and scalability of the BAS algorithm. The comparative results are also performed using Particle Swarm Optimizer (PSO), Genetic Algorithm (GA), Pattern Search (PS), and gradient-based fmincon (interior-point search) as benchmarks. The comparison results show that the BAS algorithm is six times faster in the worst case (25 times in the best case) as compared to the rival algorithms while achieving the same level of performance

Initial Solution Heuristic for Portfolio Optimization of Electricity Markets Participation

Meta-heuristic search methods are used to find near optimal global solutions for difficult optimization problems. These meta-heuristic processes usually require some kind of knowledge to overcome the local optimum locations. One way to achieve diversification is to start the search procedure from a solution already obtained through another method. Since this solution is already validated the algorithm will converge easily to a greater global solution. In this work, several well-known meta-heuristics are used to solve the problem of electricity markets participation portfolio optimization. Their search performance is compared to the performance of a proposed hybrid method (ad-hoc heuristic to generate the initial solution, which is combined with the search method). The addressed problem is the portfolio optimization for energy markets participation, where there are different markets where it is possible to negotiate. In this way the result will be the optimal allocation of electricity in the different markets in order to obtain the maximum return quantified through the objective function.This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 641794 (project DREAM-GO) and from FEDER Funds through COMPETE program and from National Funds through FCT under the project UID/EEA/00760/2013.info:eu-repo/semantics/publishedVersio

Differential Evolution and Combinatorial Search for Constrained Index Traking

Index tracking is a valuable low-cost alternative to active portfolio management. The implementation of a quantitative approach, however, is a major challenge from an optimization perspective. The optimal selection of a group of assets that can replicate the index of a much larger portfolio requires both to find the optimal subset of assets and to fine-tune their weights. The former is a combinatorial, the latter a continuous numerical problem. Both problems need to be addressed simultaneously, because whether or not a selection of assets is promising depends on the allocation weights and vice versa. Moreover, the problem is usually of high dimension. Typically, an optimal subset of 30-150 positions out of 100-600 need to be selected and their weights determined. Search heuristics can be a viable and valuable alternative to traditional methods, which often cannot deal with the problem. In this paper, we propose a new optimization method, which is partly based on Differential Evolution (DE) and on combinatorial search. The main advantage of our method is that it can tackle index tracking problem as complex as it is, generating accurate and robust results

A new IPSO-SA approach for cardinality constrained portfolio optimization

The problem of portfolio optimization has always been a key concern for investors. This paper addresses a realistic portfolio optimization problem with floor, ceiling, and cardinality constraints. This problem is a mixed integer quadratic programming where traditional optimization methods fail to find the optimal solution, efficiently. The present paper develops a new hybrid approach based on an improved particle swarm optimization (PSO) and a modified simulated annealing (SA) methods to find the cardinality constrained efficient frontier. The proposed algorithm benefits simple and easy characteristics of PSO with an adaptation of inertia weights and constriction factor. In addition, incorporating an SA procedure into IPSO helps escaping from local optima and improves the precision of convergence. Computational results on benchmark problems with up to 225 assets signify that our proposed algorithm exceeds not only the standard PSO but also the other heuristic algorithms previously presented to solve the cardinality constrained portfolio problem