A Hybrid Grey based Two Steps Clustering and Firefly Algorithm for Portfolio Selection

Considering the concept of clustering, the main idea of the present study is based on the fact that all stocks for choosing and ranking will not be necessarily in one cluster. Taking the mentioned point into account, this study aims at offering a new methodology for making decisions concerning the formation of a portfolio of stocks in the stock market. To meet this end, Multiple-Criteria Decision-Making, Data Mining, and Multi-objective Optimization were employed. First, candidate stocks were clustered using two-step clustering method. Available stocks in each cluster were independently ranked using grey relational analysis. Firefly algorithm was employed for Pareto analysis of risk and ranking. The results of clustering in the stocks revealed that all candidate stocks were not placed in one cluster. The results of robustness analysis employed in ranking method verified the accuracy of calculations in the grey relational analysis through stock repetition of candidates in each cluster

Markowitz-based cardinality constrained portfolio selection using Asexual Reproduction Optimization (ARO)

The Markowitz-based portfolio selection turns to an NP-hard problem when considering cardinality constraints. In this case, existing exact solutions like quadratic programming may not be efficient to solve the problem. Many researchers, therefore, used heuristic and metaheuristic approaches in order to deal with the problem. This work presents Asexual Reproduction Optimization (ARO), a model free metaheuristic algorithm inspired by the asexual reproduction, in order to solve the portfolio optimization problem including cardinality constraint to ensure the investment in a given number of different assets and bounding constraint to limit the proportions of fund invested in each asset. This is the first time that this relatively new metaheuristic is in the field of portfolio optimization, and we show that ARO results in better quality solutions in comparison with some of the well-known metaheuristics stated in the literature. To validate our proposed algorithm, we measured the deviation of obtained results from the standard efficient frontier. We report our computational results on a set of publicly available benchmark test problems relating to five main market indices containing 31, 85, 89, 98, and 225 assets. These results are used in order to test the efficiency of our proposed method in comparison to other existing metaheuristic solutions. The experimental results indicate that ARO outperforms Genetic Algorithm(GA), Tabu Search (TS), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) in most of test problems. In terms of the obtained error, by using ARO, the average error of the aforementioned test problems is reduced by approximately 20 percent of the minimum average error calculated for the above-mentioned algorithms

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. (C) 2015 Elsevier Ltd. All rights reserved