Evolutionary Algorithms and the Cardinality Constrained Portfolio Optimization Problem

Abstract. In financial engineering the problem of portfolio selection has drawn much attention in the last decades. But still unsolved problems remain, while on the one hand the type of model to use is still debated, even the most common models cannot be solved efficiently, if real world constraints are added. This is not only because the portfolio selection problem is multi-objective, but also because constraints may turn a formerly continuous problem into a discrete one. Therefore, we suggest to use a Multi-Objective Evolutionary Algorithm and compare discrete and continuous representations. To meet constraints we apply a repair mechanism and examine the impact of Lamarckism and the Baldwin Effect on several instances of the portfolio selection problem.

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“…These parameters for the operators were selected to allow a fair comparison. The general parameters were found in preliminary experiments [14].…”

Section: Multi-objective Evolutionary Algorithmmentioning

confidence: 99%

Comparing Discrete and Continuous Genotypes on the Constrained Portfolio Selection Problem

Streichert

Ulmer

Zell

2004

Lecture Notes in Computer Science

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“…Alternatively, some funds may look very attractive once their low risk was taken into account. Streichert et al (2004) investigated the same portfolio optimization problem using evolutionary algorithms by considering the cardinality constrained. Maringer and Kellerer (2003) studied the same optimization of portfolios using a hybrid local search algorithm.…”

Section: Introductionmentioning

confidence: 99%

Asset management using an extended Markowitz theorem

Raei¹,

Karimi²

2014

10.5267/j.msl

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Markowitz theorem is one of the most popular techniques for asset management. The method has been widely used to solve many applications, successfully. In this paper, we present a multi objective Markowitz model to determine asset allocation by considering cardinality constraints. The resulted model is an NP-Hard problem and the proposed study uses two metaheuristics, namely genetic algorithm (GA) and particle swarm optimization (PSO) to find efficient solutions. The proposed study has been applied on some data collected from Tehran Stock Exchange over the period 2009-2011. The study considers four objectives including cash return, 12-month return, 36-month return and Lower Partial Moment (LPM). The results indicate that there was no statistical difference between the implementation of PSO and GA methods.

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“…They also showed the differences arising in the shape of this efficient frontier when such constraints imposed and solved the resulted model using three heuristic algorithms based upon genetic algorithms, tabu search and simulated annealing for locating the cardinality constrained efficient frontier. Streichert et al (2004) also solved the same portfolio optimization problem using evolutionary algorithms by considering the cardinality constrained. Maringer and Kellerer (2003) considered the same optimization of cardinality constrained portfolios with a hybrid local search algorithm.…”

Section: Introductionmentioning

confidence: 99%

An application of Markowitz theorem on Tehran Stock Exchange

Ghodrati¹,

Mohammad²

2014

10.5267/j.msl

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During the past 65 years, there have been tremendous efforts on portfolio selection problem. The standard Markowitz mean-variance model to portfolio selection includes tracing out an efficient frontier, a continuous curve demonstrating the tradeoff between return and risk. This frontier can be often detected via standard quadratic programming, categorized in convex optimization. Traditional Markowitz problem has been recently extended into a new form of mixed integer nonlinear problems by considering various constraints such as cardinality constraints, industry limitation, etc. This paper proposes a mixed integer nonlinear programming to determine optimal asset allocation on Tehran Stock Exchange. The results have indicated that a petrochemical firm named Farabi has gained 44% of the portfolio followed by a drug firm named Kosar Pharmacy gaining 28%. In addition, banking sector was the third winning firm where Eghtesad Novin bank gained nearly 10% of the portfolio. Minerals and mining firms were the next sector in our portfolio where Gol Gohar Iron Ore and Tehran Cement collected 0.73% and 0.57% of the portfolio, respectively. In our survey, auto industry gained only 0.26% of the portfolio, which belonged to Saipa group.

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Evolutionary Algorithms and the Cardinality Constrained Portfolio Optimization Problem

Cited by 76 publications

References 4 publications

Comparing Discrete and Continuous Genotypes on the Constrained Portfolio Selection Problem

Comparing Discrete and Continuous Genotypes on the Constrained Portfolio Selection Problem

Asset management using an extended Markowitz theorem

An application of Markowitz theorem on Tehran Stock Exchange

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