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Portfolio selection using neural networks
, 2007
"... In this paper we apply a heuristic method based on artificial neural networks (NN) in order to trace out the efficient frontier associated to the portfolio selection problem.We consider a generalization of the standard Markowitz meanvariance model which includes cardinality and bounding constraints ..."
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In this paper we apply a heuristic method based on artificial neural networks (NN) in order to trace out the efficient frontier associated to the portfolio selection problem.We consider a generalization of the standard Markowitz meanvariance model which includes cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset. We present some experimental results obtained with the NN heuristic and we compare them to those obtained with three previous heuristicmethods.The portfolio selection problem is an instance from the family of quadratic programmingproblems when the standard Markowitz meanvariance model is considered. But if this model is generalized to include cardinality and bounding constraints, then the portfolio selection problem becomes a mixed quadratic and integer programming problem. When considering the latter model, there is not any exact algorithm able to solve the portfolio selection problem in an efficient way. The use of heuristic algorithms in this case is imperative. In the past some heuristic methods based mainly on evolutionary algorithms, tabu search and simulated annealing have been developed. The purpose of this paper is to consider a particular neural network (NN) model, the Hopfield network, which has been used to solve some other optimisation problems and apply it here to the portfolio selection problem, comparing the new results to those obtained with previous heuristic algorithms.
Portfolio Optimization with an Envelopebased Multiobjective Evolutionary Algorithm
"... The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical meanvariance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case o ..."
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The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical meanvariance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case of linear constraints, the problem can be solved efficiently by parametric quadratic programming (i.e., variants of Markowitz ’ critical line algorithm). However, there are many realworld constraints that lead to a nonconvex search space, e.g. cardinality constraints which limit the number of different assets in a portfolio, or minimum buyin thresholds. As a consequence, the efficient approaches for the convex problem can no longer be applied, and new solutions are needed. In this paper, we propose to integrate an active set algorithm optimized for portfolio selection into a multiobjective evolutionary algorithm (MOEA). The idea is to let the MOEA come up with some convex subsets of the set of all feasible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions to form the solution of the original nonconvex problem. We show that the resulting envelopebased MOEA significantly outperforms existing MOEAs. 1 1
Metaheuristics for the portfolio selection problem
, 2008
"... The Portfolio selection problem is a relevant problem arising in finance and economics. Some practical formulations of the problem include various kinds of nonlinear constraints and objectives and can be efficiently solved by approximate algorithms. Among the most effective approximate algorithms, ..."
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The Portfolio selection problem is a relevant problem arising in finance and economics. Some practical formulations of the problem include various kinds of nonlinear constraints and objectives and can be efficiently solved by approximate algorithms. Among the most effective approximate algorithms, are metaheuristic methods that have been proved to be very successful in many applications. This paper presents an overview of the literature on the application of metaheuristics to the portfolio selection problem, trying to provide a general descriptive scheme.
Hybrid local search for constrained financial portfolio selection problems
 Proceedings of the CPAIOR. 2007
, 2007
"... Abstract. Portfolio selection is a relevant problem arising in finance and economics. While its basic formulations can be efficiently solved through linear or quadratic programming, its more practical and realistic variants, which include various kinds of constraints and objectives, have in many cas ..."
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Abstract. Portfolio selection is a relevant problem arising in finance and economics. While its basic formulations can be efficiently solved through linear or quadratic programming, its more practical and realistic variants, which include various kinds of constraints and objectives, have in many cases to be tackled by approximate algorithms. In this work, we present a hybrid technique that combines a local search, as master solver, with a quadratic programming procedure, as slave solver. Experimental results show that the approach is very promising and achieves results comparable with, or superior to, the state of the art solvers. 1
Portfolio Selection: How to Integrate Complex Constraints
 Journal of Financial Planning
, 2005
"... For the standard MeanVariance model for portfolio selection with linear constraints, there are several algorithms that can efficiently compute both a single point on the Pareto front and even the whole front. Unfortunately, commonly used constraints (e.g. cardinality constraints or buyin threshold ..."
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For the standard MeanVariance model for portfolio selection with linear constraints, there are several algorithms that can efficiently compute both a single point on the Pareto front and even the whole front. Unfortunately, commonly used constraints (e.g. cardinality constraints or buyin thresholds) result in the optimization problem to become intractable by standard algorithms. In this paper, two paradigms to deal with this kind of constraint are presented and their advantages and disadvantages are highlighted.
Abstract IMPROVING PORTFOLIO EFFICIENCY: A GENETIC ALGORITHM APPROACH
"... In this paper, I present a decisionmaking process that incorporates a Genetic Algorithm (GA) into a state dependent dynamic portfolio optimization system. A GA is a probabilistic search approach and thus can serve as a stochastic problem solving technique. A Genetic Algorithm solves the model by fo ..."
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In this paper, I present a decisionmaking process that incorporates a Genetic Algorithm (GA) into a state dependent dynamic portfolio optimization system. A GA is a probabilistic search approach and thus can serve as a stochastic problem solving technique. A Genetic Algorithm solves the model by forwardlooking and backwardinduction, which incorporates both historical information and future uncertainty when estimating the asset returns. It significantly improves the accuracy of expected return estimation and thus improves the overall portfolio efficiency over the classical meanvariance method. In addition a GA could handle a large variety of future uncertainties, which overcome the computational difficulties in the traditional Bayesian approach.
Journal homepage: www.ijorlu.ir Comparison of Simulated Annealing and Electromagnetic Algorithms for Solution of Extended Portfolio Model
, 2013
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MeanVariance Portfolio Optimization: EigendecompositionBased Methods MeanVariance Portfolio Optimization: EigendecompositionBased Methods
"... Abstract Modern portfolio theory is about determining how to distribute capital among available securities such that, for a given level of risk, the expected return is maximized, or for a given level of return, the associated risk is minimized. In the pioneering work of Markowitz in 1952, variance ..."
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Abstract Modern portfolio theory is about determining how to distribute capital among available securities such that, for a given level of risk, the expected return is maximized, or for a given level of return, the associated risk is minimized. In the pioneering work of Markowitz in 1952, variance was used as a measure of risk, which gave rise to the wellknown meanvariance portfolio optimization model. Although other meanrisk models have been proposed in the literature, the meanvariance model continues to be the backbone of modern portfolio theory and it is still commonly applied. The scope of this thesis is a solution technique for the meanvariance model in which eigendecomposition of the covariance matrix is performed. The first part of the thesis is a review of the meanrisk models that have been suggested in the literature. For each of them, the properties of the model are discussed and the solution methods are presented, as well as some insight into possible areas of future research. The second part of the thesis is two research papers. In the first of these, a solution technique for solving the meanvariance problem is proposed. This technique involves making an eigendecomposition of the covariance matrix and solving an approximate problem that includes only relatively few eigenvalues and corresponding eigenvectors. The method gives strong bounds on the exact solution in a reasonable amount of computing time, and can thus be used to solve largescale meanvariance problems. The second paper studies the meanvariance model with cardinality constraints, that is, with a restricted number of securities included in the portfolio, and the solution technique from the first paper is extended to solve such problems. Nearoptimal solutions to largescale cardinality constrained meanvariance portfolio optimization problems are obtained within a reasonable amount of computing time, compared to the time required by a commercial generalpurpose solver. v Populärvetenskaplig sammanfattning För den som har kapital att investera kan det vara svårt att avgöra vilka investeringar som är mest fördelaktiga. Till stöd för beslutet kan matematiska modeller användas och denna avhandling handlar om hur man kan beräkna lösningar till sådana modeller. De investeringsalternativ som betraktas är finansiella instrument som är föremål för daglig handel, som aktier och obligationer. En investerare placerar kapital i finansiella instrument eftersom de förväntas ge en god avkastning över tiden. Samtidigt är sådana placeringar alltid förknippade med risktagande. Förväntad avkastning och risk varierar kraftigt mellan olika instrument. Till exempel ger placeringar i statsobligationer typiskt mycket låg avkastning till mycket låg risk, medan placeringar i aktier i nystartade bolag som utvecklar nya läkemedel kan ge mycket hög avkastning samtidigt som risken är mycket hög. Att investera kan ses som en avvägning mellan den förväntade avkastningen och den risk som investeringen innebär, och typiskt är hög förväntad avkastning också associerade med en hög risk, vilken kan leda till stora förluster. En rationell investerare vill undvika alltför stora risker, men för att investeringen ska bli rimligt lönsam måste en viss risk accepteras. För att minska den totala risken sprider en investerare normalt sitt kapital på en portfölj av finansiella instrument. Dock är vanligen avkastningarna för instrumenten i en portfölj inte oberoende av varandra, utan samvarierar. Till exempel kan alla bolag inom en och samma bransch förväntas ha likartade beroenden av den ekonomiska konjunkturen. Denna omständighet försvårar avsevärt problemet att sätta samman en portfölj. Instrumenten och de kapital som investeras i var och en av dem väljs så att både den samlade avkastningen och den samlade risken för portföljen blir acceptabel utifrån investerarens preferenser. Matematiska modeller som kan användas för att finna en portfölj av investeringar som är optimal med avseende på den önskade avvägningen mellan förväntad avkastning och risk med de investeringsalternativ som finns tillgängliga på marknaden är typiskt beräkningskrävande, samtidigt som man på kort tid vill kunna ta fram flera olika förslag på portföljer. I denna avhandling presenteras en ny typ av beräkningsmetoder som är bra på att ta fram optimala portföljer på kort tid. vii
Recent Advances in Mathematical Programming with Semicontinuous Variables and Cardinality Constraint
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Using QuantumBehaved Particle Swarm Optimization for Portfolio Selection Problem IAJIT First Online Publication
, 2010
"... Abstract: One of the popular methods for optimizing combinational problems such as portfolio selection problem is swarmbased methods. In this paper, we have proposed an approach based on QuantumBehaved Particle Swarm Optimization (QPSO) for the portfolio selection problem. The particle swarm optimi ..."
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Abstract: One of the popular methods for optimizing combinational problems such as portfolio selection problem is swarmbased methods. In this paper, we have proposed an approach based on QuantumBehaved Particle Swarm Optimization (QPSO) for the portfolio selection problem. The particle swarm optimization (PSO) is a wellknown populationbased swarm intelligence algorithm. QPSO is also proposed by combining the classical PSO philosophy and quantum mechanics to improve performance of PSO. Generally, investors, in portfolio selection, simultaneously consider such contradictory objectives as the rate of return, risk and liquidity. We employed QuantumBehaved Particle Swarm Optimization (QPSO) model to select the best portfolio in 50 supreme Tehran Stock Exchange companies in order to optimize the objectives of the rate of return, systematic and nonsystematic risks, return skewness, liquidity and sharp ratio. Finally, the obtained results were compared with Markowitz`s classic and Genetic Algorithms (GA) models indicated that although return of the portfolio of QPSO model was less that that in Markowitz’s classic model, the QPSO had basically some advantages in decreasing risk in the sense that it completely covers the rate of return and leads to better results and proposes more versatility portfolios in compared with the other models. Therefore, we could conclude that as far as selection of the best portfolio is concerned, QPSO model can lead to better results and may help the investors to make the best portfolio selection.