Evolutionary approaches for 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. Markowitz’s mean variance (MV) model is widely regarded as the foundation of modern portfolio theory and provides a quantitative framework for portfolio optimization problems. In real market, investors commonly face real-world trading restrictions and it requires that the constructed portfolios have to meet trading constraints. When additional constraints are added to the basic MV model, the problem thus becomes more complex and the exact optimization approaches run into difficulties to deliver solutions within reasonable time for large problem size. By introducing the cardinality constraint alone already transformed the classic quadratic optimization model into a mixed-integer quadratic programming problem which is an NP-hard problem. Evolutionary algorithms, a class of metaheuristics, are one of the known alternatives for optimization problems that are too complex to be solved using deterministic techniques. This thesis focuses on single-period portfolio optimization problems with practical trading constraints and two different risk measures. Four hybrid evolutionary algorithms are presented to efficiently solve these problems with gradually more complex real world constraints. In the first part of the thesis, the mean variance portfolio model is investigated by taking into account real-world constraints. A hybrid evolutionary algorithm (PBILDE) for portfolio optimization with cardinality and quantity constraints is presented. The proposed PBILDE is able to achieve a strong synergetic effect through hybridization of PBIL and DE. A partially guided mutation and an elitist update strategy are proposed in order to promote the efficient convergence of PBILDE. Its effectiveness is evaluated and compared with other existing algorithms over a number of datasets. A multi-objective scatter search with archive (MOSSwA) algorithm for portfolio optimization with cardinality, quantity and pre-assignment constraints is then presented. New subset generations and solution combination methods are proposed to generate efficient and diverse portfolios. A learning-guided multi-objective evolutionary (MODEwAwL) algorithm for the portfolio optimization problems with cardinality, quantity, pre-assignment and round lot constraints is presented. A learning mechanism is introduced in order to extract important features from the set of elite solutions. Problem-specific selection heuristics are introduced in order to identify high-quality solutions with a reduced computational cost. An efficient and effective candidate generation scheme utilizing a learning mechanism, problem specific heuristics and effective direction-based search methods is proposed to guide the search towards the promising regions of the search space. In the second part of the thesis, an alternative risk measure, VaR, is considered. A non-parametric mean-VaR model with six practical trading constraints is investigated. A multi-objective evolutionary algorithm with guided learning (MODE-GL) is presented for the mean-VaR model. Two different variants of DE mutation schemes in the solution generation scheme are proposed in order to promote the exploration of the search towards the least crowded region of the solution space. Experimental results using historical daily financial market data from S &P 100 and S & P 500 indices are presented. When the cardinality constraints are considered, incorporating a learning mechanism significantly promotes the efficient convergence of the search.