Studies on Computational Intelligence Based Strategies for Financial Portfolio Optimization

Abstract

A financial portfolio is a basket of tradable assets such as stocks,bonds, commodities etc., that is held by an investor. The problem of portfoliooptimization deals with determining the optimal proportions of capital that theinvestor should invest on each asset of the portfolio to meet the twinobjectives of maximizing return and minimizing the risk associated with theinvestment. The optimization problem in its naïve form can be easily solvedusing traditional methods. However, when constraints reflective of investorpreferences, investment strategies and/or market frictions are included in theproblem model, the mathematical model turns complex for direct solving bytraditional methods. It is in such cases that heuristic methods have beenlooked up to for their solution.Computational Intelligence (CI) is a consortium of nature inspiredcomputational methodologies and strategies that have proved to be efficient insolving problems on which traditional methods of solution had been renderedineffective or infeasible. Some of the prominent CI methodologies includeNeural Networks, Swarm Intelligence, Evolutionary algorithms, Waveletnetworks, Fuzzy Logic etc.This thesis broadly deals with studies on CI based strategies for thesolution of complex constrained portfolio optimization problems. The ivconstraints that have been considered for inclusion in the mathematical modelare one or more combinations of basic, bounding, cardinality, class, shortsales and transaction costs constraints. The specific CI based methodologiesconsidered in the work are neural networks, wavelet networks andevolutionary strategies. The studies undertaken in the thesis have been viewedunder four segments.In the first part of the work, studies on obtaining a better noise filterfor the estimation of the empirical covariance matrix, which is one of the keyinputs to the constrained portfolio optimization problem have beenundertaken. The empirical covariance matrix deduced from the financialreturn series is dominated by a high degree of noise. This leads to seriousinstability in the optimal portfolios. Hence, in order to obtain reliableportfolio sets, better estimators are required to remove the noise significantlyfrom the covariance matrix. Some of the recent and widely used estimatorsare Random Matrix Theory (RMT) based filters and k-means cluster analysis.Since wavelet based filters are believed to reduce high frequencynoises, a wavelet shrinkage denoising technique is employed to estimate theempirical covariance matrix. Several experiments are undertaken to study thewavelet shrinkage denoising technique with different wavelet functions beforejustifying the choice of ‘symlet 3’ as the mother wavelet, due to the highcorrelation between the original covariance matrix and symlet 3 based filteredcovariance matrix. Experiments undertaken have proved that the wavelet vbased filter is more reliable, in terms of the predicted and realized risks whencompared with those reported by the Markowitz model or other noise filterssuch as RMT based filters or k-means cluster analysis.The second part of the work pertains to the solution of a complexconstrained portfolio optimization problem. The single objective function is aweighted formulation of the bi-criterion objective function of the portfoliooptimization problem model. Two hybrid solution strategies viz., Evolutionbased Hopfield Neural Network (EHNN) and Evolution based WaveletHopfield Neural Network (EWHNN) have been proposed to solve theoptimization problems. The experimental results show better performance byway of faster convergence, lesser computations and in the ability to handlediversification in both large and small portfolios when compared to otherexisting strategies. Finally, to measure the quality of the portfolios obtainedby the two methods, viz., EWHNN and EHNN, a Data Envelopment Analysishas been undertaken over the two methods.In the third part, a new hybrid strategy named Pareto-archivedEvolutionary Wavelet Network (PEWN) is proposed to solve the constrainedmulti objective portfolio optimization problem. The major limitations in thesingle objective weighted formulation are fixed by the PEWN solutionstrategy. The key feature which helps to tackle the twin objectives in theportfolio optimization problem is the efficient mapping of objective functionsin the portfolio optimization problem with the ‘concept of dominance’ in the vimulti objective problem. The experimental studies show that PEWN strategygives better pareto-optimal set in a single simulation run in contrast to otherstrategies and executes faster when compared to EHNN and EWHNNstrategies. Finally, the efficiency of the portfolio sets obtained using all thethree strategies are tested using Data Envelopment Analysis. The results showthat PEWN strategy is more robust when compared with the other twostrategies.In the last segment, the need for the inclusion of transaction costs inthe multi-period portfolio rebalancing problem has been studied. Two hybridsolution strategies named Hopfield Evolutionary Network (HEN) andWavelet Evolutionary Network (WEN) have been proposed for the solution ofthe complex constrained portfolio rebalancing problem, which includes basic,bounding, cardinality, class and transaction cost constraints. The performanceanalysis, experimental analysis and Data Envelopment Analysis discussed inthe previous segments have been undertaken to test the robustness andefficiency of the WEN strategy over the HEN strategy.All the aforementioned hybrid strategies have been implementedusing MATLAB and demonstrated on the Bombay Stock Exchange (BSE200index: July 2001 to July 2006) and Tokyo Stock Exchange (Nikkei225 index:March 2002 to March 2007) data sets.