The multi-objective portfolio optimization problem is too complex to find direct solutions by traditional methods when constraints reflecting investor's preferences and/or market frictions are included in the mathematical model and hence heuristic approaches are sought for their solution.
In this paper we propose the solution of a multi-criterion (bi-objective) portfolio optimization problem of minimizing risk and maximizing expected return of the portfolio which includes basic, bounding, cardinality, class and short sales constraints using a Pareto-archived evolutionary wavelet network (PEWN) solution strategy. Initially, the empirical covariance matrix is denoised by employing a wavelet shrinkage denoising technique. Second, the cardinality constraint is eliminated by the application of k-means cluster analysis. Finally, a PEWN heuristic strategy with weight standardization procedures is employed to obtain Pareto-optimal solutions satisfying all the constraints. The closeness and diversity of Pareto-optimal solutions obtained using PEWN is evaluated using different measures and the results are compared with existing only solution strategies (evolution-based wavelet Hopfield neural network and evolution-based Hopfield neural network) to prove its dominance. Eventually, data envelopment analysis is also used to test the efficiency of the non-dominated solutions obtained using PEWN.
Experimental results are demonstrated on the Bombay Stock Exchange, India (BSE200 index: period July 2001–July 2006), and the Tokyo Stock Exchange, Japan (Nikkei225 index: period March 2002–March 2007), data sets. Copyright © 2010 John Wiley & Sons, Ltd.