Constrained portfolio rebalancing with transaction costs using Evolutionary Wavelet Hopfield Network Strategy

Portfolio rebalancing problem is an extension of the basic portfolio optimization problem in which invested portfolio is rebalanced by incurring proportional transaction costs. The constraints included in this problem formulation are basic, cardinality, bounding and class constraints. Due to complex constraints, the solution to the problem has been beyond the reach of traditional methods. Hence, heuristic approaches have been sought for its solution. In this paper, the empirical covariance matrix, which is one of the primary inputs to the constrained portfolio rebalancing problem, is initially de-noised using wavelet shrinkage de-noising technique for proper estimation of risk. Secondly, cardinality constraint is eliminated by employing k-means cluster analysis. Finally, the proposed evolutionary wavelet Hopfield network strategy (EWHNS) with weight standardization procedures is employed to solve a class of portfolio rebalancing problem. EWHNS reports faster convergence and efficiently handles diversification in both large and small portfolios. Experimental studies of EWHNS on newly proposed portfolio rebalancing problem have been undertaken on the Bombay Stock Exchange, India (BSE200 index, period: July 2001 - July 2006) and Tokyo Stock Exchange, Japan (Nikkei225 index: period: March 2002 - March 2007) data sets and the results are compared with those obtained using evolutionary Hopfield network strategy (EHNS), the only existing alternative solution strategy for this proposed model. Finally, data envelopment analysis (DEA) is also carried out to prove the efficiency of EWHNS over EHNN.