Evolutionary Optimization for Multiobjective Portfolio Selection under Markowitz's Model with Application to the Caracas Stock Exchange

Several problems in the area of financial optimization can be naturally dealt with optimization techniques under multiobjective approaches, followed by a decision-making procedure on the resulting efficient solutions. The problem of portfolio optimization is one of them. This chapter studies the use of evolutionary multiobjective techniques to solve such problems, focusing on Venezuelan market mutual funds between years 1994 and 2002. We perform a comparison of different evolutionary multiobjective approaches, namely NSGA-II, SPEA2, and IBEA, and show how these algorithms provide different optimization profiles. The subsequent step of solution selection is done using Sharpe’s index as a measure of risk premium. We firstly show that NSGA-II provides similar results to SPEA2 on mixed and fixed funds, and better (according to Sharpe’s index) solutions than SPEA2 on variable funds, indicating that NSGA-II provides a better coverage of the region containing interesting solutions for Sharpe’s index. Furthermore, IBEA outperforms both NSGA-II and SPEA2 in terms of index value attained. Finally, we also show that this procedure results in a more profitable solution than an indexed portfolio by the Caracas Stock Exchange.