Fuzzy decision theory based optimization of constrained portfolios using metaheuristics

To tackle uncertainty in the financial markets, fund managers resort to market scenario generation, which are an essential component of the portfolio selection process. However, when constraints reflecting investor preferences are also included in the portfolio selection process, the problem can turn complex, for direct solving by traditional methods. In this work a portfolio selection problem that incorporates basic, bounding, cardinality and class constraints, and which employs fuzzy decision theory to tackle the uncertainty arising out of possible market scenarios in the fund managers´ view point, has been discussed. The complex constrained portfolio optimization problem employs Evolution Computation based metaheuristics, augmented with appropriate weight standardization functions, to navigate the search for the optimal portfolio through feasible solution space, thereby ensuring quick convergence. The experimental simulations have been undertaken on the Bombay Stock Exchange (BSE 200 index, Period: July 2001 - July 2006) and Tokyo Stock Exchange (Nikkei225 index, Period: March 2002-March 2007) data sets. The performance efficiencies of the optimal fuzzy portfolios have been measured using Sharpe and Treynor ratios and compared with those of their crisp counterparts.