Fuzzy Decision Theory Based Metaheuristic Portfolio Optimization and Active Rebalancing Using Interval Type-2 Fuzzy Sets

This paper discusses a hitherto unexplored problem of fuzzy portfolio optimization with its tripartite stages of portfolio optimization, market scenario forecasting, and portfolio rebalancing. The portfolio optimization phase, which determines the original portfolio to be invested in, deals with the multiobjectives of maximizing its diversification ratio and its expected portfolio return, subject to the nonlinear constraints of risk budgeting and other investor preferential constraints. The complex problem model necessarily depends on metaheuristics to arrive at the optimal portfolio. The market scenario forecasting phase, where the investor desires to generate future market scenarios to handle the uncertainty in the markets while attempting to rebalance the portfolio, adopts a strategically refined Monte Carlo simulation to generate close-to-real future market scenarios. The last stage of portfolio rebalancing, which is crucial to the investor, employs fuzzy decision theory based metaheuristics using Interval Type-2 fuzzy sets, to cleverly exploit the uncertainty modeled by the market scenarios generated, to arrive at the ultimate optimal rebalanced portfolio. In the absence of reported work for a complex problem of such a nature and scale, two metaheuristic strategies chosen from two different genres of evolutionary algorithms, viz., multiobjective differential evolution and multiobjective evolution strategy, have been strategically evolved to solve the multistaged problem, for comparison of results. The experimental studies have been undertaken over a high-risk portfolio of BSE 200 index (March 1999-March 2009, Bombay Stock Exchange, India). Extensive simulations including data envelopment analysis have been undertaken to analyze the performance and robustness of the solution strategies.