Metaheuristic optimization of marginal risk constrained long - short portfolios

The problem of portfolio optimization with its twin objectives of maximizing expected portfolio return and minimizing portfolio risk renders itself difficult for direct solving using traditional methods when constraints reflective of investor preferences, risk management and market conditions are imposed on the underlying mathematical model. Marginal risk that represents the risk contributed by an asset to the total portfolio risk is an important criterion during portfolio selection and risk management. However, the inclusion of the constraint turns the problem model into a notorious non-convex quadratic constrained quadratic programming problem that seeks acceptable solutions using metaheuristic methods. In this work, two metaheuristic methods, viz., Evolution Strategy with Hall of Fame and Differential Evolution (rand/1/bin) with Hall of Fame have been evolved to solve the complex problem and compare the quality of the solutions obtained. The experimental studies have been undertaken on the Bombay Stock Exchange (BSE200) data set for the period March 1999-March 2009. The efficiency of the portfolios obtained by the two metaheuristic methods have been analyzed using Data Envelopment Analysis.