Evolutionary optimization of Risk Budgeted long-short portfolios

Risk Budgeting is a relatively recent investment strategy instrumental in building long-short portfolios and notionally expected to enhance investment exposure and market protection. However, the inclusion of the strategy in the Portfolio Optimization problem model yields a complex constraint that is difficult to handle using traditional methods, justifying a compelling need to look for heuristic solutions. In this paper we discuss an Evolutionary Computation (EC) based solution for an integrated optimization of long-short portfolios, when the Risk Budgeting strategy is incorporated in the problem model, besides inclusion of constraints reflective of investor preferences. Two EC based strategies 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) and Tokyo Stock Exchange (Nikkei 225) data sets and specifically for the period March 1999-March 2009 which included both upturns and downturns in the markets. The efficiency of the portfolios obtained by the two EC based methods have been analyzed using a portfolio productivity indicator employing the efficiency improvement possibility function which is a variant of Luenberger's shortage function.