Differential evolution based optimization of risk budgeted Equity Market Neutral Portfolios

Abstract

An Equity Market Neutral Portfolio (EMNP) is an assortment of long and short positions that ensures a riskless portfolio in terms of its exposure to the relevant market benchmark. While a naïve formulation of the EMNP optimization problem can be easily solved using linear programming techniques, the inclusion of the Risk Budget constraint on the high risk assets, together with the other EMNP specific constraints of zero net market exposure, close-to-zero portfolio beta and zero financial leveraging, besides the bounding constraints imposed on the long-short positions and high risk assets, can turn the problem difficult for direct solving using traditional methods. This work aims to solve such a complex constrained EMNP optimization problem using a meta-heuristic method viz., Differential Evolution (rand/1/bin) with Hall of Fame (DE HOF). The DE HOF exploits a penalty function strategy and employs weight standardization procedures to ensure faster convergence and an efficient tackling of complex constraints to yield optimal portfolios within realistic time. Experimental studies which include a rigorous out of sample performance analysis have been undertaken on the Bombay Stock Exchange data set (BSE 200: March 1999–March 2009) which included both upturns and downturns in the global markets.