Multi-objective Metaheuristics for Managing Futures Portfolio Risk

Trading with futures in the Derivatives financial markets, is fraught with risks. To mitigate the risks, a multipronged approach such as diversification in different asset classes across dissimilar markets or imposing risk budgets on individual assets and/or asset classes or enforcing capital budgets and other investor preferential constraints modeling their risk appetites and allocation limits, needs to be adopted. However, the enforcement of such constraints turns the futures portfolio optimization problem model complex, rendering it difficult for direct solving using traditional methods engendering the need to look for metaheuristic solutions.In this work, we discuss the metaheuristic optimization of a long-only futures portfolio with the objective of maximizing its diversification index, in the face of Risk Budgeting and other investor specific constraints that serve to curtail risk. Adopting Diversification Ratio for its diversification index and enforcing risk budgets on the individual assets as well as on asset classes turns the transformed problem model into a Multi-objective Non-linear Non Convex Constrained Fractional Programming problem, to solve which metaheuristics has been applied. In the absence of reported work for a problem of such a nature and scale, two strategies from two different genres of metaheuristics, viz., Multi-objective Differential Evolution and Multi-objective Evolution Strategy have been evolved to obtain the Pareto Optimal solution set and their results and performances have been compared. Experimental simulations have been undertaken over a futures portfolio of equity indices and bonds spread across global markets, making use of a historical data set for the period March 2004-June 2013.