Metaheuristic Construction of Long-Only Risk Budgeted Futures Portfolio with Maximal Diversification Index

34 Pages Posted: 26 Jun 2015 Last revised: 29 Jun 2015

Date Written: June 25, 2015


Trading with futures is complex and abounds with risks, to mitigate which a multi-pronged 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, can be adopted. However, the enforcement of such constraints turns the 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 construction 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. 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 a metaheuristic strategy, viz., Multi-objective Differential Evolution, has been evolved to obtain the Pareto Optimal solution set.

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.

Keywords: Futures portfolio; Diversification Ratio; Risk Budgeting; Multi-objective Optimization; Differential Evolution

JEL Classification: C61,G11

Suggested Citation

Pai, Vijayalakshmi G A and Michel, Thierry, Metaheuristic Construction of Long-Only Risk Budgeted Futures Portfolio with Maximal Diversification Index (June 25, 2015). Available at SSRN: or

Vijayalakshmi G A Pai (Contact Author)

PSG College of Technology ( email )

Coimbatore, TN 641004

Thierry Michel

Lombard Odier & Cie ( email )

11 rue de la Corraterie
Geneva, 1211

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