A surrogate similarity measure for the mean-variance frontier optimisation problem under bound and cardinality constraints

Abstract

This article deals with the mean-variance optimisation frontier problem when realistic constraints are considered. Our proposed methodology hybridises a heuristic algorithm with an exact solution approach. A genetic algorithm is applied for the identification of the assets in the portfolio, whilst the asset weights in the portfolios are obtained by a quadratic programming model. The proposed algorithmic framework produces a constrained frontier that actually fulfils the bound and cardinality constraints, unlike other proposals where the frontier is composed of several subfrontiers, each one considering the cardinality constraint but with different assets in each sub-frontier, thus violating the cardinality constraint. This brings us to propose a surrogate similarity measure for the optimisation of the constrained frontier, which differs from a previous proposal where no bound constraints were considered.

Keywords:

• Portfolio optimisation
• cardinality constraint
• bound constraint
• genetic algorithm

Acknowledgements

We would like to thank two anonymous referees for their constructive comments and suggestions that substantially improved this article.

Disclosure statement

No potential conflict of interest was reported by the authors.