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

This paper deals with the mean-variance optimization frontier problem when realistic constraints are considered. Our proposed methodology hybridizes 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 fulfills the bound and cardinality constraints, unlike other proposals where the frontier is composed of several sub-frontiers, 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 optimization of the constrained frontier, which differs from a previous proposal where no bound constraints were considered. Regarding the genetic algorithm, we propose an initial population to boost the convergence of the optimization process, whilst the adopted mutation and crossover genetic operators result in feasible individuals. An illustrative example using components of five major stock market indices is provided to demonstrate the effectiveness of the proposed method.