A parallel variable neighborhood search algorithm with quadratic programming for cardinality constrained portfolio optimization

Abstract Over the years, portfolio optimization remains an important decision-making strategy for investment. The most familiar and widely used approach in the field of portfolio optimization is the mean–variance framework introduced by Markowitz. Following this pioneering work, many researchers have extended this model to make it more practical and adapt to real-life problems. In this study, one of these extensions, the cardinality constrained portfolio optimization problem, is considered. Cardinality constraints transform the quadratic optimization model into the mixed-integer quadratic programming problem, which is proved to be NP-Hard, making it harder to obtain an optimal solution within a reasonable time by using exact solution methodologies. Hence, the vast majority of the researchers have taken advantage of approximate algorithms to overcome arising computational difficulties. To develop an efficient solution approach for cardinality constrained portfolio optimization, in this study, a parallel variable neighborhood search algorithm combined with quadratic programming is proposed. While the variable neighborhood search algorithm decides the combination of assets to be held in the portfolio, quadratic programming quickly calculates the proportions of assets. The performance of the proposed algorithm is tested on five well-known datasets and compared with other solution approaches in the literature. Obtained results confirm that the proposed solution approach is very efficient especially on the portfolios with low risk and highly competitive with state-of-the-art algorithms.