Model and efficient algorithm for the portfolio selection problem with real-world constraints under value-at-risk measure

Value-at-risk (VaR) is a widely acceptable risk measure in finance and particularly, in the portfolio selection problem (PSP). However, due to the non-convexity, its incorporation into an optimization model makes it challenging and difficult to solve. Hence, the development of iterative-based heuristic algorithms (IBHAs) utilizing the problem structure would be valuable. The existing IBHAs are either inefficient in terms of solution quality and running time or are just applicable to solve simple PSPs without any real-world constraint (i.e., cardinality, position size, and transaction cost constraints). To overcome these shortcomings, in this paper, we present a novel IBHA to efficiently solve the PSP with real-world constraints under VaR measure. Our method is based on iterative resolution of two restricted versions of the original model in which some of the binary variables utilized in the formulation of VaR measure are fixed at specific values. Computational experiments over real-world instances indicate that not only the running time of our algorithm is short, but also its solution quality is much better than the existing IBHAs in 97% of instances with an average improvement of about 10%.