A new method for mean-variance portfolio optimization with cardinality constraints

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM) model, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model based on a reformulation as a Standard Quadratic Program, on a new lower bound that we establish, and on other recent theoretical and computational results for such problem. These results lead to an exact algorithm for solving the LAM model for small size problems. For larger problems, such algorithm can be relaxed to an efficient and accurate heuristic procedure that is able to find the optimal or the best-known solutions for problems based on some standard financial data sets that are used by several other authors. We also test our method on five new data sets involving real-world capital market indices from major stock markets. We compare our results with those of CPLEX and with those obtained with very recent heuristic approaches in order to illustrate the effectiveness of our method in terms of solution quality and of computation time. All our data sets and results are publicly available for use by other researchers.