Factor Model Based Clustering Approach for Cardinality Constrained Portfolio Selection

Portfolio selection concerns identifying an optimal composition of various risky assets and their corresponding holding amounts such that the corresponding investment strategy strikes a balance between maximizing the expected investment return and minimizing investment risk. While market frictions make full diversification impractical, cardinality constrained mean-variance (CCMV) portfolio selection problem emerges as a natural remedy: Given an asset pool with total n assets and a given cardinality s < n, optimally choose s assets from the entire asset pool such as to achieve a mean-variance efficiency. Unfortunately, CCMV has been proved to be NP hard and has been posted in front of optimization society as a long-standing challenge. By invoking structural market information and utilizing fast clustering algorithm for classification, we develop in this paper an effective heuristic scheme to identify approximate solutions for large-scale CCMV problems. More specifically, by constructing grouping constraints generated from factor-model based clustering algorithm and attaching them to the mixed integer programming formulation associated with the CCMV problem, we are able to significantly reduce the computational complexity, thus offering a fast algorithm with relatively high quality solution.