Computing cardinality constrained portfolio selection efficient frontiers via closest correlation matrices

Abstract

In this paper, we demonstrate a completely new approach for computing cardinality constrained mean-variance efficient frontiers. By cardinality constrained, it is meant that if there is to be investment in a security, it is to be of at least some minimum amount (a buyin threshold), and that there is also a specification on the number of securities to be held in a portfolio (called a cardinality constraint). Whereas the usual strategy, as such problems are NP-hard, is to take the original exact problem and apply heuristics to solve, in this paper the strategy is to perturb the original problem and then apply exact procedures to solve. The advantages of the approach are that the perturbations are tiny, they are only applied to the problem’s correlation matrix, and they allow for the accurate computation of cardinality constrained efficient frontiers in problems with up to at least 1000 securities in remarkably little time. Moreover, the simplicity of the approach is such that it can be inserted into existing portfolio management systems without requiring any re-training beyond what a typical portfolio analyst would already know.11The authors have benefited from associations with Markus Hirschberger and Sebastian Utz in this research.