Sparsity penalized mean-variance portfolio selection: computation and analysis

Abstract

The problem of selecting the best portfolio of assets, so-called mean-variance portfolio (MVP) selection, has become a prominent mathematical problem in the asset management framework. We consider the problem of MVP selection regu-larized with ℓ0-penalty term to control the sparsity of the portfolio. We analyze the structure of local and global minimizers, show the existence of global mini-mizers and develop a necessary condition for the global minimizers in the form of a componentwise lower bound for the global minimizers. We use the results in the design of a Branch-and-Bound algorithm. Extensive computational results with real-world data as well as comparisons with an off-the-shelf and state-of-the-art mixed-integer quadratic programming (MIQP) solver are reported. The behavior of the portfolio’s risk against the expected return and penalty parameter is ex-amined by numerical experiments. Finally, we present the accumulated returns over time according to the solutions yielded by the Branch-and-Bound and Lasso for the instances that the MIQP solver fails to find.