Seyreklik ile düzenlenmiş ortalama varyans portföy seçme problemi: Hesaplama ve analiz

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 regularized 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 minimizers 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 examined 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.