Portfolio Selection with a Rank-Deficient Covariance Matrix

Abstract In this paper, we consider optimal portfolio selection when the covariance matrix of asset returns is rank-deficient. For case, original Markowitz’ problem does not have a unique solution. The possible solutions belong to either two subspaces namely range- or nullspace matrix. former case has been treated elsewhere but latter. We derive an analytical solution, assuming solution in null space, that risk-free and minimum norm. Furthermore, analyse iterative method which called discrete functional particle rank-deficient case. It shown convergent giving initial condition gives smallest weights Finally, simulation results on artificial problems as well real-world applications verify both efficient stable.