Scandinavian Working Papers in Business Administration
Working Papers,
Örebro University, School of Business
No 2019:3: An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection
Mårten Gulliksson () and Stepan Mazur ()
Additional contact information
Mårten Gulliksson: Örebro University School of Science and Technology, Postal: Örebro University, School of Science and Technology, SE - 701 82 ÖREBRO, Sweden
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Abstract: Covariance matrix of the asset returns plays an important role in the portfolio selection. A number of papers is focused on the case when the covariance matrix is positive definite. In this paper, we consider portfolio selection with a singular covariance matrix. We describe an iterative method based on a second order damped dynamical systems that solves the linear rank-deficient problem approximately. Since the solution is not unique, we suggest one numerical solution that can be chosen from the iterates that balances the size of portfolio and the risk. The numerical study confirms that the method has good convergence properties and gives a solution as good as or better than the constrained least norm Moore-Penrose solution. Finally, we complement our result with an empirical study where we analyze a portfolio with actual returns listed in S&P 500 index.
Keywords: Mean-variance portfolio; singular covariance matrix; linear ill-posed problems; second order damped dynamical systems
21 pages, May 22, 2019
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