Efficient one asset replacement scheme for an optimized portfolio

Abstract

The traditional mean-variance portfolio optimization models in practice have suffered from complexity and heavy computation loads in the process of selecting the best assets for constructing a portfolio. If not, they are considerably departed from the theoretically optimized values. In this work, we develop the optimized portfolio investment strategy in which only one asset substitution occurs when re-balancing a portfolio. To do this, we briefly look into a quadratically constrained quadratic programming (QCQP), which has been well-studied for the non-negative solution. Based on the quadratic programming, an efficient scheme is presented for solving the large-scale inverse problem. We more precisely update the rank of an inverse matrix, so that the optimal solution can be easily and quickly obtained by our proposed scheme. Various numerical and practical experiments are presented to demonstrate the validity and reliability of our scheme. Our empirical application to the U.S. and South Korea stock markets is tested and highlighted. Moreover, comparisons of a random allocation strategy and our proposed scheme reveal the better performance in the lower risks and higher expected returns obtained by our scheme.

Keywords

• market portfolio
• low-rank update
• portfolio optimization
• asset substitution problem
• covariance matrix