Identifying Sparse L₂-Norm Regularized Portfolios via Semi-Definite Relaxation

Abstract

For portfolio management in the real-world, it is required that a portfolio has a manageable number of assets and stable performance. However, much research has pointed out that the Markowitz model, which is a classical model in portfolio theory, forms a portfolio with many different assets that may have unstable performance. Therefore, in this paper, we focus on developing a portfolio selection model which constructs a sparse and stable optimal portfolio. In order to achieve our research goal we introduce a L₂-norm regularization and a cardinality constraint on portfolio weights to the Markowitz model. Moreover, using semidefinite relaxation, we formulate a convex optimization problem for the proposed model. The outcomes of our empirical test show that portfolios obtained by our model have desired cardinalities and better out-of-sample performances than those of Markowitz optimal portfolios.

Keywords: Portfolio selection, L2-norm regularization, Cardinality constraint, Semi-definite relaxation