Sparse and robust mean–variance portfolio optimization problems

Abstract

Mean–variance portfolios have been criticized because of unsatisfying out-of-sample performance and the presence of extreme and unstable asset weights. The bad performance is caused by estimation errors in inputs parameters, that is the covariance matrix and the expected return vector, especially the expected return vector. This topic has attracted wide attention. In this paper, we aim to find better portfolio optimization model to reduce the undesired impact of parameter uncertainty and estimation errors of mean–variance portfolio model. Firstly, we introduce a sparse mean–variance portfolio model, and give some insight about sparsity. Secondly, we propose two sparse and robust portfolio models by using objective function regularization and robust optimization. Finally, three empirical studies are proposed with real market data.