Some new efficient mean–variance portfolio selection models

The poor out‐of‐sample performance of mean–variance portfolio model is mainly caused by estimation errors in the covariance matrix and the mean return, especially the mean return vector. Meanwhile, in financial practice, what most investors actually like is to hold a few stocks in their portfolio. The goal of this paper is to propose some new efficient mean–variance portfolio selection models by considering the following aspects: (i) use the L 1 ‐regularization in objective function to obtain sparse portfolio; (ii) use the shrinkage method of Ledoit and Wolf, Journal of Economics Financial, 2003, 10, 603–621 to estimate the covariance matrix; (iii) use the robust optimization method to mitigate the estimation errors of the expected return. Finally, empirical analysis demonstrates that the proposed strategies have better out‐of‐sample performance.