Before revision:  To resolve this issue, we consider the decomposition of low-rank and sparse components. This strategy allows us to consistently estimate the optimal portfolio in high dimensions, even when the covariance matrix is ill-behaved. We establish consistency of the portfolio weights in a high-dimensional setting without assuming sparsity on the covariance or precision matrix of stock returns .
After revision:  To resolve this issue, we consider the decomposition of low-rank and sparse components .