Before revision:  One obstacle in this large dimensional setup is the singularity of the sample covariance matrix of the excess asset returns. To solve this issue, we benefit from a technique called nodewise regression , which was developed by Meinshausen and Buhlmann (2006). It provides a sparse/weakly sparse and consistent estimate of the precision matrix , using the Lasso method.
After revision:  One obstacle in this large dimensional setup is the singularity of the sample covariance matrix of the idiosyncratic terms is assumed to be sparse, but the respective covariance matrix can be non-sparse. Since the nodewise regression is not feasible due to the unknown nature of errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix , using the Lasso method.