This paper introduces a new approach to constructing optimal mean-variance portfolios. The approach relies on a novel unconstrained regression representation of the mean-variance optimization problem combined with high-dimensional sparse-regression methods. Our estimated portfolio, under a mild...

We propose a high dimensional minimum variance portfolio estimator under statistical factor models, and show that our estimated portfolio enjoys sharp risk consistency. Our approach relies on properly integrating l1 constraint on portfolio weights with an appropriate covariance matrix estimator....

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators...

For many multi-factor asset pricing models proposed in the recent literature, their implied tang-ency portfolios have substantially higher sample Sharpe ratios than that of the value-weighted market portfolio. In contrast, such high sample Sharpe ratio is rarely delivered by professional fund...

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et. al. (2008b). The required high-dimensional volatility matrix can be estimated by using high frequency...