Making distributionally robust portfolios feasible in high dimension

Robust estimation for modern portfolio selection on a large set of assets becomes more important due to the large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance portfolio problems, aiming to select an optimal conservative portfolio allocation by considering distributional uncertainty. With the help of factor structure, we extend the distributionally robust mean-variance problem investigated by Blanchet et al. (2022, Management Science) to the high-dimensional scenario and transform it to a new penalized risk minimization problem. Furthermore, we propose a data-adaptive method to quantify both the uncertainty size and the lowest acceptable target return. Since the selection of these quantities requires knowledge of certain unknown population parameters, we further develop an estimation procedure, and establish its corresponding asymptotic consistency. Our Monte-Carlo simulation results show that the estimated uncertainty size and target return from the proposed procedure are very close to the corresponding oracle level, and the newly proposed robust portfolio
achieves high out-of-sample Sharpe ratio. Finally, we conduct empirical studies based on the components of the S&P 500 index and the Russell 2000 index to demonstrate the superior return-risk balancing performance of our proposed portfolio selection, in comparison with various existing strategies.