Uncertainty Learning for High-dimensional Mean-variance Portfolio

Abstract: Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance portfolio problem, aiming to select an optimal conservative portfolio allocation by taking distribution uncertainty into account. 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 estimate the quantified uncertainty size, which is the radius around the empirical probability measured by the Wasserstein distance. Asymptotic consistency is derived for the estimation of the population parameters involved in selecting the uncertainty size and the selected portfolio return. Our Monte-Carlo simulation results show that the chosen uncertainty size and target return from the proposed procedure are very close to the corresponding oracle version, and the new portfolio strategy is of low risk. Finally, we conduct empirical studies based on S&P index components to show the robust performance of our proposal in terms of risk controlling and return-risk balancing.