  Accounting for uncertainty in Data quality is important for accurate
statistical inference. We aim to an optimal conservative allocation for a large
universe of assets in mean-variance portfolio (MVP), which is the worst choice
within uncertainty in data distribution. Unlike the low dimensional MVP studied
in Blanchet et al. (2022, Management Science), the large number of assets
raises a challenging problem in quantifying the uncertainty, due to the big
deviation of the sample covariance matrix from the population version. To
overcome this difficulty, we propose a data-adaptive method to quantify the
uncertainty with the help of a factor structure. Monte-Carlo Simulation is
conducted to show the superiority of our method in high-dimensional cases,
that, avoiding the over-conservative results in Blanchet et al. (2022), our
allocation is closer to the oracle version in terms of risk minimization and
expected portfolio return controlling.
