  The expanding number of assets offers more opportunities for investors but
poses new challenges for modern portfolio management (PM). As a central plank
of PM, portfolio selection by expected utility maximization (EUM) faces
uncontrollable estimation and optimization errors in ultrahigh-dimensional
scenarios. Past strategies for high-dimensional PM mainly concern only
large-cap companies and select many stocks, making PM impractical. We propose a
sample-average approximation-based portfolio strategy to tackle the
difficulties above with cardinality constraints. Our strategy bypasses the
estimation of mean and covariance, the Chinese walls in high-dimensional
scenarios. Empirical results on S&P 500 and Russell 2000 show that an
appropriate number of carefully chosen assets leads to better out-of-sample
mean-variance efficiency. On Russell 2000, our best portfolio profits as much
as the equally-weighted portfolio but reduces the maximum drawdown and the
average number of assets by 10% and 90%, respectively. The flexibility and the
stability of incorporating factor signals for augmenting out-of-sample
performances are also demonstrated. Our strategy balances the trade-off among
the return, the risk, and the number of assets with cardinality constraints.
Therefore, we provide a theoretically sound and computationally efficient
strategy to make PM practical in the growing global financial market.
