High Dimensional Portfolio Selection with Cardinality Constraints

TL;DR

This paper introduces a sample-average approximation-based portfolio strategy with cardinality constraints that improves out-of-sample efficiency and reduces complexity in high-dimensional portfolio management, demonstrated on major stock indices.

Contribution

It proposes a novel, estimation-error bypassing portfolio method that balances return, risk, and asset number, enhancing practicality in ultrahigh-dimensional settings.

Findings

Better out-of-sample mean-variance efficiency on S&P 500 and Russell 2000.

Reduces maximum drawdown and number of assets by 10% and 90%.

Incorporates factor signals for improved stability and performance.

Abstract

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.