High Dimensional Portfolio Selection with Cardinality Constraints
Title: High Dimensional Portfolio Selection with Cardinality Constraints
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 aforementioned difficulties 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 twice more than the best mean-variance portfolio but reduces the maximum drawdown by 47%. While no more than 30 assets can form diversified portfolios for S&P 500, near 100 assets are needed for Russell 2000 due to higher volatility and lower signal-noise ratios. 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.
报告人简介：王学钦，中国科学技术大学管理学院教授。2003年毕业于纽约州立大学宾厄姆顿分校。目前现担任教育部高等学校统计学类专业教学指导委员会委员、统计学国际期刊《JASA》等的Associate Editor、高等教育出版社《Lecture Notes: Data Science, Statistics and Probability》系列丛书的副主编。