A Synthetic Regression Model for Large Portfolio Allocation

Abstract

Portfolio allocation is an important topic in financial data analysis. In this article, based on the mean-variance optimization principle, we propose a synthetic regression model for construction of portfolio allocation, and an easy to implement approach to generate the synthetic sample for the model. Compared with the regression approach in existing literature for portfolio allocation, the proposed method of generating the synthetic sample provides more accurate approximation for the synthetic response variable when the number of assets under consideration is large. Due to the embedded leave-one-out idea, the synthetic sample generated by the proposed method has weaker within sample correlation, which makes the resulting portfolio allocation more close to the optimal one. This intuitive conclusion is theoretically confirmed to be true by the asymptotic properties established in this article. We have also conducted intensive simulation studies in this article to compare the proposed method with the existing ones, and found the proposed method works better. Finally, we apply the proposed method to real datasets. The yielded returns look very encouraging.

Keywords:

• Leave-one-out
• Penalized least-square estimation
• Portfolio allocation

Acknowledgments

The authors are grateful for the Editor, Associate Editor and two referees for their helpful comments that substantially improve this work.

Additional information

Funding

This research is supported by National Natural Science Foundation of China (Grant Numbers 11931014, 11871001, 11901315, 72033002), the Beijing Natural Science Foundation (Grant Number 1182003) and the Fundamental Research Funds for the Central Universities (Grant Numbers 2019NTSS18, 2682020ZT113).