A Synthetic Regression Model for Large Portfolio Allocation
基于均值-方差优化原理，提出一种合成回归模型用于构建投资组合，并给出生成合成样本的简便方法，在大规模资产下能更准确逼近最优组合，理论证明渐近性质，模拟和真实数据表现良好。
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.