稀疏学习、资产共线性与投资组合选择  

Sparse Learning,Asset Colinearity and Portfolio Selection

作　　者：李爱忠 任若恩[2] 董纪昌 LI Aizhong;REN Ruo’en;DONG Jichang(School of Public Finance Economics,Shanxi University of Finance and Economics,Taiyuan 030006;School of Economics and Management,Beihang University,Beijing 100191;School of Economics and Management,University of Chinese Academy of Sciences,Beijing 100190)

机构地区：[1]山西财经大学财政与公共经济学院,太原030006 [2]北京航空航天大学经济管理学院,北京100191 [3]中国科学院大学经济与管理学院,北京100190

出　　处：《系统科学与数学》2021年第11期3128-3138,共11页Journal of Systems Science and Mathematical Sciences

基　　金：国家社会科学基金(19BTJ026)资助课题。

摘　　要：通过核范数正交约束的稀疏学习方法深度挖掘市场特征,选择相对效率较高的重要指数构建市场有效组合并动态跟踪市场运行趋势,运用正交最小一乘的自适应权重学习方法进行泛组合资产配置优化,最终通过稀疏投影及分散优化策略获得最优组合配置.研究发现多目标核范数正交约束的稀疏回归策略可以更好地把握市场主要运行趋势并构建有效前沿,有效地克服资产共线性现象,自适应地表征资产之间的关联关系.稀疏分散的多目标回归策略在集中优势重点配置优质资源和稀疏分散风险及稳定提高收益方面实现了良好的统一,风险收益的均衡性更强,组合的稳健性更明显.实证结论对量化组合配置、风险平衡及投资管理具有重要指导意义.This paper constructs a sparse learning method with kernel norm orthogonal constraints to deeply explore market characteristics,and selects important indexes with relatively high efficiency to build effective market combinations and dynamically track market operation trends.We use the orthogonal least absolute deviations adaptive weight learning method for portfolio optimization,and finally obtain the desired portfolio configuration through sparse projection and decentralized optimization strategies.The research finds that the sparse regression strategy with multi-objective kernel norm orthogonal constraints can better grasp the main operating trends of the market and build an effective frontier,effectively overcome the phenomenon of asset co-linearity,and adaptively represent the relationship between assets.The sparse and diversified multi-objective regression strategy achieves a good unity in focusing on the allocation of high-quality resources,sparsely diversifying risks,and steadily increasing returns.The balance of risks and returns is stronger and the robustness of the combination is more obvious.The empirical conclusions have important guiding significance for quantitative portfolio allocation,risk balance,and investment management.

关 键 词：核范数正交回归 最小一乘法 低秩稀疏 资产共线性 组合优化 

分 类 号：F224[经济管理—国民经济] F830.91