基于高频高维协方差矩阵收缩估计的最小方差投资组合

Shrinkage Estimation of High Frequency and High Dimensional Covariance Matrix and Its Application in Minimum Variance Portfolio

高频金融数据背景下金融资产收益率序列普遍存在微观噪声结构,并且存在较为明显的重尾特征;同时,金融资产收益率的协方差矩阵具有高维性和稀疏性特征。基于预平均方法和Huber损失函数,采用收缩估计方法,得到高频金融数据背景下金融资产收益率的协方差矩阵的估计。模拟结果显示收缩估计方法有着较好的效果。此外,以中国A股市场资产的高频数据为样本进行实证分析,探究估计量在最小方差投资组合上的投资绩效。分析的结果显示:(1)预平均方法可以剔除绝大部分微观结构噪声对协方差矩阵估计的影响;Huber损失函数也可以减弱重尾现象对协方差矩阵估计的影响;(2)收缩估计量均能更好地估计总体协方差矩阵,并且在最小方差投资策略的比较中也拥有良好的投资绩效。

Microstructure noise and heavy tail phenomena are very common in financial asset return series under the background of high-frequency trading.At the same time,the covariance matrix of financial asset returns is characterized by high dimensionality and sparsity.Based on the pre average method with Huber loss function,a shrinkage estimation of the covariance matrix of financial asset returns in the context of high-frequency financial data is proposed.The simulation results show that the shrinkage estimation performs well.Finally,high-frequency data of Chinese A-share stock market is applied for empirical analysis to explore the investment performance of the estimator on the minimum variance portfolio.The results show that:(1)The pre average method can eliminate the influence of most microstructure noises on covariance matrix estimation;Huber loss function can also weaken the influ-ence of heavy tail on covariance matrix estimation;(2)Shrinkage estimators can better estimate the overall covariance matrix,and have the better performance in the comparison of minimum variance investment strategies.