高维协方差矩阵估计在A股市场的实证研究

An Empirical Study on Estimation of High-dimensionalCcovariance Matrix in China′s A-share Market

对于高维协方差矩阵估计问题,基于传统的压缩估计理论,从优化角度提出新的估计方法,即寻找距离多个已知估计量的凸组合最近的对称正定矩阵作为高维协方差矩阵的估计量。对带惩罚项和不带惩罚项的两种模型进行研究,给出了相应的求解算法和收敛证明,其中带惩罚项的模型是为了保证优化结果具有良好的稀疏性。实证研究发现,相较于基准指数,基于所给估计量的资产组合获得了超额收益,具有极高的实践价值。

For the high-dimensional covariance matrix estimation problem,a new estimation method based on shrinkage is proposed from the perspective of optimization,that is,finding the symmetric positive definite matrix closest to the convex combination of multiple known estimators as the estimator of the high-dimensional covariance matrix.Two models,with and without penalty are studied,the corresponding algorithm and convergence proof are given.The model with penalty is to ensure a good sparsity of the optimization results.According to the empirical study results,compared with the benchmark portfolio,the portfolio based on the given estimator has obtained excess returns,which has extremely high practical value.