A Sparse Approximate Factor Model for High-Dimensional Covariance Matrix Estimation and Portfolio Selection
提出一种基于L1正则化近似因子模型的稀疏协方差矩阵估计方法，允许弱因子存在，放松了标准模型的普遍性假设，在模拟和实际投资组合预测中表现优于其他方法。
Abstract We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model (AFM). Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard AFM. We prove the consistency of the covariance matrix estimator under the Frobenius norm as well as the consistency of the factor loadings and the factors. Our Monte Carlo simulations reveal that the SAF covariance estimator has superior properties in finite samples for low and high dimensions and different designs of the covariance matrix. Moreover, in an out-of-sample portfolio forecasting application, the estimator uniformly outperforms alternative portfolio strategies based on alternative covariance estimation approaches and modeling strategies including the 1/N-strategy.