A Regularized K-means Autoregressive Shrinkage Method to Portfolio Optimization

Abstract

Estimation is always an issue of portfolio optimization. To address this issue this paper started from addressing global minimum variance (GMV) portfolio, which gives the weights as the function of estimated covariance matrix of the asset net returns. The inverse operation of the matrix always leads to ill-conditioned matrix due to the noise in the return series. Therefore, regularized sample covariance matrix is often used to address this problem. In this work, a regularized autoregressive shrinkage method for covariance matrix estimation with the historical data is developed, which regards the future covariance matrix as the function of the historical covariance matrix. K-means clustering algorithm is also added to enhance the performance of the regularized autoregressive model. The results demonstrate that the performance of GMV portfolio can be enhanced with regularization under autoregressive shrinkage model.