Large-scale Minimum Variance Portfolio Allocation Using Double Regularization, a paper co-authored by our school’s Professor Zhang Xueyong, Professor Bian Zhicun from Nanjing University of Finance and Economics, Associate Professor Lin Liao from Macquarie University, Michael O’Neill from Investors Mutual Limited, and Jing Shi from Shandong University of Finance and Economics, was officially published on the 2020 116th Volume of Journal of Economic Dynamics and Control, a prestigious journal on economics.
Estimation of time-varying covariance matrices is a crucial input in minimum variance (MV) portfolio allocations. Rolling window-based sample estimates are widely used for this purpose, but they usually suffer from two major issues when applied to a moderately large number of assets: the “curse of dimensionality” and “temporal instability.” In this paper, the authors adopt a cutting-edge machine learning method and propose a doubly-regularized estimator for a high dimensional covariance matrix in which they impose both a temporal and cross-sectional sparsity regularization on the sample-based estimates to simultaneously address these two issues. It investigates the performance of the new estimation method for MV portfolio construction using Monte Carlo experiments and empirical examples. It then finds that the resulting MV portfolio strikes a good balance between risk and turnover reduction, and produces more accurate equivalent returns after transaction costs are taken into account when compared with four other MV strategies.
The paper not only proposes a new methodology, but also examines the effectiveness thereof from experimental and empirical perspectives. In simulation studies, the authors experiment with three scenarios: (1) The real covariance matrix is time-invariant; (2) The real covariance matrix changes discretely with large magnitudes; and (3) The real covariance matrix changes continuously with small magnitudes. This paper builds five MV portfolios based on the DRRW method, and, by comparing their performance with portfolios derived from other estimators, finds that the performance of the DRRW-based portfolios is far better than other portfolios under the above three scenarios. In empirical analysis, it compares the DRRW-based portfolios with Kenneth French’s diversified portfolios, and the random portfolios of the American Stock Exchange and the New York Stock Exchange, and finds that the DRRW-based portfolios all fulfill lower out-of-sample risk levels and more accurate equivalent returns after transaction costs are taken into account. MV strategies built on the DRRW method can not only obtain more stable investment returns, but also strike a good balance between readjusting portfolios to reflect new data and avoiding excessive trading which can result in higher transaction costs.
All in all, the paper comes up with a new DRRW method to estimate covariance matrices, and the MV strategies built on this basis can deliver better investment performance. Meanwhile, it also points out that the DRRW method can be applied to other investment optimization methods and holds great potential for future studies.
