Portfolio selection: shrinking the time-varying inverse conditional covariance matrix
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Portfolio selection: shrinking the time-varying inverse conditional covariance matrix Ruili Sun1 · Tiefeng Ma1 · Shuangzhe Liu2 Received: 9 July 2017 / Revised: 15 October 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract In this paper we consider a portfolio selection problem under the global minimum variance model where the optimal portfolio weights only depend on the covariance matrix of asset returns. First, to reflect the rapid changes of financial markets, we incorporate a time-varying factor in the covariance matrix. Second, to improve the estimation of the covariance matrix we use the shrinkage method. Based on these two key aspects, we propose a framework for shrinking the time-varying inverse conditional covariance matrix in order to enhance the performance of the portfolio selection. Furthermore, given the shortcoming that the inverse covariance matrix is inaccurate in a number of cases, we develop a new method that transforms the inverse of the covariance matrix into a product to improve the performance of the inverse covariance matrix, and prove its theoretical availability. The proposed portfolio selection strategy is applied to analyze real-world data and the numerical studies show it performs well. Keywords Inverse conditional covariance matrix · Portfolio selection · Shrinkage · Time-varying
1 Introduction Markowitz’s groundbreaking mean-variance work has profound implications for the development of portfolio selection, see e.g. Markowitz (1952), Gohout and Specht (2007) and Ding et al. (2017). Markowitz (1952) obtained the optimal portfolio weights by maximizing the agent’s utility function. The optimal portfolio weights depend on two parameters, the mean and the covariance matrix of risky asset returns. The true values of the parameters are unknown in practice and investors traditionally estimate
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Shuangzhe Liu [email protected]
1
School of Statistics, Center of Statistical Research, Southwestern University of Finance and Economics, Chengdu 611130, China
2
Faculty of Science and Technology, University of Canberra, Canberra, ACT 2601, Australia
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R. Sun et al.
them using historical data. Then, the estimation error is presented by using the sample estimates to replace the truely unknown parameters. Jobson and Korkie (1980) pointed out that the estimation error was so large that the portfolio weights under the meanvariance framework were likely inefficient. Although a number of results are established to reduce the estimation error, the problem still remains largely unresolved (DeMiguel et al. 2009a). Merton (1980) showed that it was more difficult to estimate the means than the covariances of asset returns. In addition, Chopra and Ziemba (1993) suggested that the estimation errors in the means were typically large. The “problematic” mean of asset returns makes the global minimum variance (GMV) model tend to yield a better performance than the mean-variance model (Kourtis et al. 2012), so the GMV model is widely used in the portfolio selection prob
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