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In the field of portfolio management, practitioners are focusing increasingly on risk-based portfolios rather than on mean-variance portfolios. Risk-based portfolios are constructed based solely on covariance matrices, and include methods such as minimum variance (MV), risk parity (RP), and maximum diversification (MD). It is well known that the performance of a mean-variance portfolio depends on the accuracy of the estimations of the inputs. However, no studies have examined the relationship between the performance of risk-based portfolios and the estimated accuracy of covariance matrices. In this research, we compare the performance of risk-based portfolios for several estimation methods of covariance matrices in the Japanese stock market. In addition, we propose a highly accurate estimation method called cDCC-NLS, which incorporates nonlinear shrinkage into the cDCC-GARCH model. The results confirm that (1) the cDCC-NLS method shows the best estimation accuracy, (2) the RP and MD do not depend on the estimation accuracy of the covariance matrix, and (3) the MV does depend on the estimation accuracy of the covariance matrix.

Risk-Based Portfolios with Large Dynamic Covariance Matrices