Abstract
Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroskedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present paper aims to marry these two strands of literature in order to deliver improved estimation of large dynamic covariance matrices.
Highlights
Multivariate GARCH models derived from the ARCH/GARCH family started by Engle (1982) are popular tools for risk management and portfolio selection
This paper demonstrates that there is a ‘division of labor’ between composite likelihood and nonlinear shrinkage in the estimation of a Dynamic Conditional Correlation (DCC) model: The former takes care of the dynamic correlation parameters whereas the latter takes care of the correlation targeting matrix
Their actions complement each other. They enable DCC to conquer large dimensions on the order of a thousand, which are frequently encountered in modern portfolio theory and risk management
Summary
Multivariate GARCH models derived from the ARCH/GARCH family started by Engle (1982) are popular tools for risk management and portfolio selection. The number of assets in the investment universe generally poses a challenge to such models. When this number is large, say on the order of a thousand, many multivariate GARCH models exhibit unsatisfactory performance or cannot even be estimated in the first place due to computational problems. The aim of this paper is to robustify the Dynamic Conditional Correlation (DCC) model originally proposed by Engle (2002) against large dimensions. To this end we combine two tools. The second tool is the nonlinear shrinkage method of Ledoit and Wolf (2012) which results in improved estimation of the correlation targeting matrix of a DCC model: Nonlinear shrinkage ensures that DCC performs well when the number of assets is large
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