VaR-implied tail-correlation matrices

•We propose a new method for estimating tail correlations.•The method permits direct estimation of complete tail-correlation matrices.•The results are useful for risk assessment and risk management.•Important restrictions, such as positive semidefiniteness, can be imposed.•An empirical application to 30 stocks demonstrates practical usefulness.

Empirical evidence suggests that asset returns correlate more strongly in bear markets than conventional correlation estimates imply. We propose a method for determining complete tail-correlation matrices based on Value-at-Risk (VaR) estimates. We demonstrate how to obtain more efficient tail-correlation estimates by use of overidentification strategies and how to guarantee positive semidefiniteness, a property required for valid risk aggregation and Markowitz-type portfolio optimization. An empirical application to a 30-asset universe illustrates the practical applicability and relevance of the approach in portfolio management.