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.