Decomposing and Backtesting a Flexible Specification for CoVaR

The Conditional Value-at-Risk (CoVaR) proposed by Adrian and Brunnermeier (2016) - which quantifies the impact of a company in distress on the Value-at-Risk (VaR) of the financial system - has established itself as a reference measure of systemic risk. In this study, we extend the CoVaR along two dimensions, which lead respectively to: i) the Conditional Autoregressive VaR (CoCaViaR), in which we include autoregressive components of conditional quantiles to explicitly capture volatility clustering and heteroskedasticity; ii) the Conditional Quantile Located VaR (QL-CoVaR), which accentuates the degree of distress in the connections between the conditioning companies and the financial system, as the parameters are estimated by directly linking the left tails of their returns' distributions. By combining the two new risk measures, we also build the Conditional Autoregressive Quantile-Located VaR (QL-CoCaViaR) and introduce a new backtesting method. A large empirical analysis highlights the validity of such approaches and critically discuss their pros and cons. In particular, including quantile-located relationships leads to relevant improvements in terms of predictive accuracy during stressed periods and, therefore, provides a valuable tool for regulators to assess systemic events