The taxonomy of tail risk

We use tail events at different levels of severity to define an asset's tail risk and to decompose the latter into a systematic and an idiosyncratic component. The systematic component captures an asset's tendency to experience joint tail losses with the market and generalizes a classic tail dependence coefficient. However, the idiosyncratic component consists of two parts: idiosyncratic tail risk that leads to asset-specific tail losses and tail risk cushioning that dampens the tail losses emanating from the market. Tail risk cushioning is a novel concept that arises naturally in our framework, is consistent with the previous two and completes the taxonomy of tail risk. We examine the performance of our tail risk decomposition on a large dataset, confirming some previous results on tail risk and uncovering new theoretical and empirical findings.