I recommend you to read a quite current paper in the Journal of Financial Economics which mainly covers the analysis of tail risks (and references to papers which focus on its decomposition):
Agarwal/Ruenzi/Weigert (2017): Tail risk in hedge funds: A unique view from portfolio holdings
They mainly analyze
[...] if tail risk explains the cross-sectional and time-series variation in equity-oriented hedge fund performance and if tail risk in hedge funds arises from their dynamic trading strategies and/or their investments in stocks that are sensitive to equity market crashes.
In summary, they conclude:
Our results therefore suggest that both, funds’ investments in stocks with high tail risk as well as their dynamic trading strategies, contribute to the tail risk.
The clearly and precise written paper also offers you an extensive reference for further papers you are looking for.