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With the recent financial crisis and the increasing interconnectedness of financial institutions, regulators have started to pay more attention to the concept of systemic risk. Whereas most of the systemic risk literature focuses on the banking industry, there has also been a growing interest in the contribution of unregulated funds, e.g. hedge funds. In this study, we propose to look at systemic risk in a universe of funds by the prism of con- ditional extremal tail dependence across the different investment strategies of the funds. Relying on univariate and multivariate extreme value the- ory, we first model the dynamics of style-specific extreme fund losses with a non-stationary generalized Pareto distribution depending on the return characteristics and then study the dynamics of the tail dependencies be- tween fund styles conditional on measures of the economic uncertainty and the stock market performance. We show that economic uncertainty and market stress influence the links between strategy-specific extreme losses.