Efficient estimation in extreme value regression models of hedge funds tail risks

Extreme value regression offers a convenient framework to assess the effect of market variables on hedge funds tail risks, proxied by the tail index of the cross-section of hedge funds returns. However, its major limitation lies in the need to select a threshold below which data are discarded, leading to significant estimation inefficiencies. In this paper, our main contribution consists in introducing a method to estimate simultaneously the tail index and the threshold parameter from the entire sample at hand, improving estimation efficiency. To do so, we extend the tail regression model to non-tail observations with an auxiliary splicing density, enabling the threshold to be internally determined without truncating the data. We then apply an artificial censoring mechanism to decrease specification issues at the estimation stage. Empirically, we investigate the determinants of hedge funds tail risks over time, and find a significant link with funding liquidity indicators. We also find that our tail risk measure has a significant predictive ability for the returns of around 25\% of the funds. In addition, sorting funds along a tail risk sensitivity measure, we are able to discriminate between high- and low-alpha funds under some asset pricing models.