We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions of investment vehicles such as hedge funds. However, a major limitation is the need to select ex ante a threshold below which data are discarded, leading to estimation inefficiencies. To solve these issues, we extend the tail regression model to non-tail observations with an auxiliary splicing density, enabling the threshold to be selected automatically. We then apply an artificial censoring mechanism of the likelihood contributions in the bulk of the data to decrease specification issues at the estimation stage. We illustrate the superiority of our approach for inference over classical peaks-over-threshold methods in a simulation study. Empirically, we investigate the determinants of hedge fund tail risks over time, using pooled returns of 1,484 hedge funds. We find a significant link between tail risks and factors such as equity momentum, financial stability index, and credit spreads. Moreover, sorting funds along exposure to our tail risk measure discriminates between high and low alpha funds, supporting the existence of a fear premium.

翻译：我们提出一种方法，用于同时估计极值回归模型的尾部参数和阈值参数。该标准模型在金融领域用于评估市场变量对对冲基金等投资工具极端损失分布的影响。然而，其主要局限在于需要事先选择阈值，低于该阈值的数据将被舍弃，从而导致估计效率低下。为解决这些问题，我们将尾部回归模型扩展到非尾部观测值，借助辅助拼接密度实现阈值的自动选择。随后，我们对数据主体部分的似然贡献应用人工审查机制，以减少估计阶段的设定问题。通过模拟研究，我们证明该方法在推断上优于传统的峰值超过阈值方法。在实证分析中，我们利用1,484只对冲基金的合并收益数据，考察对冲基金尾部风险随时间变化的决定因素。研究发现尾部风险与股票动量、金融稳定指数及信用利差等因素之间存在显著关联。此外，根据我们对尾部风险敞口的暴露程度对基金进行分组，能够区分高阿尔法与低阿尔法基金，支持恐惧溢价的存在。