对冲基金尾部风险的极值回归模型中的高效估计
Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risks
AI总结：
本文提出一种自动选择阈值的极值回归模型估计方法，通过辅助拼接密度和人工删失机制提高尾部风险估计效率，并基于1,484只对冲基金数据验证其优于传统方法，揭示尾部风险与市场因素及恐惧溢价的关系。
摘要：
我们提出一种同时估计极值回归模型尾部参数和阈值参数的方法。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，一个主要局限是需要事先选择一个阈值，低于该阈值的数据被丢弃，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，引入辅助拼接密度，使阈值能够自动选择。随后，我们对数据主体部分的似然贡献施加人工删失机制，以减少估计阶段的设定问题。我们通过模拟研究说明了该方法在推断上优于经典的超阈值方法。在实证部分，我们利用1,484只对冲基金的合并收益，研究了对冲基金尾部风险随时间变化的决定因素。我们发现尾部风险与股票动量、金融稳定指数和信用利差等因素之间存在显著关联。此外，根据对我们尾部风险度量的暴露程度对基金进行排序，能够区分高alpha和低alpha基金，支持了恐惧溢价的存在。
英文摘要：
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.
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