Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risks

Paper: arXiv 2304.06950

Authors: Julien Hambuckers, Marie Kratz, Antoine Usseglio-Carleve

Abstract

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated extension to extreme value regression models by addressing threshold selection via auxiliary splicing and artificial censoring. It backs up this theoretical contribution with both a thorough simulation study and extensive empirical analysis using a large panel of hedge fund returns.

Research Flowchart

  flowchart TD
    A[Goal: Automate Threshold Selection & Estimate Tail Risks in EV Regression] --> B[Model Development: Tail Regression + Auxiliary Splicing Density]
    B --> C[Method: Artificial Censoring of Bulk Data Likelihood]
    D[Input: 1,484 Hedge Fund Pooled Returns & Market Factors] --> E[Estimation & Empirical Analysis]
    C --> E
    E --> F[Finding 1: Tail Risk Driven by Equity Momentum, Credit Spreads & Financial Stability]
    E --> G[Finding 2: High Tail Risk Exposure Commands a Fear Premium / Higher Alpha]