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Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics

Author

Listed:
  • Paulo M.M. Rodrigues
  • João Nicolau
Abstract
This paper provides novel theoretical results for the estimation of the conditional tail index of Pareto and Pareto-type distributions in a time series context. We show that both the estimators and relevant test statistics are normally distributed in the limit, when independent and identically distributed or dependent data are considered. Simulation results provide support for the theoretical findings and highlight the good finite sample properties of the approach in a time series context. The proposed methodology is then used to analyze stock returns’ tail risk dynamics. Two empirical applications are provided. The first consists in testing whether the time-varying tail exponents across firms follow Kelly and Jiang’s (2014) assumption of common firm level tail dynamics. The results obtained from our sample seem not to favour this hypothesis. The second application, consists of the evaluation of the impact of two market risk indicators, VIX and Expected Shortfall (ES) and two firm specific covariates, capitalization and market-to-book on stocks tail risk dynamics. Although all variables seem important drivers of firms’ tail risk dynamics, it is found that overall ES and firms’ capitalization seem to have overall wider impact.

Suggested Citation

  • Paulo M.M. Rodrigues & João Nicolau, 2023. "Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics," Working Papers w202306, Banco de Portugal, Economics and Research Department.
    • Handle: RePEc:ptu:wpaper:w202306
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    Cited by:

    1. Yuya Sasaki & Jing Tao & Yulong Wang, 2024. "High-Dimensional Tail Index Regression: with An Application to Text Analyses of Viral Posts in Social Media," Papers 2403.01318, arXiv.org, revised Oct 2024.
    2. Jo~ao Nicolau & Paulo M. M. Rodrigues, 2024. "A simple but powerful tail index regression," Papers 2409.13531, arXiv.org.
    3. Federico Gatta & Fabrizio Lillo & Piero Mazzarisi, 2024. "CAESar: Conditional Autoregressive Expected Shortfall," Papers 2407.06619, arXiv.org.

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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