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CVaR sensitivity with respect to tail thickness

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  • Stoyanov, Stoyan V.
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.

Abstract

We consider the sensitivity of conditional value-at-risk (CVaR) with respect to the tail index assuming regularly varying tails and exponential and faster-than-exponential tail decay for the return distribution. We compare it to the CVaR sensitivity with respect to the scale parameter for stable Paretian, the Student's t, and generalized Gaussian laws and discuss implications for the modeling of daily returns and marginal rebalancing decisions. Finally, we explore empirically the impact on the asymptotic variability of the CVaR estimator with daily returns which is a standard choice for the return frequency for risk estimation.

Suggested Citation

  • Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Fabozzi, Frank J., 2011. "CVaR sensitivity with respect to tail thickness," Working Paper Series in Economics 29, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    • Handle: RePEc:zbw:kitwps:29
    DOI: 10.5445/IR/1000023240
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    3. Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010. "Tempered stable and tempered infinitely divisible GARCH models," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2096-2109, September.
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    7. Mittnik, Stefan & Paolella, Marc S., 2003. "Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions," CFS Working Paper Series 2003/04, Center for Financial Studies (CFS).
    8. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2008. "Financial market models with Lévy processes and time-varying volatility," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1363-1378, July.
    9. Chen, Carl R. & Su, Yuli & Huang, Ying, 2008. "Hourly index return autocorrelation and conditional volatility in an EAR-GJR-GARCH model with generalized error distribution," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 789-798, September.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    1. Berninghaus, Siegfried K. & Todorova, Lora & Vogt, Bodo, 2011. "A simple questionnaire can change everything: Are strategy choices in coordination games stable?," Working Paper Series in Economics 37, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    2. Li, Leon, 2017. "Testing and comparing the performance of dynamic variance and correlation models in value-at-risk estimation," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 116-135.
    3. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    4. Meyborg, Mirja, 2011. "The impact of West-German universities on regional innovation activities: A social network analysis," Working Paper Series in Economics 35, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    5. Schosser, Stephan & Vogt, Bodo, 2011. "The public loss game: An experimental study of public bads," Working Paper Series in Economics 33, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    6. Choi, Jaehyung & Kim, Young Shin & Mitov, Ivan, 2015. "Reward-risk momentum strategies using classical tempered stable distribution," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 194-213.
    7. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Sensitivity analysis of Mixed Tempered Stable parameters with implications in portfolio optimization," Computational Management Science, Springer, vol. 16(1), pages 71-95, February.
    8. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2020. "Risk Analysis through the Half-Normal Distribution," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    9. Mikhail Semenov & Daulet Smagulov, 2017. "Portfolio Risk Assessment using Copula Models," Papers 1707.03516, arXiv.org.
    10. Schaffer, Axel, 2011. "Appropriate policy measures to attract private capital in consideration of regional efficiency in using infrastructure and human capital," Working Paper Series in Economics 31, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    11. Walter Farkas & Ludovic Mathys & Nikola Vasiljevi'c, 2020. "Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps," Papers 2002.04675, arXiv.org, revised Jan 2021.
    12. Akhtaruzzaman, Md & Banerjee, Ameet Kumar & Boubaker, Sabri & Moussa, Faten, 2023. "Does green improve portfolio optimisation?," Energy Economics, Elsevier, vol. 124(C).
    13. Marwa Elnahass & Mohamed Marie & Mohammed Elgammal, 2022. "Terrorist attacks and bank financial stability: evidence from MENA economies," Review of Quantitative Finance and Accounting, Springer, vol. 59(1), pages 383-427, July.
    14. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    15. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    16. Walter Farkas & Ludovic Mathys & Nikola Vasiljević, 2021. "Intra‐Horizon expected shortfall and risk structure in models with jumps," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 772-823, April.
    17. Stoyanov, Stoyan V. & Rachev, Svetlozar T. & Racheva-Iotova, Boryana & Fabozzi, Frank J., 2011. "Fat-tailed models for risk estimation," Working Paper Series in Economics 30, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.

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    More about this item

    Keywords

    fat-tailed distributions; regularly varying tails; conditional value-at-risk; marginal rebalancing; asymptotic variability;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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