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Efficient and robust portfolio optimization in the multivariate Generalized Hyperbolic framework

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  • Martin Hellmich
  • Stefan Kassberger

Abstract

In this paper, we apply the multivariate Generalized Hyperbolic (mGH) distribution to portfolio modelling, using Conditional Value at Risk (CVaR) as a risk measure. Exploiting the fact that portfolios whose constituents follow an mGH distribution are univariate GH distributed, we prove some results relating to measurement and decomposition of portfolio risk, and show how to efficiently tackle portfolio optimization. Moreover, we develop a robust portfolio optimization approach in the mGH framework, using Worst Case Conditional Value at Risk (WCVaR) as risk measure.

Suggested Citation

  • Martin Hellmich & Stefan Kassberger, 2011. "Efficient and robust portfolio optimization in the multivariate Generalized Hyperbolic framework," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1503-1516.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:10:p:1503-1516
    DOI: 10.1080/14697680903280483
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    Cited by:

    1. Leovardo Mata Mata & José Antonio Núñez Mora & Ramona Serrano Bautista, 2021. "Multivariate Distribution in the Stock Markets of Brazil, Russia, India, and China," SAGE Open, , vol. 11(2), pages 21582440211, April.
    2. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    3. Nuerxiati Abudurexiti & Erhan Bayraktar & Takaki Hayashi & Hasanjan Sayit, 2024. "Two-fund separation under hyperbolically distributed returns and concave utility function," Papers 2410.04459, arXiv.org.
    4. Jose Luis Alayon G., 2015. "Distribucion hiperbolica generalizada: una aplicacion en la seleccion de portafolios y en cuantificacion de medidas de riesgo de mercado," Revista de Economía del Rosario, Universidad del Rosario, vol. 18(2), pages 249-308, December.
    5. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    6. Akihiko Takahashi & Kyo Yamamoto, 2009. "Generating a Target Payoff Distribution with the Cheapest Dynamic Portfolio: An Application to Hedge Fund Replication," CARF F-Series CARF-F-308, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2013.
    7. Akihiko Takahashi & Kyo Yamamoto, 2009. "Generating a Target Payoff Distribution with the Cheapest Dynamic Portfolio: An Application to Hedge Fund Replication," CIRJE F-Series CIRJE-F-624, CIRJE, Faculty of Economics, University of Tokyo.
    8. Hasanjan Sayit, 2022. "A discussion of stochastic dominance and mean-risk optimal portfolio problems based on mean-variance-mixture models," Papers 2202.02488, arXiv.org, revised Jul 2023.
    9. Jiang, Yifu & Olmo, Jose & Atwi, Majed, 2024. "Dynamic robust portfolio selection under market distress," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).
    10. Kim, Joseph H.T. & Kim, So-Yeun, 2019. "Tail risk measures and risk allocation for the class of multivariate normal mean–variance mixture distributions," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 145-157.
    11. Wang, Chou-Wen & Liu, Kai & Li, Bin & Tan, Ken Seng, 2022. "Portfolio optimization under multivariate affine generalized hyperbolic distributions," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 49-66.
    12. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    13. Maria Scutellà & Raffaella Recchia, 2013. "Robust portfolio asset allocation and risk measures," Annals of Operations Research, Springer, vol. 204(1), pages 145-169, April.
    14. Mikl'os R'asonyi & Hasanjan Sayit, 2022. "Exponential utility maximization in small/large financial markets," Papers 2208.06549, arXiv.org, revised Feb 2024.
    15. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.

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