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Heavy tails and copulas: Limits of diversification revisited

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  • Ibragimov, Rustam
  • Prokhorov, Artem

Abstract

We show that diversification does not reduce Value-at-Risk for a large class of dependent heavy tailed risks. The class is characterized by power law marginals with tail exponent no greater than one and by a general dependence structure which includes some of the most commonly used copulas.

Suggested Citation

  • Ibragimov, Rustam & Prokhorov, Artem, 2016. "Heavy tails and copulas: Limits of diversification revisited," Economics Letters, Elsevier, vol. 149(C), pages 102-107.
    • Handle: RePEc:eee:ecolet:v:149:y:2016:i:c:p:102-107
    DOI: 10.1016/j.econlet.2016.10.024
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    14. Chen, Die & Mao, Tiantian & Pan, Xiaoqing & Hu, Taizhong, 2012. "Extreme value behavior of aggregate dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 99-108.
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    19. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    20. Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
    21. Walden, Johan & Ibragimov, Rustam, 2008. "Portfolio Diversification under Local and Moderate Deviations from Power Laws," Scholarly Articles 2640586, Harvard University Department of Economics.
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    Citations

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    Cited by:

    1. Di Lascio, F. Marta L. & Giammusso, Davide & Puccetti, Giovanni, 2018. "A clustering approach and a rule of thumb for risk aggregation," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 236-248.
    2. Fries, Sébastien, 2018. "Conditional moments of noncausal alpha-stable processes and the prediction of bubble crash odds," MPRA Paper 97353, University Library of Munich, Germany, revised Nov 2019.
    3. Ling Peng & Dong Han, 2021. "The Convergence Rate of High-Dimensional Sample Quantiles for φ -Mixing Observation Sequences," Mathematics, MDPI, vol. 9(6), pages 1-8, March.
    4. Umberto Cherubini & Paolo Neri, 2017. "Value-at-Risk Diversification of $\alpha$-stable Risks: The Tail-Dependence Puzzle," Papers 1704.07235, arXiv.org.
    5. Gkillas, Konstantinos & Katsiampa, Paraskevi, 2018. "An application of extreme value theory to cryptocurrencies," Economics Letters, Elsevier, vol. 164(C), pages 109-111.
    6. Marina Friedrich & Sébastien Fries & Michael Pahle & Ottmar Edenhofer, 2020. "Rules vs. Discretion in Cap-and-Trade Programs: Evidence from the EU Emission Trading System," CESifo Working Paper Series 8637, CESifo.
    7. Alexander Shulzhenko, 2023. "Copula-based deviation measure of cointegrated financial assets," Papers 2312.02081, arXiv.org.
    8. Pertaia, Giorgi & Prokhorov, Artem & Uryasev, Stan, 2022. "A new approach to credit ratings," Journal of Banking & Finance, Elsevier, vol. 140(C).
    9. Hans Rau-Bredow, 2019. "Bigger Is Not Always Safer: A Critical Analysis of the Subadditivity Assumption for Coherent Risk Measures," Risks, MDPI, vol. 7(3), pages 1-18, August.

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    More about this item

    Keywords

    Value at risk; Diversification; Power law; Power-type copulas;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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