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Portfolio diversification and value at risk under thick-tailedness

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  • Rustam Ibragimov

Abstract

This paper focuses on the study of portfolio diversification and value at risk analysis under heavy-tailedness. We use a notion of diversification based on majorization theory that will be explained in the text. The paper shows that the stylized fact that portfolio diversification is preferable is reversed for extremely heavy-tailed risks or returns. However, the stylized facts on diversification are robust to heavy-tailedness of risks or returns as long as their distributions are moderately heavy-tailed. Extensions of the results to the case of dependence, including convolutions of α-symmetric distributions and models with common shocks are provided.

Suggested Citation

  • Rustam Ibragimov, 2009. "Portfolio diversification and value at risk under thick-tailedness," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 565-580.
  • Handle: RePEc:taf:quantf:v:9:y:2009:i:5:p:565-580 DOI: 10.1080/14697680802629384
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    Cited by:

    1. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    2. Hyung, Namwon & de Vries, Casper G., 2012. "Simulating and calibrating diversification against black swans," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1162-1175.
    3. Ibragimov, Rustam & Prokhorov, Artem, 2016. "Heavy tails and copulas: Limits of diversification revisited," Economics Letters, Elsevier, vol. 149(C), pages 102-107.
    4. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2015. "Conditional risk measures in a bipartite market structure," Papers 1510.00616, arXiv.org.
    5. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2012. "International diversification: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 871-885.
    6. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Sanctions and the Russian stock market," Research in International Business and Finance, Elsevier, pages 150-162.
    7. Huang, Wei & Liu, Qianqiu & Ghon Rhee, S. & Wu, Feng, 2012. "Extreme downside risk and expected stock returns," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1492-1502.
    8. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    9. Enrico Biffis & Erik Chavez, 2014. "Tail Risk in Commercial Property Insurance," Risks, MDPI, Open Access Journal, vol. 2(4), pages 1-18, September.
    10. Oliver Kley & Claudia Kluppelberg & Gesine Reinert, 2014. "Risk in a large claims insurance market with bipartite graph structure," Papers 1410.8671, arXiv.org, revised Nov 2015.
    11. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    12. Tong, Bin & Wu, Chongfeng & Xu, Weidong, 2012. "Risk concentration of aggregated dependent risks: The second-order properties," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 139-149.
    13. Michael Grabchak, 2014. "Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes?," Annals of Finance, Springer, vol. 10(4), pages 553-568, November.
    14. Ibragimov, Rustam, 2014. "On the robustness of location estimators in models of firm growth under heavy-tailedness," Journal of Econometrics, Elsevier, vol. 181(1), pages 25-33.
    15. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Extreme movements of the Russian stock market and their consequences for management and economic modeling," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 45, pages 75-92.
    16. repec:eee:ememar:v:32:y:2017:i:c:p:200-219 is not listed on IDEAS
    17. Lundtofte, Frederik, 2015. "Banks’ pooling of corporate debt: An application of the restated diversification theorem," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 249-263.
    18. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
    19. Ibragimov, Rustam & Jaffee, Dwight & Walden, Johan, 2011. "Diversification disasters," Journal of Financial Economics, Elsevier, vol. 99(2), pages 333-348, February.

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