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Diversification in heavy-tailed portfolios: properties and pitfalls

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  • Mainik, Georg
  • Embrechts, Paul

Abstract

We discuss risk diversification in multivariate regularly varying models and provide explicit formulas for Value-at-Risk asymptotics in this case. These results allow us to study the influence of the portfolio weights, the overall loss severity, and the tail dependence structure on large portfolio losses. We outline sufficient conditions for the sub- and superadditivity of the asymptotic portfolio risk in multivariate regularly varying models and discuss the case when these conditions are not satisfied. We provide several examples to illustrate the resulting variety of diversification effects and the crucial impact of the tail dependence structure in infinite mean models. These examples show that infinite means in multivariate regularly varying models do not necessarily imply negative diversification effects. This implication is true if there is no loss-gain compensation in the tails, but not in general. Depending on the loss-gain compensation, asymptotic portfolio risk can be subadditive, superadditive, or neither.

Suggested Citation

  • Mainik, Georg & Embrechts, Paul, 2013. "Diversification in heavy-tailed portfolios: properties and pitfalls," Annals of Actuarial Science, Cambridge University Press, vol. 7(1), pages 26-45, March.
  • Handle: RePEc:cup:anacsi:v:7:y:2013:i:01:p:26-45_00
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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. Einmahl, John & Yang, Fan & Zhou, Chen, 2018. "Testing the Multivariate Regular Variation Model," Other publications TiSEM dd3c4dd0-7181-40f3-af44-f, Tilburg University, School of Economics and Management.
    3. Georg Mainik & Georgi Mitov & Ludger Ruschendorf, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Papers 1505.04045, arXiv.org.
    4. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    5. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    6. Andreas Muhlbacher & Thomas Guhr, 2018. "Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations," Papers 1803.00261, arXiv.org.
    7. Peter Tankov, 2014. "Tails of weakly dependent random vectors," Papers 1402.4683, arXiv.org, revised Jan 2016.

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