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On optimal portfolio diversification with respect to extreme risks

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Abstract

Extreme losses of portfolios with heavy-tailed components are studied in the framework of multivariate regular variation. Asymptotic distributions of extreme portfolio losses are characterized by a functional γ ξ =γ ξ (α,Ψ) of the tail index α, the spectral measure Ψ, and the vector ξ of portfolio weights. Existence, uniqueness, and location of the optimal portfolio are analysed and applied to the minimization of risk measures. It is shown that diversification effects are positive for α>1 and negative for α<1. Strong consistency and asymptotic normality are established for a semiparametric estimator of the mapping ξ ↦ γ ξ . Strong consistency is also established for the estimated optimal portfolio.

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Authors and Affiliations

  1. Department of Mathematical Stochastics, University of Freiburg, Eckerstr. 1, 79104, Freiburg, Germany

    Georg Mainik & Ludger Rüschendorf

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  1. Georg Mainik
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  2. Ludger Rüschendorf
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Correspondence to Georg Mainik.

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Mainik, G., Rüschendorf, L. On optimal portfolio diversification with respect to extreme risks. Finance Stoch 14, 593–623 (2010). https://doi.org/10.1007/s00780-010-0122-z

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