Diversification Limit of Quantiles Under Dependence Uncertainty

Extremes. Statistical Theory and Applications in Science, Engineering and Economics ISSN: 1386-1999 (Print) 1572-915X (Online). 2016

26 Pages Posted: 23 Apr 2015 Last revised: 23 Feb 2016

See all articles by Valeria Bignozzi

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance

Bin Wang

Beijing Technology and Business University - Department of Mathematics

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: February 17, 2016

Abstract

In this paper, we investigate the asymptotic behavior of the portfolio diversification ratio based on Value-at-Risk (quantile) under dependence uncertainty, which we refer to as "worst-case diversification limit." We show that the worst-case diversification limit is equal to the upper limit of the worst-case diversification ratio under mild conditions on the portfolio marginal distributions. In the case of regularly varying margins, we provide explicit values for the worst-case diversification limit. Under the framework of dependence uncertainty the worst-case diversification limit is significantly higher compared to classic results obtained in the literature of multivariate regularly varying distributions. The results carried out in this paper bring together extreme value theory and dependence uncertainty, two popular topics in the recent study of risk aggregation.

Keywords: Value-at-Risk, diversification ratio, extreme value analysis, asymptotics, dependence uncertainty

Suggested Citation

Bignozzi, Valeria and Mao, Tiantian and Wang, Bin and Wang, Ruodu, Diversification Limit of Quantiles Under Dependence Uncertainty (February 17, 2016). Extremes. Statistical Theory and Applications in Science, Engineering and Economics ISSN: 1386-1999 (Print) 1572-915X (Online). 2016, Available at SSRN: https://ssrn.com/abstract=2597286 or http://dx.doi.org/10.2139/ssrn.2597286

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Via Bicocca degli Arcimboldi, 8
Milano, 20126
Italy

Tiantian Mao (Contact Author)

University of Science and Technology of China (USTC) - Department of Statistics and Finance ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Bin Wang

Beijing Technology and Business University - Department of Mathematics ( email )

No. 11/33, Fucheng Road, Haidian District
Liangxiang
Beijing, 102488
China

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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