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Dependence Modeling

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Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

Xisong Jin / Thorsten Lehnert
Published Online: 2018-02-07 | DOI: https://doi.org/10.1515/demo-2018-0002


Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1) Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4) Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a flexible and applicable alternative for optimal portfolio risk management.

Keywords: risk management; assets allocation; VaR; ES; dynamic conditional correlation (DCC); dynamic equicorrelation (DECO); dynamic copula

MSC 2010: 62H20; 62P05; 91B30


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About the article

Received: 2016-12-08

Accepted: 2017-12-22

Published Online: 2018-02-07

Citation Information: Dependence Modeling, Volume 6, Issue 1, Pages 19–46, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2018-0002.

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© 2018, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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