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On the aggregation of credit, market and operational risks

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Abstract

Risk aggregation considering inter-risk dependence has always been a challenge to both researchers and practitioners. The objective of this study is to formulate ways of aggregation of bank risks and comprehensively compare simple summation, variance–covariance and copula approach. Firstly, the three popular approaches are adopted to aggregate credit risk, market risk and operational risk of banks based on Austrian banking data. Then, two comparisons are mainly made. Total risks aggregated by different approaches are compared to analyze their relative magnitudes. Diversification benefits of different approaches are further compared to investigate their tail dependence structures. Based on the empirical analysis, some facts are verified and some interesting findings are uncovered, leading to the conclusions that simple summation approach is too conservative and variance–covariance approach is overly optimistic, so it is suggested that copula approach is the future major trend for bank risk aggregation. Especially, t copula with degree of freedom between 1 and 10 is a good choice to capture tail dependence while Gaussian copula is not recommended. Besides, the proposed mixture copula consisting of t copula and Gumbel copula exhibits heavier right tail dependence than single t copula.

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Acknowledgments

This research has been supported by Grants from the National Natural Science Foundation of China (71071148, 70701033), Key Research Program of Institute of Policy and Management, Chinese Academy of Sciences (Y201171Z05) and Youth Innovation Promotion Association of the Chinese Academy of Sciences. The author also would like to thank the anonymous reviewers for their very valuable and professional suggestions.

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Authors and Affiliations

  1. Institution of Policy and Management, Chinese Academy of Sciences, Beijing, 100190, China

    Jianping Li, Xiaoqian Zhu & Dengsheng Wu

  2. University of Chinese Academy of Sciences, Beijing, 100190, China

    Xiaoqian Zhu

  3. Department of Finance and Economics, Rutgers University, Newark, NJ, 08854, USA

    Cheng-Few Lee

  4. Industrial Bank Co., Ltd., Fuzhou, 350003, Fujian, China

    Jichuang Feng

  5. School of Management, University of Chinese Academy of Sciences, Beijing, 100190, China

    Yong Shi

  6. College Information Science and Technology, University Nebraska, Omaha, NE, 68182, USA

    Yong Shi

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  1. Jianping Li
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Correspondence to Jianping Li.

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Li, J., Zhu, X., Lee, CF. et al. On the aggregation of credit, market and operational risks. Rev Quant Finan Acc 44, 161–189 (2015). https://doi.org/10.1007/s11156-013-0426-0

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