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Risk Aggregation by a Copula with a Stressed Condition

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  • Toshinao Yoshiba

    (Bank of Japan)

Abstract

This paper examines the marginal distributions of stocks and bonds, and a copula between the movement of stock prices and interest rates. Because some widely used aggregation methods such as variance-covariance tend to underestimate the risk of an aggregated portfolio, a copula is utilized for risk aggregation, which captures various dependencies in the median and the tail of marginal distributions, unlike a linear correlation. In this study, various types of copula, including one that simultaneously captures both positive and negative linear correlations, are analyzed under several time periods. We examine data related to the Euro crisis and the post-bubble period in Japan. Our analyses show that widely used risk aggregation methods may overestimate the diversification effect.

Suggested Citation

  • Toshinao Yoshiba, 2013. "Risk Aggregation by a Copula with a Stressed Condition," Bank of Japan Working Paper Series 13-E-12, Bank of Japan.
    • Handle: RePEc:boj:bojwps:13-e-12
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    File URL: http://www.boj.or.jp/en/research/wps_rev/wps_2013/data/wp13e12.pdf
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    References listed on IDEAS

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    1. repec:oup:rfinst:v:25:y::i:12:p:3711-3751 is not listed on IDEAS
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    3. Peter Christoffersen & Vihang Errunza & Kris Jacobs & Hugues Langlois, 2012. "Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach," The Review of Financial Studies, Society for Financial Studies, vol. 25(12), pages 3711-3751.
    4. Yoshiyuki Fukuda & Kazutoshi Kan & Yoshihiko Sugihara, 2013. "Banks' Stockholdings and the Correlation between Bonds and Stocks: A Portfolio Theoretic Approach," Bank of Japan Working Paper Series 13-E-6, Bank of Japan.
    5. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309.
    6. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
    7. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
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    Cited by:

    1. Toshinao Yoshiba, 2015. "Risk Aggregation with Copula for Banking Industry," IMES Discussion Paper Series 15-E-01, Institute for Monetary and Economic Studies, Bank of Japan.
    2. Takaaki Koike & Mihoko Minami, 2017. "Estimation of Risk Contributions with MCMC," Papers 1702.03098, arXiv.org, revised Jan 2019.

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    Keywords

    copula; multivariate distribution; tail dependency; risk aggregation; economic capital;
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