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VaR-implied tail-correlation matrices

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  • Mittnik, Stefan

Abstract

Empirical evidence suggests that asset returns correlate more strongly in bear markets than conventional correlation estimates imply. We propose a method for determining complete tail-correlation matrices based on Value-at-Risk (VaR) estimates. We demonstrate how to obtain more effi cient tail-correlation estimates by use of overidenti cation strategies and how to guarantee positive semidefi niteness, a property required for valid risk aggregation and Markowitz-type portfolio optimization. An empirical application to a 30-asset universe illustrates the practical applicability and relevance of the approach in portfolio management.

Suggested Citation

  • Mittnik, Stefan, 2013. "VaR-implied tail-correlation matrices," CFS Working Paper Series 2013/05, Center for Financial Studies (CFS).
    • Handle: RePEc:zbw:cfswop:201305
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    References listed on IDEAS

    as
    1. Mittnik, Stefan, 2014. "VaR-implied tail-correlation matrices," Economics Letters, Elsevier, vol. 122(1), pages 69-73.
    2. Karolyi, G Andrew & Stulz, Rene M, 1996. "Why Do Markets Move Together? An Investigation of U.S.-Japan Stock Return Comovements," Journal of Finance, American Finance Association, vol. 51(3), pages 951-986, July.
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    19. Markus Haas & Stefan Mittnik, 2009. "Portfolio Selection with Common Correlation Mixture Models," Contributions to Economics, in: Georg Bol & Svetlozar T. Rachev & Reinhold Würth (ed.), Risk Assessment, pages 47-76, Springer.
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    Cited by:

    1. Mittnik, Stefan, 2014. "VaR-implied tail-correlation matrices," Economics Letters, Elsevier, vol. 122(1), pages 69-73.
    2. Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
    3. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    4. Joachim Paulusch, 2017. "The Solvency II Standard Formula, Linear Geometry, and Diversification," JRFM, MDPI, vol. 10(2), pages 1-12, May.
    5. Paulusch, Joachim & Schlütter, Sebastian, 2021. "Sensitivity-implied tail-correlation matrices," ICIR Working Paper Series 33/19, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR), revised 2021.
    6. Aigner, Philipp, 2023. "Identifying scenarios for the own risk and solvency assessment of insurance companies," ICIR Working Paper Series 48/23, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    7. Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    Downside risk; Estimation efficiency; Portfolio optimization; Positive semidefiniteness; Solvency II; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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