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Stress testing correlation matrices for risk management

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  • So, Mike K.P.
  • Wong, Jerry
  • Asai, Manabu

Abstract

Evaluating portfolio risk typically requires that correlation estimates of security returns be made. Historical financial events have shown that correlations can rise quickly, causing a huge increase in portfolio risk. Therefore, in stress testing portfolios, it is important to consider the influence of a sudden surge in selected correlations. Standard correlation stress testing mechanisms require us to change the selected correlations to designated values. However, the correlation matrix may become non-positive definite after some of its entries are altered. This paper proposes a blocking method by which an existing correlation matrix can be converted to incorporate change while keeping the matrix positive definite. In comparison with existing methods that usually only achieve semi-positive definiteness, the proposed method outperforms in the revised elements, while the approximation error of the non-revised elements is maintained within acceptable levels. Simulations show that our method is efficient and performs well for dimensions of 100, 500 and 1000. Our method is also shown to be more reliable in stress testing higher dimension correlation matrices. Information on the performance of the blocking method using a high-dimensional real data is also provided.

Suggested Citation

  • So, Mike K.P. & Wong, Jerry & Asai, Manabu, 2013. "Stress testing correlation matrices for risk management," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 310-322.
  • Handle: RePEc:eee:ecofin:v:26:y:2013:i:c:p:310-322
    DOI: 10.1016/j.najef.2013.02.007
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    References listed on IDEAS

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    1. Chang, Chia-Lin & McAleer, Michael & Tansuchat, Roengchai, 2013. "Conditional correlations and volatility spillovers between crude oil and stock index returns," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 116-138.
    2. Vineer Bhansali & Mark B. Wise, 2001. "Forecasting Portfolio Risk in Normal and Stressed Markets," Papers nlin/0108022, arXiv.org, revised Sep 2001.
    3. Jeremy Berkowitz, 1999. "A coherent framework for stress-testing," Finance and Economics Discussion Series 1999-29, Board of Governors of the Federal Reserve System (U.S.).
    4. Tan, Kok-Hui & Chan, Inn-Leng, 2003. "Stress testing using VaR approach--a case for Asian currencies," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 13(1), pages 39-55, February.
    5. Alexander, Carol & Sheedy, Elizabeth, 2008. "Developing a stress testing framework based on market risk models," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2220-2236, October.
    6. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
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    Cited by:

    1. Chia-Lin Chang & Allen, David & McAleer, Michael, 2013. "Recent developments in financial economics and econometrics: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 217-226.
    2. Paraschiv, Florentina & Mudry, Pierre-Antoine & Andries, Alin Marius, 2015. "Stress-testing for portfolios of commodity futures," Economic Modelling, Elsevier, vol. 50(C), pages 9-18.
    3. Busch, Ramona & Koziol, Philipp & Mitrovic, Marc, 2015. "Many a little makes a mickle: Macro portfolio stress test for small and medium-sized German banks," Discussion Papers 23/2015, Deutsche Bundesbank.
    4. Yu, Philip L.H. & Li, W.K. & Ng, F.C., 2014. "Formulating hypothetical scenarios in correlation stress testing via a Bayesian framework," The North American Journal of Economics and Finance, Elsevier, vol. 27(C), pages 17-33.

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