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Measures of systemic risk and financial fragility in Korea


This paper provides a quantitative metric for financial stability of Korean commercial banking system based on the Tsomocos (J Math Econ 39(5–6):619–655, 2003) model, for which we use market data as proxies for probabilities of default and equity valuation of the banking sector. We estimate the effect of the probability of default and the equity valuation of the banking sector on real output using a vector error correction model (VECM). In addition, we estimate the contributions of individual banks to systemic risk using CoVaR and MES (Marginal Expected Shortfall). CoVaR is estimated based on the methodology of Adrian and Brunnermeier (2010), and MES is estimated based on Shapley value methodology which has been introduced by Tarashev et al. (2010).

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  1. See Berg (1999), Čihák and Schaeck (2007), Dermirguc-Kunt and Detragiache (1998), Disyatat (2001), Kaminsky and Reinhart (1996), Logan (2000), Vallés and Weistroffer (2008), and Vila (2000).

  2. See BCBS (2011).

  3. See Drehmann and Tarashev (2011).

  4. See Tsomocos (2003); Tsomocos (2004).

  5. In the general version of the model, an increase in default and a decrease in profitability are, typically, associated with a reduction in agents’ welfare (see, Goodhart et al. 2006b).

  6. See Aspachs-Bracons et al. (2007, 2012).

  7. Data of Hana, KB, Shinhan and Woori beyond a specific point (Hana: ’05.12.12, KB: ’08.10.10, Shinhan: ’03.1.1, Woori: ’03.1.1) are stock prices of their holding companies. The data for 2012 Q1 are the average of those for 2012 January and February.

  8. For example, Seo and Lee (2010) argue that CDS spreads of Korea do not represent the unique credit risks of individual banks, as they tend to be highly dependent on macroeconomic and foreign exchange sector variables.

  9. See Segoviano (2009).

  10. Additional analysis will be necessary to discern which JPoD estimation, based either on both data sets or on only one of the data sets, represents the status of the Korea’s financial system more appropriately. Meanwhile, according to our estimation for the financial stability index, each using CDS spreads, bond spreads, or both sets of data, the results exhibit no significant difference.

  11. The monthly average of JPoD is not stationary, and I(1). These monthly data {ipi, eq, jpod} are also cointegrated.

  12. As real interest rate and inflation are representative macroeconomic variables that may have significant effects on GDP, they are frequently used in small macroeconomic VAR models. So we tried to add these variables to our baseline model to check robustness.

  13. The real TB03 is not stationary, and I(1). All the data sets for robustness check based on both quarterly and monthly are also cointegrated.

  14. The relative weights are similar to the results of Aspachs-Bracons et al. (2012) that analyses ten countries, including Belgium, France, Germany, Italy, Japan, Netherlands, Spain, Switzerland, UK and US.

  15. Co-developed by Adrian and Brunnermeier (2008, 2009) and Adrian and Brunnermeier (2010).

  16. CoVaR means the extent to which banks’ returns move together. \(\Delta \)CoVaR, however, implies a single institution’s contribution to the entire systemic risk in the case where \(j\) = system, i.e., when the return of the portfolio of all financial institutions is at its VaR level according to Adrian and Brunnermeier (2010). They argue that the measure \(\Delta \text{ CoVaR}^{i}\) quantiles how much an institution adds to overall systemic risk. The measure should capture externalities that arise because an institution is “too big to fail”, or “too interconnected to fail”, or takes on positions or relies on funding that can lead to crowded trades. For more details, please refer to the pp. 9–10, Adrian and Brunnermeier (2010).

  17. However, BCBS agreed that more review is needed to use \(\Delta \)CoVaR for the purpose of regulation.

  18. The initial work of Adrian and Brunnermeier (2008, 2009) on CoVaR defines \(\Delta \textit{CoVa}R_q^{\textit{system}|i} \) as the difference between CoVaR and VaR (In other words,\(\Delta \textit{CoVa}R_q^{\textit{system}|i} =\textit{CoVaR}_q^{\textit{system}|i} -VaR_q^{\textit{system}} )\), but in 2010 elaborate the definition.

  19. Under the assumption that the return of a financial institution is the function of state variables M, we estimate time-varying \(\Delta \)VaR using quantile regression. We include a set of state variables M that are well known to capture time variation in conditional moments of asset return, and are liquid and easily tradable (Adrian and Brunnermeier 2010).

  20. State variable vector consists of the VIX (KOSPI200 Volatility Index), Short term liquidity spread (CD (91 days)- Government bonds (3-month)), Changes of government bonds (3-month), Changes in yield curve (Difference of Government bonds (10-year)—Government bonds (3-month)), Changes in credit spread (Difference of corporate bonds (BBB-, 3-year)—Government bonds (3-year)), and Stock market return (KOSPI volatility rate).

  21. This seems to be due mainly to the fact that, unlike the relationships among banks in advanced countries such as the US, the interconnectedness among Korean commercial banks, which is captured as the \(\Delta \)CoVaR, is low, so that the \(\Delta \)CoVaR is not much different from the VaR measuring individual banks’ losses. In addition, according to an anonymous referee of this paper, the reason for a high correlation between CoVaR and VaR measures is probably due to the difference of the financial institutions in the samples. That is, the difference can be caused by the fact that the paper is studying commercial banks while Adrian and Brunnermeier (2010) include investment banks and insurance companies.

  22. Acharya et al. (2010) and Brownless and Engle (2010) have also estimated MES.

  23. Monte Carlo simulations are usually used in cases where there is a lack of previous direct time series of variables to be measured, credibility is low due to insufficient information on previous time series or ample noise, and it is impossible to measure time series of variables directly.

  24. Allocation part using Shapley value methodology in the program for MES estimation is developed by Lee Seung Hwan, Marcroprudential Analysis Department of Bank of Korea. We verified the accuracy of the program. We would like to thank him for his help.

  25. If any financial institution does not exist in financial system, the systemic risk is 0.


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We are grateful to Gong Pil Choi, Charles Goodhart, Tae Soo Kang, Dae Sik Kim, Hoon Kim, Li Lin, Juan Francisco Martinez, Byung Hee Seong, Jong Suk Won, an anonymous referee and the participants of the “Systemic Risk and Financial Stability” seminar at the Bank of Korea in January 2012 for their helpful comments. We especially thank an anonymous referee, Seung Hwan Lee and Miguel Segoviano for providing us with excellent technical assistance and computer codes. However, all remaining errors are ours. This work is compiled with the financial support of the Bank of Korea. Dimitrios Tsomocos gratefully acknowledges the support and the hospitality of the Bank of Korea.

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Correspondence to Dimitrios P. Tsomocos.

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The views expressed herein are those of the authors and do not necessarily reflect the official views of the Bank of Korea.

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Lee, J.H., Ryu, J. & Tsomocos, D.P. Measures of systemic risk and financial fragility in Korea. Ann Finance 9, 757–786 (2013).

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  • Financial stability
  • Systemic risk
  • JPoD
  • CoVaR
  • MES
  • Shapley value

JEL Classification

  • E30
  • E44
  • G01
  • G10
  • G18
  • G20
  • G28