Annals of Operations Research

, Volume 253, Issue 1, pp 21–41 | Cite as

The equity risk posed by the too-big-to-fail banks: a Foster–Hart estimation

  • Abhinav Anand
  • Tiantian Li
  • Tetsuo Kurosaki
  • Young Shin Kim
Original Paper


The measurement of financial risk relies on two factors: determination of riskiness by use of an appropriate risk measure; and the distribution according to which returns are governed. Wrong estimates of either, severely compromise the accuracy of computed risk. We identify the too-big-to-fail banks with the set of “Global Systemically Important Banks” (G-SIBs) and analyze the equity risk of its equally weighted portfolio by means of the “Foster–Hart risk measure”—a bankruptcy-proof, reserve based measure of risk, extremely sensitive to tail events. We model banks’ stock returns as an ARMA–GARCH process with multivariate “Normal Tempered Stable” innovations, to capture the skewed and leptokurtotic nature of stock returns. Our union of the Foster–Hart risk modeling with fat-tailed statistical modeling bears fruit, as we are able to measure the equity risk posed by the G-SIBs more accurately than is possible with current techniques.


Financial risk Normal Tempered Stable distribution Foster–Hart risk Value-at-Risk (VaR) Average Value-at-Risk (AVaR) 



The opinions, findings, conclusions or recommendations expressed in this paper are our own and do not necessarily reflect the views of the Bank of Japan. Abhinav Anand gratefully acknowledges financial support by the Science Foundation Ireland Under Grant Number 08/SRC/FMC1389. Tiantian Li thanks financial support by the National Natural Science Foundation of China Under Grant Number 71471119. We would like to express our gratitude to Svetlozar Rachev for methodological guidance and constant encouragement without which this research would have been impossible. We also thank Sandro Brusco, Yair Tauman and Hugo Benitez-Silva; and to Xin Tang for their critical commentary on an earlier version of this work. Special thanks are in order to Bruno Badia, for suggestions for improvements on a previous draft of this working paper. All remaining flaws of course, are entirely our own.


  1. Admati, A., & Hellwig, M. (2013). The Bankers’ new clothes: What’s wrong with banking and what to do about it. Princeton, NJ: Princeton University Press.Google Scholar
  2. Alexander, S. S. (1961). Price movements in speculative markets: Trends or random walks. Industrial Management Review, 2, 7–25.Google Scholar
  3. Anand, A., Li, T., Kurosaki, T., & Kim, Y. S. (2016). Foster-Hart optimal portfolios. Journal of Banking and Finance, 68, 117–130.CrossRefGoogle Scholar
  4. Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1998). Coherent measures of risk. Mathematical Finance, 6(3), 203–228.Google Scholar
  5. Barndorff-Nielsen, O. E., & Shephard, N. (2001). Normal modified stable processes. Economics Series Working Papers from University of Oxford, Department of Economics 72.Google Scholar
  6. Barndorff-Nielsen, O. E., & Levendorskii, S. Z. (2001). Feller processes of normal inverse gaussian type. Quantitative Finance, 1(3), 318–331.CrossRefGoogle Scholar
  7. Berkowitz, J. (2001). Testing density forecasts, with applications to risk management. Journal of Business and Economic Statistics, 19, 465–474.CrossRefGoogle Scholar
  8. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307–327.CrossRefGoogle Scholar
  9. Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 39(4), 841–862.CrossRefGoogle Scholar
  10. Engle, R. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica, 4, 987–1008.CrossRefGoogle Scholar
  11. Fama, E. F. (1963). Mandelbrot and the stable Paretian hypothesis. Journal of Business, 36, 420–429.CrossRefGoogle Scholar
  12. Fama, E. F. (1965). The behavior of stock market prices. Journal of Business, 38, 34–105.CrossRefGoogle Scholar
  13. FinAnalytica Inc. (2014). Cognity 4.0.
  14. Foster, D. P., & Hart, S. (2009). An operational measure of riskiness. Journal of Political Economy, 117(5), 785–814.CrossRefGoogle Scholar
  15. Haas, M., & Pigorsch, C. (2009). Financial economics, fat-tailed distributions. In R. A. Meyers (Ed.), Complex systems in finance and econometrics (pp. 308–339). New York: Springer.Google Scholar
  16. Hodrick, R., & Prescott, E. C. (1997). Postwar U.S. business cycles: An empirical investigation. Journal of Money, Credit and Banking, 29(1), 1–16.CrossRefGoogle Scholar
  17. Kim, Y. S., Giacometti, R., Rachev, S. T., Fabozzi, F. J., & Mignacca, D. (2012). Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model. Annals of Operations Research, 201(1), 325–343.CrossRefGoogle Scholar
  18. Kim, Y. S., Rachev, S. T., Bianchi, M. L., & Fabozzi, F. J. (2008). Financial market models with Levy processes and time-varying volatility. Journal of Banking and Finance, 32(7), 1363–1378.CrossRefGoogle Scholar
  19. Kim, Y. S., Rachev, S. T., Bianchi, M. L., & Fabozzi, F. J. (2010). Tempered stable and tempered infinitely divisible GARCH models. Journal of Banking and Finance, 34, 2096–2109.CrossRefGoogle Scholar
  20. Kim, Y. S., Rachev, S. T., Bianchi, M. L., Mitov, I., & Fabozzi, F. J. (2011). Time series analysis for financial market meltdowns. Journal of Banking and Finance, 35, 1879–1891.CrossRefGoogle Scholar
  21. Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 6, 6–24.Google Scholar
  22. Kurosaki, T., & Kim, Y. S. (2013). Sytematic risk measurement in the global banking stock market with time series analysis and CoVaR. Investment Management and Financial Innovations, 10(1), 184–196.Google Scholar
  23. Mandelbrot, B. (1963a). New methods in statistical economics. Journal of Political Economy, 71, 421–440.CrossRefGoogle Scholar
  24. Mandelbrot, B. (1963b). The variation of certain speculative prices. Journal of Business, 36, 394–419.CrossRefGoogle Scholar
  25. Mandelbrot, B. (1967). The variation of some other speculative prices. Journal of Business, 40, 393–413.CrossRefGoogle Scholar
  26. Rachev, S. T., Schwartz, E., & Khindanova, I. (2003). Stable modeling of credit risk. In S. T. Rachev (Ed.), Handbook of heavy tailed distributions in finance. Amsterdam: North Holland.Google Scholar
  27. Rachev, S. T., Stoyanov, S., Biglova, A., & Fabozzi, F. (2005). An empirical examination of daily stock return distributions for US stocks. In D. Baier, R. Decker & L. Schmidt-Thieme (Eds.), Data analysis and decision support. Berlin: Springer.Google Scholar
  28. Rachev, S. T., & Mittnik, S. (2000). Stable Paretian models in finance. Hoboken, NJ: Wiley.Google Scholar
  29. Riedel, F., & Hellmann, T. (2015). The Foster–Hart measure of riskiness for general gambles. Theoretical Economics, 10, 1–9.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Abhinav Anand
    • 1
  • Tiantian Li
    • 2
  • Tetsuo Kurosaki
    • 3
  • Young Shin Kim
    • 4
  1. 1.Financial Mathematics and Computation Cluster, Michael Smurfit Graduate Business SchoolUniversity College DublinDublinIreland
  2. 2.Department of Applied Mathematics and StatisticsSUNY Stony BrookStony BrookUSA
  3. 3.Bank of JapanTokyoJapan
  4. 4.College of BusinessSUNY Stony BrookStony BrookUSA

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