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Conditional autoregressive valu at risk by regression quantile: Estimatingmarket risk for major stock markets

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Author Info

  • George Kouretas

    ()
    (Department of Economics, University of Crete, Greece)

  • Leonidas Zarangas

    (Department of Finance and Auditing, Technological Educational Institute of Epirus, Greece)

Abstract

This paper employs a new approach due to Engle and Manganelli (2004) in order to examine market risk in several major equity markets, as well as for major companies listed in New York Stock Exchange and Athens Stock Exchange. By interpreting the VaR as the quantile of future portfolio values conditional on current information, Engle and Manganelli (2004) propose a new approach to quantile estimation that does not require any of the extreme assumptions of the existing methodologies, mainly normality and i.i.d. returns. The CAViaR model shifts the focus of attention from the distribution of returns directly to the behaviour of the quantile. We provide a comparative evaluation of the predictive performance of four alternative CAViaR specifications, namely Adaptive, Symmetric Absolute Value, Asymmetric Slope and Indirect GARCH(1,1) models. The main findings of the present analysis is that we are able to confirm some stylized facts of financial data such as volatility clustering while the Dynamic Quantile criterion selects different models for different confidence intervals for the case of the five general indices, the US companies and the Greek companies respectively.

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Bibliographic Info

Paper provided by University of Crete, Department of Economics in its series Working Papers with number 0521.

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Length: 46 pages
Date of creation: 00 Nov 2005
Date of revision:
Handle: RePEc:crt:wpaper:0521

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Keywords: Non-linear Regression Quantile; Value-at-Risk; Risk Management;

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References

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  1. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
  2. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  3. Jón Daníelsson & Casper G. de Vries, 1998. "Value-at-Risk and Extreme Returns," Tinbergen Institute Discussion Papers 98-017/2, Tinbergen Institute.
  4. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  5. Bekiros, Stelios D. & Georgoutsos, Dimitris A., 2005. "Estimation of Value-at-Risk by extreme value and conventional methods: a comparative evaluation of their predictive performance," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 15(3), pages 209-228, July.
  6. John Drzik, 2005. "New Directions in Risk Management," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(1), pages 26-36.
  7. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  8. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  10. Singh, Ajit & Weisse, Bruce A., 1998. "Emerging stock markets, portfolio capital flows and long-term economie growth: Micro and macroeconomic perspectives," World Development, Elsevier, vol. 26(4), pages 607-622, April.
  11. Portnoy, Stephen, 1991. "Asymptotic behavior of regression quantiles in non-stationary, dependent cases," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 100-113, July.
  12. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2002. "An Evaluation Framework for Alternative VaR Models," CEPR Discussion Papers 3403, C.E.P.R. Discussion Papers.
  13. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 0075, European Central Bank.
  14. Brooks, C. & Clare, A.D. & Dalle Molle, J.W. & Persand, G., 2005. "A comparison of extreme value theory approaches for determining value at risk," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 339-352, March.
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  16. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
  17. repec:cup:etheor:v:12:y:1996:i:5:p:793-813 is not listed on IDEAS
  18. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  19. Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2010. "The Use of GARCH Models in VaR Estimation," Working Papers 0048, University of Peloponnese, Department of Economics.
  20. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January.
  21. Stelios Bekiros & Dimitris Georgoutsos, 2007. "Extreme returns and the contagion effect between the foreign exchange and the stock market: evidence from Cyprus," Applied Financial Economics, Taylor & Francis Journals, vol. 18(3), pages 239-254.
  22. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
  23. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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Citations

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Cited by:
  1. Benjamin Hamidi & Emmanuel Jurczenko & Bertrand Maillet, 2009. "D'un multiple conditionnel en assurance de portefeuille : CAViaR pour les gestionnaires ?," Post-Print halshs-00389773, HAL.
  2. Rubia, Antonio & Sanchis-Marco, Lidia, 2013. "On downside risk predictability through liquidity and trading activity: A dynamic quantile approach," International Journal of Forecasting, Elsevier, vol. 29(1), pages 202-219.
  3. Huang, Dashan & Yu, Baimin & Fabozzi, Frank J. & Fukushima, Masao, 2009. "CAViaR-based forecast for oil price risk," Energy Economics, Elsevier, vol. 31(4), pages 511-518, July.
  4. Lidia Sanchis-Marco & Antonio Rubia Serrano, 2011. "On downside risk predictability through liquidity and trading activity: a quantile regression approach," Working Papers. Serie AD 2011-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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