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Assessing value at risk with CARE, the Conditional Autoregressive Expectile models

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  • Kuan, Chung-Ming
  • Yeh, Jin-Huei
  • Hsu, Yu-Chin

Abstract

In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index [theta] of an EVaR is the relative cost of the expected margin shortfall and hence reflects the level of prudentiality. It is also shown that a given expectile corresponds to the quantiles with distinct tail probabilities under different distributions. Thus, an EVaR may be interpreted as a flexible QVaR, in the sense that its tail probability is determined by the underlying distribution. We further consider conditional EVaR and propose various Conditional AutoRegressive Expectile models that can accommodate some stylized facts in financial time series. For model estimation, we employ the method of asymmetric least squares proposed by Newey and Powell [Newey, W.K., Powell, J.L., 1987. Asymmetric least squares estimation and testing. Econometrica 55, 819-847] and extend their asymptotic results to allow for stationary and weakly dependent data. We also derive an encompassing test for non-nested expectile models. As an illustration, we apply the proposed modeling approach to evaluate the EVaR of stock market indices.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 150 (2009)
Issue (Month): 2 (June)
Pages: 261-270

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Handle: RePEc:eee:econom:v:150:y:2009:i:2:p:261-270

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Asymmetric least squares CARE model Expectile Quantile Prudentiality Value at Risk;

References

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  1. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-26, March.
  2. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
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  7. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
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  9. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
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  12. Koenker, Roger, 1992. "When Are Expectiles Percentiles?," Econometric Theory, Cambridge University Press, vol. 8(03), pages 423-424, September.
  13. G. Geoffrey Booth & John Paul Broussard & Teppo Martikainen & Vesa Puttonen, 1997. "Prudent Margin Levels in the Finnish Stock Index Futures Market," Management Science, INFORMS, vol. 43(8), pages 1177-1188, August.
  14. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  15. Wooldridge, J.M, 1989. "An Encompassing Approach To Conditional Mean Tests With Applications To Testing Nonnested Hypotheses," Working papers 511, Massachusetts Institute of Technology (MIT), Department of Economics.
  16. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  17. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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Citations

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Cited by:
  1. Ngoc Mai Tran & Maria Osipenko & Wolfgang Karl Härdle, 2014. "Principal Component Analysis in an Asymmetric Norm," SFB 649 Discussion Papers SFB649DP2014-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Huang, Alex YiHou, 2010. "An optimization process in Value-at-Risk estimation," Review of Financial Economics, Elsevier, vol. 19(3), pages 109-116, August.
  3. Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
  4. Bastianin, Andrea & Galeotti, Marzio & Manera, Matteo, 2014. "Causality and predictability in distribution: The ethanol–food price relation revisited," Energy Economics, Elsevier, vol. 42(C), pages 152-160.
  5. Wolfgang Karl Härdle & Ya’acov Ritov & Song Song, 2010. "Partial Linear Quantile Regression and Bootstrap Confidence Bands," SFB 649 Discussion Papers SFB649DP2010-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
  7. Huang, Xiaolin & Shi, Lei & Suykens, Johan A.K., 2014. "Asymmetric least squares support vector machine classifiers," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 395-405.
  8. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
  9. Zhijie Xiao & Roger Koenker, 2009. "Conditional Quantile Estimation for GARCH Models," Boston College Working Papers in Economics 725, Boston College Department of Economics.
  10. Shih-Kang Chao & Wolfgang Karl Härdle & Weining Wang, 2012. "Quantile Regression in Risk Calibration," SFB 649 Discussion Papers SFB649DP2012-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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