IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v150y2009i2p261-270.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
  • Handle: RePEc:eee:econom:v:150:y:2009:i:2:p:261-270
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(08)00223-6
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wooldridge, Jeffrey M., 1990. "An encompassing approach to conditional mean tests with applications to testing nonnested hypotheses," Journal of Econometrics, Elsevier, vol. 45(3), pages 331-350.
    2. Gilbert W. Bassett, 2004. "Pessimistic Portfolio Allocation and Choquet Expected Utility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 477-492.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    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.
    8. 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.
    9. 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.
    10. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    11. 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.
    12. 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.
    13. Koenker, Roger, 1992. "When Are Expectiles Percentiles?," Econometric Theory, Cambridge University Press, vol. 8(03), pages 423-424, September.
    14. Baer, Herbert L. & France, Virginia G. & Moser, James T., 1994. "Opportunity cost and prudentiality : an analysis of futures clearinghouse behavior," Policy Research Working Paper Series 1340, The World Bank.
    15. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    16. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    17. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(2), pages 231-252, Spring.
    18. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:150:y:2009:i:2:p:261-270. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.