IDEAS home Printed from https://ideas.repec.org/a/pal/risman/v19y2017i3d10.1057_s41283-017-0017-9.html
   My bibliography  Save this article

A VaR assuming Student t distribution not significantly different from a VaR assuming normal distribution

Author

Listed:
  • Su Xu

    (Anhui University of Science and Technology)

Abstract

In estimating VaR using the variance–covariance approach, the returns of a portfolio are commonly assumed to follow a Student t distribution rather than a normal distribution, given the Student distribution’s ability to capture more tail events. However, it is not clear to what measurable extent the Student t distribution is superior to the normal distribution in this exercise. This paper shows that the two assumptions do not produce significantly different VaR values when the degrees of freedom are greater than 4. This paper also determines a sigma threshold for the Student t distribution, which generally lies between 3 and 4 sigma’s when the degrees of freedom are greater than 4.

Suggested Citation

  • Su Xu, 2017. "A VaR assuming Student t distribution not significantly different from a VaR assuming normal distribution," Risk Management, Palgrave Macmillan, vol. 19(3), pages 189-201, August.
    • Handle: RePEc:pal:risman:v:19:y:2017:i:3:d:10.1057_s41283-017-0017-9
    DOI: 10.1057/s41283-017-0017-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/s41283-017-0017-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1057/s41283-017-0017-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Baillie, Richard T. & DeGennaro, Ramon P., 1990. "Stock Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(2), pages 203-214, June.
    2. Cheng, Wan-Hsiu & Hung, Jui-Cheng, 2011. "Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 160-173, January.
    3. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    4. Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 531-554, December.
    5. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    6. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    7. Arnold Polanski & Evarist Stoja, 2011. "Dynamic density forecasts for multivariate asset returns," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(6), pages 523-540, September.
    8. Angelidis, Timotheos & Benos, Alexandros & Degiannakis, Stavros, 2004. "The Use of GARCH Models in VaR Estimation," MPRA Paper 96332, University Library of Munich, Germany.
    9. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    10. Anonymous, 2009. "Abstract of the discussion," British Actuarial Journal, Cambridge University Press, vol. 15(1), pages 202-217, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nupur Moni Das & Bhabani Sankar Rout, 2024. "Equity Price Risk of Commercial Banks in India," Arthaniti: Journal of Economic Theory and Practice, , vol. 23(2), pages 179-201, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheng-Few Lee & Jung-Bin Su, 2012. "Alternative statistical distributions for estimating value-at-risk: theory and evidence," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 309-331, October.
    2. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
    3. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    4. de Lima, Pedro J. F., 1997. "On the robustness of nonlinearity tests to moment condition failure," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 251-280.
    5. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    6. Frank J. Fabozzi & Radu Tunaru & Tony Wu, 2004. "Modeling Volatility for the Chinese Equity Markets," Annals of Economics and Finance, Society for AEF, vol. 5(1), pages 79-92, May.
    7. Stavros Degiannakis & Alexandra Livada & Epaminondas Panas, 2008. "Rolling-sampled parameters of ARCH and Levy-stable models," Applied Economics, Taylor & Francis Journals, vol. 40(23), pages 3051-3067.
    8. De Santis, Giorgio & imrohoroglu, Selahattin, 1997. "Stock returns and volatility in emerging financial markets," Journal of International Money and Finance, Elsevier, vol. 16(4), pages 561-579, August.
    9. Angelidis, Timotheos & Benos, Alexandros & Degiannakis, Stavros, 2004. "The Use of GARCH Models in VaR Estimation," MPRA Paper 96332, University Library of Munich, Germany.
    10. Bryan Kelly & Hao Jiang, 2013. "Tail Risk and Asset Prices," NBER Working Papers 19375, National Bureau of Economic Research, Inc.
    11. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    12. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.
    13. ROCKINGER, Michael & JONDEAU, Eric, 2000. "Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence," HEC Research Papers Series 710, HEC Paris.
    14. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    15. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    16. Dimitrios Koutmos, 2015. "Is there a Positive Risk†Return Tradeoff? A Forward†Looking Approach to Measuring the Equity Premium," European Financial Management, European Financial Management Association, vol. 21(5), pages 974-1013, November.
    17. Philipp Hartmann & Stefan Straetmans & Casper de Vries, 2007. "Banking System Stability. A Cross-Atlantic Perspective," NBER Chapters, in: The Risks of Financial Institutions, pages 133-188, National Bureau of Economic Research, Inc.
    18. Su, Jung-Bin & Lee, Ming-Chih & Chiu, Chien-Liang, 2014. "Why does skewness and the fat-tail effect influence value-at-risk estimates? Evidence from alternative capital markets," International Review of Economics & Finance, Elsevier, vol. 31(C), pages 59-85.
    19. Ghose, Devajyoti & Kroner, Kenneth F., 1995. "The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 225-251, September.
    20. Benjamin Mögel & Benjamin R. Auer, 2018. "How accurate are modern Value-at-Risk estimators derived from extreme value theory?," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 979-1030, May.

    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:pal:risman:v:19:y:2017:i:3:d:10.1057_s41283-017-0017-9. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.