IDEAS home Printed from https://ideas.repec.org/p/wop/pennin/97-34.html
   My bibliography  Save this paper

Converting 1-Day Volatility to h-Day Volatitlity: Scaling by Root-h is Worse Than You Think

Author

Listed:
  • Francis X. Diebold
  • Andrew Hickman
  • Atsushi Inoue
  • Til Schuermann

Abstract

We show that the common practice of converting 1-day volatility estimates to h-day estimates by scaling by the sqaure root of h is inappropriate and produces overestimates of the variability of long-horizon volatility. We conclude that volatility models are best tailored to tasks: if interest centers on long-horizon volatility, then a long-horizon volatility model should be used. Economic considerations, however, confound even that prescription and point to important directions for future research.

Suggested Citation

  • Francis X. Diebold & Andrew Hickman & Atsushi Inoue & Til Schuermann, 1997. "Converting 1-Day Volatility to h-Day Volatitlity: Scaling by Root-h is Worse Than You Think," Center for Financial Institutions Working Papers 97-34, Wharton School Center for Financial Institutions, University of Pennsylvania.
  • Handle: RePEc:wop:pennin:97-34
    as

    Download full text from publisher

    File URL: http://fic.wharton.upenn.edu/fic/papers/97/9734.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    2. Diebold & Lopez, "undated". "Modeling Volatility Dynamics," Home Pages _062, University of Pennsylvania.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. 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.
    5. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    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. Odening, Martin & Hinrichs, Jan, 2003. "Die Quantifizierung von Marktrisiken in der Tierproduktion mittels Value-at-Risk und Extreme-Value-Theory," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 52(02), pages 1-11.
    2. Wolff, Christian & Lehnert, Thorsten, 2001. "Modelling Scale-Consistent VaR with the Truncated Lévy Flight," CEPR Discussion Papers 2711, C.E.P.R. Discussion Papers.
    3. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "VaR performance during the subprime and sovereign debt crises: An application to emerging markets," Emerging Markets Review, Elsevier, vol. 20(C), pages 23-41.
    4. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    5. Erik Kole & Thijs Markwat & Anne Opschoor & Dick van Dijk, 2017. "Forecasting Value-at-Risk under Temporal and Portfolio Aggregation," Journal of Financial Econometrics, Oxford University Press, vol. 15(4), pages 649-677.
    6. Gonzalez-Rivera, Gloria & Lee, Tae-Hwy & Mishra, Santosh, 2004. "Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood," International Journal of Forecasting, Elsevier, vol. 20(4), pages 629-645.
    7. Saadi, Samir & Rahman, Abdul, 2008. "Evidence of non-stationary bias in scaling by square root of time: Implications for Value-at-Risk," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(3), pages 272-289, July.
    8. Odening, Martin & Hinrichs, Jan, 2002. "Assessment Of Market Risk In Hog Production Using Value-At-Risk And Extreme Value Theory," 2002 Annual meeting, July 28-31, Long Beach, CA 19907, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    9. Mark R. Manfredo & Raymond M. Leuthold, 1998. "Agricultural Applications of Value-at-Risk Analysis: A Perspective," Finance 9805002, University Library of Munich, Germany.
    10. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February.
    11. Th'eophile Griveau-Billion & Ben Calderhead, 2019. "A Dynamic Bayesian Model for Interpretable Decompositions of Market Behaviour," Papers 1904.08153, arXiv.org, revised Jan 2020.
    12. Kam Fong Chan & Christopher Gan & Patricia A. McGraw, 2003. "A Hedging Strategy for New Zealand’s Exporters in Transaction Exposure to Currency Risk," Multinational Finance Journal, Multinational Finance Journal, vol. 7(1-2), pages 25-54, March-Jun.
    13. Wang, Jying-Nan & Du, Jiangze & Hsu, Yuan-Teng, 2018. "Measuring long-term tail risk: Evaluating the performance of the square-root-of-time rule," Journal of Empirical Finance, Elsevier, vol. 47(C), pages 120-138.
    14. Peter F. Christoffersen & Francis X. Diebold & Til Schuermann, 1998. "Horizon problems and extreme events in financial risk management," Economic Policy Review, Federal Reserve Bank of New York, vol. 4(Oct), pages 109-118.
    15. Kavussanos, Manolis G. & Dimitrakopoulos, Dimitris N., 2011. "Market risk model selection and medium-term risk with limited data: Application to ocean tanker freight markets," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 258-268.
    16. Kai Schindelhauer & Chen Zhou, 2018. "Value-at-Risk prediction using option-implied risk measures," DNB Working Papers 613, Netherlands Central Bank, Research Department.
    17. Agnieszka Borowska & Lennart Hoogerheide & Siem Jan Koopman, 2019. "Bayesian Risk Forecasting for Long Horizons," Tinbergen Institute Discussion Papers 19-018/III, Tinbergen Institute.
    18. Smith, J.Q. & Santos, Antonio A.F., 2006. "Second-Order Filter Distribution Approximations for Financial Time Series With Extreme Outliers," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 329-337, July.
    19. Danielsson, Jon & Zigrand, Jean-Pierre, 2006. "On time-scaling of risk and the square-root-of-time rule," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2701-2713, October.
    20. Fritzsch, Simon & Timphus, Maike & Weiß, Gregor, 2024. "Marginals versus copulas: Which account for more model risk in multivariate risk forecasting?," Journal of Banking & Finance, Elsevier, vol. 158(C).
    21. Amy S. K. Wong, 2006. "Basel II and the Risk Management of Basket Options with Time-Varying Correlations," International Journal of Central Banking, International Journal of Central Banking, vol. 2(4), December.
    22. Wang, Jying-Nan & Yeh, Jin-Huei & Cheng, Nick Ying-Pin, 2011. "How accurate is the square-root-of-time rule in scaling tail risk: A global study," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1158-1169, May.
    23. Simon Fritzsch & Maike Timphus & Gregor Weiss, 2021. "Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?," Papers 2109.10946, arXiv.org.

    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. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    2. McMillan, David G. & Speight, Alan E. H., 2001. "Non-ferrous metals price volatility: a component analysis," Resources Policy, Elsevier, vol. 27(3), pages 199-207, September.
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
    5. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.
    6. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    7. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    8. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    9. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    11. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    12. Torben G. Andersen & Tim Bollerslev, 1997. "Answering the Critics: Yes, ARCH Models Do Provide Good Volatility Forecasts," NBER Working Papers 6023, National Bureau of Economic Research, Inc.
    13. David McMillan & Alan Speight, 2005. "Long-memory and heterogeneous components in high frequency Pacific-Basin exchange rate volatility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(3), pages 199-226, September.
    14. Francis X. Diebold & Jose A. Lopez, 1995. "Measuring Volatility Dynamics," NBER Technical Working Papers 0173, National Bureau of Economic Research, Inc.
    15. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    16. Doornik, Jurgen A. & Ooms, Marius, 2008. "Multimodality in GARCH regression models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 432-448.
    17. Eleni Constantinou & Robert Georgiades & Avo Kazandjian & George Kouretas, 2005. "Mean and variance causality between the Cyprus Stock Exchange and major equity markets," Working Papers 0501, University of Crete, Department of Economics.
    18. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    19. Bauer, Rob M M J & Nieuwland, Frederick G M C & Verschoor, Willem F C, 1994. "German Stock Market Dynamics," Empirical Economics, Springer, vol. 19(3), pages 397-418.
    20. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.

    More about this item

    Statistics

    Access and download statistics

    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:wop:pennin:97-34. 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: Thomas Krichel (email available below). General contact details of provider: https://edirc.repec.org/data/fiupaus.html .

    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.