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

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  • 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.

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File URL: http://fic.wharton.upenn.edu/fic/papers/97/9734.pdf
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Bibliographic Info

Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 97-34.

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Date of creation: Jul 1997
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Handle: RePEc:wop:pennin:97-34

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  1. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Francis X. Diebold & Jose A. Lopez, 1995. "Modeling volatility dynamics," Research Paper 9522, Federal Reserve Bank of New York.
  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.
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Cited by:
  1. 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.
  2. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," PIER Working Paper Archive 05-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  3. Peter F. Christoffersen & Francis X. Diebold & Til Schuermann, 1998. "Horizon Problems and Extreme Events in Financial Risk Management," Center for Financial Institutions Working Papers 98-16, Wharton School Center for Financial Institutions, University of Pennsylvania.
  4. 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.
  5. 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.
  6. Lehnert, Thorsten & Wolff, Christian C, 2001. "Modelling Scale-Consistent VaR with the Truncated Lévy Flight," CEPR Discussion Papers 2711, C.E.P.R. Discussion Papers.
  7. 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).
  8. 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.
  9. Odening, Martin & Hinrichs, Jan, 2002. "Die Quantifizierung von Marktrisiken in der Tierproduktion mittels Value-at-Risk und Extreme-Value-Theory," Working Paper Series 18826, Humboldt University Berlin, Department Agricultural Economics.
  10. 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.
  11. 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.
  12. Mark R. Manfredo & Raymond M. Leuthold, 1998. "Agricultural Applications of Value-at-Risk Analysis: A Perspective," Finance 9805002, EconWPA.

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