How accurate is the square-root-of-time rule in scaling tail risk: A global study
AbstractThe square-root-of-time rule (SRTR) is popular in assessing multi-period VaR; however, it makes several unrealistic assumptions. We examine and reconcile different stylized factors in returns that contribute to the SRTR scaling distortions. In complementing the use of the variance ratio test, we propose a new intuitive subsampling-based test for the overall validity of the SRTR. The results indicate that serial dependence and heavy-tailedness may severely bias the applicability of SRTR, while jumps or volatility clustering may be less relevant. To mitigate the first-order effect from time dependence, we suggest a simple modified-SRTR for scaling tail risks. By examining 47 markets globally, we find the SRTR to be lenient, in that it generally yields downward-biased 10-day and 30-day VaRs, particularly in Eastern Europe, Central-South America, and the Asia Pacific. Nevertheless, accommodating the dependence correction is a notable improvement over the traditional SRTR.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Banking & Finance.
Volume (Year): 35 (2011)
Issue (Month): 5 (May)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jbf
Value at risk Square-root-of-time rule Jump diffusion Serial dependence Heavy-tail Volatility clustering Subsampling-based test;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Peter F. Christoffersen & Francis X. Diebold, 1997.
"Optimal prediction under asymmetric loss,"
97-11, Federal Reserve Bank of Philadelphia.
- Peter F. Christoffersen & Francis X. Diebold, 1994. "Optimal Prediction Under Asymmetric Loss," NBER Technical Working Papers 0167, National Bureau of Economic Research, Inc.
- Peter F. Christoffersen & Francis X. Diebold, . "Optimal Prediction Under Asymmetric Loss," CARESS Working Papres 97-20, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Christoffersen & Diebold, . "Optimal Prediction Under Asymmetric Loss," Home Pages 167, 1996., University of Pennsylvania.
- Drost, F.C. & Nijman, T.E., 1993.
"Temporal aggregation of GARCH processes,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-153273, Tilburg University.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
- Dennis Jansen & Casper de Vries, 1988.
"On the frequency of large stock returns: putting booms and busts into perspective,"
1989-006, Federal Reserve Bank of St. Louis.
- 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.
- Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
- Jean-Pierre Zigrand & Jon Danielsson, 2003.
"On time-scaling of risk and the square–root–of–time rule,"
FMG Discussion Papers
dp439, Financial Markets Group.
- 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.
- Ayadi, O. Felix & Pyun, C. S., 1994. "An application of variance ratio test to the Korean securities market," Journal of Banking & Finance, Elsevier, vol. 18(4), pages 643-658, September.
- Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Andrew W. Lo, A. Craig MacKinlay, 1988.
"Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test,"
Review of Financial Studies,
Society for Financial Studies, vol. 1(1), pages 41-66.
- Tom Doan, . "VRATIO: RATS procedure to implement variance ratio unit root test procedure," Statistical Software Components RTS00231, Boston College Department of Economics.
- Andrew W. Lo & A. Craig MacKinlay, 1989. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
- Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
- Pérignon, Christophe & Smith, Daniel R., 2010. "Diversification and Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 55-66, January.
- Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
- Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
- Stavros Degiannakis & Pamela Dent & Christos Floros, 2014. "A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification," Manchester School, University of Manchester, vol. 82(1), pages 71-102, 01.
- Alexander, Carol & Lazar, Emese & Stanescu, Silvia, 2013. "Forecasting VaR using analytic higher moments for GARCH processes," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 36-45.
- Sbrana, Giacomo & Silvestrini, Andrea, 2013.
"Aggregation of exponential smoothing processes with an application to portfolio risk evaluation,"
Journal of Banking & Finance,
Elsevier, vol. 37(5), pages 1437-1450.
- SBRANA, Giacomo & SILVESTRINI, Andrea, 2010. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," CORE Discussion Papers 2010039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.