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Realized Beta GARCH: Multivariate GARCH Model with Realized Measures of Volatility and CoVolatility

  • Peter Reinhard Hansen
  • Asger Lunde
  • Valeri Voev

We introduce a multivariate GARCH model that incorporates realized measures of volatility and covolatility. The realized measures extract information about the current level of volatility and covolatility from high-frequency data, which is particularly useful for the modeling of return volatility during periods with rapid changes in volatility and covolatility. When applied to market returns in conjunction with returns on an individual asset, the model yields a dynamic model of the conditional regression coefficient that is known as the beta. We apply the model to a large set of assets and find the conditional betas to be far more variable than is usually found with rolling-window regressions based exclusively on daily returns. In the empirical part of the paper we examine the cross-sectional as well as the time variation of the conditional beta series during the financial crises.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2012/28.

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Date of creation: 2012
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Handle: RePEc:eui:euiwps:eco2012/28
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  1. Braun, Phillip A & Nelson, Daniel B & Sunier, Alain M, 1995. " Good News, Bad News, Volatility, and Betas," Journal of Finance, American Finance Association, vol. 50(5), pages 1575-1603, December.
  2. Joao Gomes & Leonid Kogan & Lu Zhang, 2003. "Equilibrium Cross Section of Returns," Journal of Political Economy, University of Chicago Press, vol. 111(4), pages 693-732, August.
  3. Peter Reinhard Hansen & Zhuo Huang, 2012. "Exponential GARCH Modeling with Realized Measures of Volatility," CREATES Research Papers 2012-44, School of Economics and Management, University of Aarhus.
  4. Lewellen, Jonathan & Nagel, Stefan, 2006. "The conditional CAPM does not explain asset-pricing anomalies," Journal of Financial Economics, Elsevier, vol. 82(2), pages 289-314, November.
  5. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series 2006fe05, Oxford Financial Research Centre.
  6. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Post-Print peer-00815564, HAL.
  7. Dovonon, Prosper & Goncalves, Silvia & Meddahi, Nour, 2010. "Bootstrapping realized multivariate volatility measures," MPRA Paper 40123, University Library of Munich, Germany.
  8. Ferson, Wayne E & Harvey, Campbell R, 1993. "The Risk and Predictability of International Equity Returns," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 527-66.
  9. Neil Shephard & Kevin Sheppard, 2009. "Realising the future: forecasting with high frequency based volatility (HEAVY) models," Economics Papers 2009-W03, Economics Group, Nuffield College, University of Oxford.
  10. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  11. Robert F. Engle & Giampiero M. Gallo, 2003. "A Multiple Indicators Model For Volatility Using Intra-Daily Data," Econometrics Working Papers Archive wp2003_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  12. Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2009. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," CREATES Research Papers 2009-45, School of Economics and Management, University of Aarhus.
  13. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  14. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  15. Griffin, Jim E. & Oomen, Roel C.A., 2011. "Covariance measurement in the presence of non-synchronous trading and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 58-68, January.
  16. Valeri Voev & Asger Lunde, 2007. "Integrated Covariance Estimation using High-frequency Data in the Presence of Noise," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 68-104.
  17. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
  18. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  19. Marcel P. Visser, 2011. "GARCH Parameter Estimation Using High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 162-197, Winter.
  20. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
  21. Bollerslev, Tim & Zhang, Benjamin Y. B., 2003. "Measuring and modeling systematic risk in factor pricing models using high-frequency data," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 533-558, December.
  22. Todorov, Viktor & Bollerslev, Tim, 2010. "Jumps and betas: A new framework for disentangling and estimating systematic risks," Journal of Econometrics, Elsevier, vol. 157(2), pages 220-235, August.
  23. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C1-C32, November.
  24. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  25. Henrik Hansen & Søren Johansen, 1999. "Some tests for parameter constancy in cointegrated VAR-models," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 306-333.
  26. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, 09.
  27. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
  28. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
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