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The Distribution of Stock Return Volatility

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Author Info
Torben G. Andersen
Tim Bollerslev
Francis X. Diebold
Heiko Ebens

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Abstract

We exploit direct model-free measures of daily equity return volatility and correlation obtained from high-frequency intraday transaction prices on individual stocks in the Dow Jones Industrial Average over a five-year period to confirm, solidify and extend existing characterizations of stock return volatility and correlation We find that the unconditional distributions of the variances and covariances for all thirty stocks are leptokurtic and highly skewed to the right, while the logarithmic standard deviations and correlations all appear approximately Gaussian. Moreover, the distributions returns scaled by the realized standard deviations are also Gaussian. Furthermore, the realized logarithmic standard deviations and correlations all show strong dependence and appear to be well described by long-memory processes, consistent with our documentation of remarkably precise scaling laws under temporal aggregation. Our results also show that positive returns have less impact on future variances and correlations than negative returns of the same absolute magnitude, although the economic importance of this asymmetry is minor. Finally, there is strong evidence that equity volatilities and correlations move together, thus diminishing the benefits to diversification when the market is most volatile. By explicitly incorporating each of these stylized facts, our findings set the stage for improved high-dimensional volatility modeling and out-of-sample forecasting, which in turn hold promise for the development of better decision making in practical situations of risk management, portfolio allocation, and asset pricing.

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Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 00-27.

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Date of creation: Oct 2000
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Handle: RePEc:wop:pennin:00-27

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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.:
  1. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September. [Downloadable!] (restricted)
  2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  3. Andersen, Torben G & Bollerslev, Tim, 1997. " Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July. [Downloadable!] (restricted)
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  4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-060, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  5. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility1," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November. [Downloadable!] (restricted)
  6. Crato, Nuno & de Lima, Pedro J. F., 1994. "Long-range dependence in the conditional variance of stock returns," Economics Letters, Elsevier, vol. 45(3), pages 281-285. [Downloadable!] (restricted)
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
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  11. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(1), pages 1-42.
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  12. 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. [Downloadable!] (restricted)
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  15. John Y. Campbell & Martin Lettau & Burton G. Malkiel & Yexiao Xu, 2000. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," NBER Working Papers 7590, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  16. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Heiko Ebens, 2000. "The Distribution of Stock Return Volatility," NBER Working Papers 7933, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  17. Young-Hye Cho & Robert F. Engle, 1999. "Time-Varying Betas and Asymmetric Effect of News: Empirical Analysis of Blue Chip Stocks," NBER Working Papers 7330, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  18. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March. [Downloadable!] (restricted)
  19. 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.
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(explanations, 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.)

  1. Hau, Harald, 2002. "The Role of Transaction Costs for Financial Volatility: Evidence from the Paris Bourse," CEPR Discussion Papers 3651, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  2. Gatfaoui Hayette, 2004. "Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton’s Credit Risk Valuation," Finance 0404004, EconWPA. [Downloadable!]
  3. Borgsen, Sina & Glaser, Markus, 2005. "Diversifikationseffekte durch Small und Mid Caps?," Sonderforschungsbereich 504 Publications 05-10, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  4. Srečko Devjak & Andraž Grum, 2006. "Third Moment Of Yield Probability Distributions For Instruments On Slovenian Financial Markets," Prague Economic Papers, University of Economics, Prague, vol. 2006(4), pages 364-373. [Downloadable!] (restricted)
  5. David S. Bates, 2003. "Maximum Likelihood Estimation of Latent Affine Processes," NBER Working Papers 9673, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. Theodoros Diasakos, 2008. "Comparative Statics of General Equilibrium Asset Prices," Carlo Alberto Notebooks 72, Collegio Carlo Alberto. [Downloadable!]
  7. Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics. [Downloadable!]
    Other versions:
  8. Stavros Degiannakis, 2004. "Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model," Applied Financial Economics, Taylor and Francis Journals, vol. 14(18), pages 1333-1342, December. [Downloadable!] (restricted)
  9. Dimitrios D. Thomakos & Michail S. Koubouros, 2005. "Realized Volatility and Asymmetries in the A.S.E. Returns," Finance 0507012, EconWPA, revised 17 Jan 2006. [Downloadable!]
    Other versions:
  10. Eugenie Hol & Siem Jan Koopman, 2000. "Forecasting the Variability of Stock Index Returns with Stochastic Volatility Models and Implied Volatility," Tinbergen Institute Discussion Papers 00-104/4, Tinbergen Institute. [Downloadable!]
  11. Sam Howison & David Lamper, 2001. "Trading volume in models of financial derivatives," Applied Mathematical Finance, Taylor and Francis Journals, vol. 8(2), pages 119-135, May. [Downloadable!] (restricted)
  12. Pandey Ajay, 2003. "Modeling and Forecasting Volatility in Indian Capital Markets," IIMA Working Papers 2003-08-03, Indian Institute of Management Ahmedabad, Research and Publication Department. [Downloadable!]
  13. John M. Maheu & Thomas H. McCurdy, 2001. "Nonlinear Features of Realized FX Volatility," CIRANO Working Papers 2001s-42, CIRANO. [Downloadable!]
    Other versions:
  14. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Heiko Ebens, 2000. "The Distribution of Stock Return Volatility," Center for Financial Institutions Working Papers 00-27, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
    Other versions:
  15. John Cotter, 2004. "Realized volatility and minimum capital requirements," Money Macro and Finance (MMF) Research Group Conference 2003 20, Money Macro and Finance Research Group. [Downloadable!]
  16. Robert-Paul Berben, 2003. "Does stock market uncertainty impair the use of monetary indicators in the euro area?," MEB Series (discontinued) 2003-15, Netherlands Central Bank, Monetary and Economic Policy Department.
  17. Juan A. Lafuente & Manuel Illueca Muñoz, 2006. "New Evidence On Expiration-Day Effects Using Realized Volatility: An Intraday Analysis For The Spanish Stock Exchange," Working Papers. Serie EC 2006-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  18. Michael W. Brandt & Qiang Kang, 2002. "On the Relationship Between the Conditional Mean and Volatility of Stock Returns: A Latent VAR Approach," NBER Working Papers 9056, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  19. Sam Howison & David lamper, 2000. "Trading Volume in Models of Financial Derivatives," OFRC Working Papers Series 2000mf03, Oxford Financial Research Centre. [Downloadable!]
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