The Distribution of Stock Return Volatility

41 Pages Posted: 30 Sep 2000 Last revised: 19 Oct 2010

See all articles by Torben G. Andersen

Torben G. Andersen

Northwestern University - Kellogg School of Management; National Bureau of Economic Research (NBER); Aarhus University - CREATES

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Francis X. Diebold

University of Pennsylvania - Department of Economics; National Bureau of Economic Research (NBER)

Heiko Ebens

Johns Hopkins University - Department of Economics

Date Written: October 2000

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 of the returns scaled by the realized standard deviations are also Gaussian. Consistent with our documentation of remarkably precise scaling laws under temporal aggregation, the realized logarithmic standard deviations and correlations all show strong temporal dependence and appear to be well described by long-memory processes. 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, possibly reducing the benefits to portfolio diversification when the market is most volatile. Our findings are broadly consistent with a latent volatility fact or structure, and they 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.

Suggested Citation

Andersen, Torben G. and Bollerslev, Tim and Diebold, Francis X. and Ebens, Heiko, The Distribution of Stock Return Volatility (October 2000). NBER Working Paper No. w7933. Available at SSRN: https://ssrn.com/abstract=244031

Torben G. Andersen (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
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Aarhus University - CREATES ( email )

School of Economics and Management
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DK-8000 Aarhus C
Denmark

Tim Bollerslev

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
919-660-1846 (Phone)
919-684-8974 (Fax)

Duke University - Department of Economics

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Francis X. Diebold

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-1507 (Phone)
215-573-4217 (Fax)

HOME PAGE: http://www.ssc.upenn.edu/~fdiebold/

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Heiko Ebens

Johns Hopkins University - Department of Economics ( email )

3400 Charles Street
Baltimore, MD 21218-2685
United States
410-516-7601 (Phone)

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