The Distribution of Stock Return Volatility

Torben G. Andersen, Tim Bollerslev, Francis X. Diebold, Heiko Ebens

NBER Working Paper No. 7933
Issued in October 2000
NBER Program(s):   AP

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.

download in pdf format
   (586 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/w7933

Published: Andersen, Torben G., Tim Bollerslev, Francis X. Diebold and Heiko Ebens. "The Distribution Of Realized Stock Return Volatility," Journal of Financial Economics, 2001, v61(1,Jul), 43-76.

Users who downloaded this paper also downloaded these:
Andersen, Bollerslev, Diebold, and Labys w8160 Modeling and Forecasting Realized Volatility
Andersen and Bollerslev w6023 Answering the Critics: Yes, ARCH Models Do Provide Good Volatility Forecasts
Andersen, Bollerslev, Diebold, and Labys w6961 The Distribution of Exchange Rate Volatility
Andersen, Bollerslev, Diebold, and Labys w7488 Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian
Acemoglu, Johnson, Robinson, and Thaicharoen w9124 Institutional Causes, Macroeconomic Symptoms: Volatility, Crises and Growth
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us