Working Paper

Time-varying Volatility and the Power Law Distribution of Stock Returns


Abstract: While many studies find that the tail distribution of high frequency stock returns follow a power law, there are only a few explanations for this finding. This study presents evidence that time-varying volatility can account for the power law property of high frequency stock returns. The power law coefficients obtained by estimating a conditional normal model with nonparametric volatility show a striking correspondence to the power law coefficients estimated from returns data for stocks in the Dow Jones index. A cross-sectional regression of the data coefficients on the model-implied coefficients yields a slope close to one, supportive of the hypothesis that the two sets of power law coefficients are identical. Further, for most of the stocks in the sample taken individually, the model-implied coefficient falls within the 95 percent confidence interval for the coefficient estimated from returns data.

Keywords: Tail distributions; high frequency returns; power laws; time-varying volatility;

JEL Classification: C58; D30; G12;

https://doi.org/10.17016/FEDS.2016.022

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Bibliographic Information

Provider: Board of Governors of the Federal Reserve System (U.S.)

Part of Series: Finance and Economics Discussion Series

Publication Date: 2016-03-18

Number: 2016-022