Time-varying volatility and the power law distribution of stock returns

While many studies find that the tail distribution of high frequency stock returns follows 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. In particular, one finds that a conditional normal model with nonparametric volatility provides a strong fit. Specifically, a cross-sectional regression of the power law coefficients obtained from stock returns on the coefficients implied by the nonparametric volatility model yields a slope close to one. 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.