Stock price synchronicity under fat-tailed stock returns

Abstract

The extensive literature on stock price synchronicity implicitly assumes that the sample R-squared of stock return regressions equals its population value. This paper demonstrates that non-normality in stock returns caused by high kurtosis inflates measures of stock price synchronicity. Variables believed to increase synchronicity by reducing firm-specific risk may, instead, elevate kurtosis, which can mimic low firm-specific risk in small samples. A simulation of synchronicity under fat-tailed firm-specific returns reveals that fat tails cause the variance of firm-specific returns to be underestimated in small samples, thereby inflating stock price synchronicity. This bias is comparable in magnitude to main effects of variables examined in the synchronicity literature. An empirical analysis of firm-specific returns identifies a large proportion of stocks with fat-tailed returns within the region where kurtosis is infinite. A case study on analyst coverage demonstrates that effects on synchronicity found in the literature can decrease in size and become insignificant when controlling for fat-tailed returns. Further empirical results indicate that fat-tailedness is associated with firm size, Tobin’s q, and industry sector. These and other variables linked to a firm’s growth potential and crash risk may thus confound analyses of stock price synchronicity by making stock returns appear to have low variance when, in reality, they exhibit high kurtosis.

Keywords: price synchronicity, return synchronicity, firm-specific information, price informativeness, Pareto law, power-law distribution, fat tails, crash risk

JEL Classification: G14, G32, C18