Stock price synchronicity under fat-tailed stock returns

Abstract

A large body of literature of has studied the effects of various firm, market or country characteristics on stock price synchronicity through their effect on the volatility of firm-specific returns. This approach assumes that the sample volatility of returns equals its population value, which is a reasonable assumption under normally distributed returns. But the non-normality of empirical returns is a well-established fact. This paper investigates the effect of high and possibly infinite kurtosis on measures of stock price synchronicity. A simulation of synchronicity under fat-tailed firm-specific returns shows that fat tails increase stock price synchronicity in small samples. This bias is large if stock returns have infinite kurtosis. This finding implies that the sample volatility of firm-specific returns in a typical small-sample study will be biased downward and synchronicity biased upward. An empirical analysis of firm-specific returns shows a large proportion of stocks with fat-tailed returns in the region where kurtosis is infinite. Fat-tailedness is related to firm size, Tobin’s q and industry sector. These and other variables related to a firm’s growth potential and crash risk may thus confound analyses of stock price synchronicity through high or infinite kurtosis and downward-biased volatility in small samples.

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

JEL Classification: G14, G32