The full paper is available at SSRN.
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.
This graph shows the absolute value of tail coefficients (i.e., tail indices). Dark bars show the central estimate of coefficients, while light bars show the upper 95% single-sided confidence interval for the same coefficients. Coefficients greater than 17 are not shown. Coefficients less than or equal to 4 cause estimates of stock price synchronicity to be invalid (i.e., kurtosis of firm-specific returns is infinite).