Stephen H. Penman, A Comparison of the Information Content of Insider Trading and Management Earnings Forecasts, The Journal of Financial and Quantitative Analysis, Vol. 20, No. 1 (Mar., 1985), pp. 1-17

This paper analyzes the empirical behavior of stock-return volatilities prior to and subsequent to the ex-dates of stock splits. The evidence demonstrates rather unambiguously that there is, on the average, an approximately 30% ‘arbitrary’ increase in the return standard deviations following the ex-date. The increase holds for both daily and weekly data, and it is not temporary. No explanatory confounding variables, such as institutional frictions affecting price observations, have been identified. We view the findings as being essentially inconsistent with the notion of ‘rational pricing’.