Skewness preference and the measurement of abnormal returns

In performing an empirical analysis of stock market returns there are certain conditions under which the quadratic characteristic line (QCL) will be the appropriate return-generating process compared to the linear characteristic line (LCL). These conditions are whether the parameter associated with the squared market term (the deviation from the mean) is significantly different from zero and whether the return on the market portfolio is asymmetrically distributed (or skewness is present). Examining abnormal returns surrounding stock splits, we find that these conditions hold for our data set. Having ascertained that the conditions for QCL hold, we find that the cumulative average returns (CARs) obtained using QCL dominate the CARs obtained using LCL in the event time and the CAR space for the dividend-increase sub-sample. Furthermore, the standardized abnormal returns for the QCL model are significantly different than those obtained using the LCL model. We find that neither the LCL nor the QCL paradigm reveals any statistically significant abnormal return for the dividend-decrease group. However, for the dividend-decrease group, the CARs for the LCL model dominate the CARs for the QCL model. The standardized abnormal returns for the QCL model are also significantly different than those of the LCL model. Using QCL, we find support for the signalling hypothesis of dividends. We also find that the extent of investor reaction obtained using QCL is statistically significantly different than that obtained using the LCL.