A Comment on the Empirical Distribution of Squared Unexpected Returns
复现了Lobo和Mahmoud关于平方意外收益检验统计量经验分布的研究，发现其统计量均值并不低于理论均值，且公司规模对统计量极端值概率的影响不明确，对相关实证方法有重要启示。
Lobo and Mahmoud [1989] (henceforth LM) draw two conclusions about empirical distributions of a normal theory test statistic (ZWr) derived from two-day squared standardized unexpected returns: (1) the empirical distribution of test statistic are lower than their normal theory means and (2) the probability of obtaining large values of those statistics is greater for firms with few analysts' forecasts or for small firms. We replicate portion of LM study that classifies firms according to firm size and find that of LM test statistics are not, on average, lower than their normal theory means. Our results on probability of obtaining large values of these statistics as a function of firm size are inconclusive. The LM findings, if true, have significant implications for how empirical research employing squared unexpected returns should be conducted and interpreted. They imply that it is inappropriate to rely on theoretically derived means, as is done by Dodd et al. [1984], in ascertaining presence or nonpresence of an increase in squared returns. It is also imperative to control for firm size when conducting comparative examinations of squared returns, something Cready and Mynatt [1991], for instance, fail to do when they employ an out-of-sample squared return simulation to interpret sample results.