Testing excess returns on event days: Log returns vs. dollar returns

The results of academic and practitioners' event studies are often translated from excess log returns into excess dollar returns. The prior literature argues for a difference between the statistical significance of excess log returns and that of excess dollar returns. In contrast, we show analytically and using simulations that specifying event study hypotheses in terms of excess dollar returns is equivalent to specifying them in terms of excess log returns. The prior literature's result was due to a bias in the estimator of expected excess dollar returns, an incorrect assumption that it is approximately normally distributed, and a misapplication of the delta method.