Optimal forecast error as an unbiased estimator of abnormal return: A proposition

In the event studies, the accuracy of the abnormal returns assessment is highly dependent on the accuracy of the preceding expected return model. If the expected return model is inadequate, there is a possibility that a part of returns is labeled as abnormal returns even though they are not. Currently, we have a variety of options to set up an expected return model. To obtain unbiased abnormal returns, one should pay attention to the performance of the expected return model. In this research, we propose that the optimal forecast lemma can be consulted beforehand so that minimizing the optimal forecast error in the expected return model will yield unbiased abnormal returns. We introduce and prove a proposition that the optimal forecast error is an unbiased estimator for abnormal return. The proposition induces assessing the performance of abnormal return estimation to preemptively evaluate the out-sample forecast accuracy of the model employed. In an illustrative dataset, we examine various models. The approach requires preliminary computational effort; however, it is useful for accurately obtaining the abnormal return predictions.