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.

中文翻译：

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最优预测误差作为异常收益的无偏估计：一个命题

在事件研究中，异常收益评估的准确性高度依赖于先前预期收益模型的准确性。如果预期收益模型不充分，则有一部分收益可能会被标记为异常收益，即使它们不是。目前，我们有多种选择来建立预期回报模型。为了获得无偏的异常收益，需要关注期望收益模型的性能。在这项研究中，我们建议可以事先咨询最优预测引理，以便最小化预期收益模型中的最优预测误差将产生无偏的异常收益。我们引入并证明了一个命题，即最优预测误差是异常收益的无偏估计量。该命题引入评估异常收益估计的性能，以抢先评估所采用模型的样本外预测准确性。在说明性数据集中，我们检查了各种模型。该方法需要初步的计算工作；但是，它对于准确获得异常收益预测很有用。