Improved Methods for Tests of Long‐Run Abnormal Stock Returns

TLDR

The study compares two methods for testing long‑run abnormal returns: a traditional event‑study approach using buy‑and‑hold abnormal returns with reference portfolios and skewness‑adjusted or empirical t‑statistics, and a calendar‑time method computing mean monthly abnormal returns with a time‑series t‑statistic. Both methods yield well‑specified test statistics in random samples, but misspecification is pervasive in nonrandom samples, making long‑run abnormal return analysis treacherous.

Abstract

We analyze tests for long‐run abnormal returns and document that two approaches yield well‐specified test statistics in random samples. The first uses a traditional event study framework and buy‐and‐hold abnormal returns calculated using carefully constructed reference portfolios. Inference is based on either a skewness‐adjusted t ‐statistic or the empirically generated distribution of long‐run abnormal returns. The second approach is based on calculation of mean monthly abnormal returns using calendar‐time portfolios and a time‐series t ‐statistic. Though both approaches perform well in random samples, misspecification in nonrandom samples is pervasive. Thus, analysis of long‐run abnormal returns is treacherous.