This paper investigates the empirical power and misspecification of test statistics based on a variety of models to measure long-run abnormal stock returns following firm-specific events by using the observed monthly returns of randomly selected Korea Exchange(KRX) securities. Based on the simulation analysis, this paper also attempts to find the long-run performance model that is well-specified and the most statistically reliable in the Korea stock market. To detect long-run abnormal returns, this paper employs three asset pricing models (two market adjusted models and market model), four reference portfolios (size, book-to-market, size/book-to-market, book-to-market/size based portfolios), four control firm methods (size, book-to-market, sizelbook-to-market, book-to-market/size matched control firms), and Fama-French three-factor model(value weights and equal weights). In order to assess the empirical power and specification of test statistics using these models, one thousand samples of 200 securities are constructed. The securities are selected at random and with replacement from the pool of 820 securities for which monthly return data of at least 3 years are available on the Stock DB of Korea Securities Research Institute (KRSI). For each security, a hypothetical event month is randomly selected with replacement using a uniform probability distribution from January, 1980 through December, 2004. Long-run abnormal returns are estimated over the following three fixed periods: 12-, 36-, and 60-month period. To analyze the power of the thirteen methods of calculating long-term performance, a particular level of excess return is artificially introduced into a given sample by adding a constant level of abnormal return, which ranges from -30% to +30% in increments of 10%, to the calculated 36-month CAR and BHAR of each sample. The results of this paper,can be summarized as follows: (1) For all the models measuring long-run abnormal returns, sample-wide mean CARs and BHARs are different from zero at the 5% significance level, which means they are positively or negatively biased depending on the performance measures. The stronger the magnitude of abnormal performance are the longer the horizon is. However, the control firm methods yield much less biased sample mean abnormal returns than any other methods, regardless of the horizon. (2) Most of the test statistics based on long-run performance measures to calculate 12-1 36-, and 60-month CARs, and BHARs are severely misspecified. For example, in 1,000 randomly selected samples of 200 securities with no systematic abnormal performance, the Fama-French three-factor model using value-weighted portfolio returns shows abnormal performance over a 36-month interval for 46.9% of the samples. The misspecification of these models can be attributed to the significantly positive or negative mean abnormal CARs and BHARs. However, one exception is the book-to-market/size matched control firm method. This model is the only one that yields well-specified test statistics at 12-, 36-, and 60-month horizons. (3) The asset pricing models, reference portfolio methods, and Farna-French three-factor model are more powerful than the control firm approach. However, the power of these three approaches are statistically meaningless, since they yield test statistics that are severely misspecified. Only BHARs calculated using the book-to-market/size matched control firm method yield well-specified test statistics and relatively symmetric power functions. In summary, I conclude that for detecting long-run abnormal stock performance, BHARs calculated using the book-to-market/size matched control firm method yield well-specified and the most statistically reliable test statistics in the Korea Stock Market.
