Improved Testing Procedures for Long-Horizon Event Studies in the Korean Stock Market (Improved Testing Procedures for Long-Horizon Event Studies in the Korean Stock Market)

서지정보

· 발행기관 : 한국증권학회
· 수록지 정보 : Asia-Pacific Journal of Financial Studies / 37권 / 5호 / 765 ~ 811페이지
· 저자명 : 정형찬

초록

This paper is to investigate how performance models and significance tests affect the empirical power and specification of tests for long-horizon event studies using the simulation method based on the observed monthly returns of randomly selected Korea Exchange (KRX) securities. In addition, this paper is also to examine the effect of the sample size on the power and specification of testing procedures. Based on these results of the simulation analysis, this paper is to present the best testing procedure that yields well specified test statistics and highest empirical power in the Korean Stock Market.
In order to evaluate testing procedures for long-horizon event studies by simulation method, I examine sample sizes of 50, 100 and 200 securities. For each sample size, I construct 1,000 samples. The securities are selected randomly from the pool of 820 securities for which monthly return data of at least 12 months are available on the Stock DB of Korea Securities Research Institute (KSRI). Furthermore, I conduct another simulation test on the samples artificially designed to be biased either by the size or book-to-market ratio. To assess the impact of size-based sampling biases on the performance of tests, I randomly select 1,000 samples separately from the smallest size quintile and the largest size quintile. I also randomly draw 1,000 samples separately from the highest book-to-market quintile and the lowest book-to-market quintile to assess the impact of book-to-market ratio based sampling biases on the performance of those tests. For each security, a hypothetical event month is randomly selected during the period of January, 1980 and December, 2004.
To detect long run abnormal returns, I calculate buy and hold abnormal returns using the five performance models. The three of them are reference portfolio methods (an equally weighted KRX market index, 25 size/book-to-market portfolios, 25 book-to-market/size portfolios); the other two are control firm methods (size/book-to-market matched, book-to-market/size matched control firm). To test the null hypothesis that the mean or median buy and hold abnormal return is equal to zero for a sample, I employ the following nine methods of significance tests: conventional t-test, conventional t-test using winsorized abnormal returns, Johnson’s skewness-adjusted t-test, bootstrapped Johnson’s t-test using shift method and normal approximation method, empirical p value approach, sign test, Wilcoxon signed-rank test, and two-groups test. Combination of the five performance models and the nine significance tests yields 45 testing procedures. To find the best combination of performance model and significance test in the Korean Stock Market, I adopt the data-based simulation method. To evaluate the power of testing procedures, I artificially set a particular level of abnormal return to a given sample by adding a constant level of abnormal return, which ranges from -40% to +40% in increments of 10%, to the calculated 12-, 36-, and 60-month buy and hold abnormal returns of each sample firm.

The results of this paper can be summarized as follows:
(1)The five of nine significance tests with a book-to-market/size matched control firm as benchmark yield test statistics that are well-specified in random samples. Those are conventional t-test, conventional t-test using winsorized abnormal returns, bootstrapped Johnson’s t-test using normal approximation method, Wilcoxon signed-rank test, and two-groups test. On the other hand, the results show that the following four tests are not well-specified in random samples: Johnson’s skewness-adjusted t-test, bootstrapped Johnson’s t-test using shift method, empirical pvalue approach, and sign test.
(2)The combination of the nonparametric Wilcoxon signed rank test with a book-to-market/size matched control firm as benchmark clearly shows much higher power than the other four tests that yield well-specified test statistics in random samples, regardless of the horizon. As holding period lengthens from 12- to 36- and to 60-month, the power of all tests drops sharply. On the other hand, as the sample size increases from 50 to 100 and to 200 securities, the power of tests increases consistently for all the testing procedures.
(3)With a book-to-market/size matched control firm as benchmark, the only significance test well-specified in nonrandom samples with size-based or book-to-market ratio based sampling biases regardless of the horizon and sample size turns out to be a two-groups test, which ignores pair-wise dependence, instead of a paired difference test.

In conclusion, the best testing procedure for long-horizon event studies in the Korean Stock Market is the combination of the Wilcoxon signed rank test with a book-to-market/size matched control firm as benchmark in the case of no clear sampling biases. However, when size-based or book-to-market ratio based sampling biases are present, a two-groups test is better than Wilcoxon signed-rank test in terms of the test’s statistical reliability.

영어초록

This paper is to investigate how performance models and significance tests affect the empirical power and specification of tests for long-horizon event studies using the simulation method based on the observed monthly returns of randomly selected Korea Exchange (KRX) securities. In addition, this paper is also to examine the effect of the sample size on the power and specification of testing procedures. Based on these results of the simulation analysis, this paper is to present the best testing procedure that yields well specified test statistics and highest empirical power in the Korean Stock Market.
In order to evaluate testing procedures for long-horizon event studies by simulation method, I examine sample sizes of 50, 100 and 200 securities. For each sample size, I construct 1,000 samples. The securities are selected randomly from the pool of 820 securities for which monthly return data of at least 12 months are available on the Stock DB of Korea Securities Research Institute (KSRI). Furthermore, I conduct another simulation test on the samples artificially designed to be biased either by the size or book-to-market ratio. To assess the impact of size-based sampling biases on the performance of tests, I randomly select 1,000 samples separately from the smallest size quintile and the largest size quintile. I also randomly draw 1,000 samples separately from the highest book-to-market quintile and the lowest book-to-market quintile to assess the impact of book-to-market ratio based sampling biases on the performance of those tests. For each security, a hypothetical event month is randomly selected during the period of January, 1980 and December, 2004.
To detect long run abnormal returns, I calculate buy and hold abnormal returns using the five performance models. The three of them are reference portfolio methods (an equally weighted KRX market index, 25 size/book-to-market portfolios, 25 book-to-market/size portfolios); the other two are control firm methods (size/book-to-market matched, book-to-market/size matched control firm). To test the null hypothesis that the mean or median buy and hold abnormal return is equal to zero for a sample, I employ the following nine methods of significance tests: conventional t-test, conventional t-test using winsorized abnormal returns, Johnson’s skewness-adjusted t-test, bootstrapped Johnson’s t-test using shift method and normal approximation method, empirical p value approach, sign test, Wilcoxon signed-rank test, and two-groups test. Combination of the five performance models and the nine significance tests yields 45 testing procedures. To find the best combination of performance model and significance test in the Korean Stock Market, I adopt the data-based simulation method. To evaluate the power of testing procedures, I artificially set a particular level of abnormal return to a given sample by adding a constant level of abnormal return, which ranges from -40% to +40% in increments of 10%, to the calculated 12-, 36-, and 60-month buy and hold abnormal returns of each sample firm.

The results of this paper can be summarized as follows:
(1)The five of nine significance tests with a book-to-market/size matched control firm as benchmark yield test statistics that are well-specified in random samples. Those are conventional t-test, conventional t-test using winsorized abnormal returns, bootstrapped Johnson’s t-test using normal approximation method, Wilcoxon signed-rank test, and two-groups test. On the other hand, the results show that the following four tests are not well-specified in random samples: Johnson’s skewness-adjusted t-test, bootstrapped Johnson’s t-test using shift method, empirical pvalue approach, and sign test.
(2)The combination of the nonparametric Wilcoxon signed rank test with a book-to-market/size matched control firm as benchmark clearly shows much higher power than the other four tests that yield well-specified test statistics in random samples, regardless of the horizon. As holding period lengthens from 12- to 36- and to 60-month, the power of all tests drops sharply. On the other hand, as the sample size increases from 50 to 100 and to 200 securities, the power of tests increases consistently for all the testing procedures.
(3)With a book-to-market/size matched control firm as benchmark, the only significance test well-specified in nonrandom samples with size-based or book-to-market ratio based sampling biases regardless of the horizon and sample size turns out to be a two-groups test, which ignores pair-wise dependence, instead of a paired difference test.

In conclusion, the best testing procedure for long-horizon event studies in the Korean Stock Market is the combination of the Wilcoxon signed rank test with a book-to-market/size matched control firm as benchmark in the case of no clear sampling biases. However, when size-based or book-to-market ratio based sampling biases are present, a two-groups test is better than Wilcoxon signed-rank test in terms of the test’s statistical reliability.

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