A modified Corrado test for assessing abnormal security returns

Abstract

Event studies typically use the methodology developed by Fama et al. [19699. Fama , E. , Fisher , L. , Jensen , M. and Roll , R. 1969 . The adjustment of stock prices to new information . International Economic Review , 10 ( 1 ) : 1 – 21 . [CrossRef] View all references. The adjustment of stock prices to new information. International Economic Review 10, no. 1: 1–21] to segregate a stock's return into expected and unexpected components. Moreover, conventional practice assumes that abnormal returns evolve in terms of a normal distribution. There is, however, an increasing tendency for event studies to employ non-parametric testing procedures due to the mounting empirical evidence which shows that stock returns are incompatible with the normal distribution. This paper focuses on the widely used non-parametric ranking procedure developed by Corrado [19896. Corrado , C. 1989 . A nonparametric test for abnormal security price performance in event studies . Journal of Financial Economics , 23 ( 2 ) : 385 – 95 . [CrossRef], [Web of Science ®] View all references. A nonparametric test for abnormal security price performance in event studies. Journal of Financial Economics 23, no. 2: 385–95] for assessing the significance of abnormal security returns. In particular, we develop a consistent estimator for the variance of the sum of ranks of the abnormal returns, and show how this leads to a more efficient test statistic (as well as to less cumbersome computational procedures) than the test originally proposed by Corrado (19896. Corrado , C. 1989 . A nonparametric test for abnormal security price performance in event studies . Journal of Financial Economics , 23 ( 2 ) : 385 – 95 . [CrossRef], [Web of Science ®] View all references). We also use the theorem of Berry [19413. Berry , A. 1941 . The accuracy of the Gaussian approximation to the sum of independent variates . Transactions of the American Mathematical Society , 49 ( 1 ) : 122 – 36 . [CrossRef] View all references. The accuracy of the Gaussian approximation to the sum of independent variates. Transactions of the American Mathematical Society 49, no. 1: 122–36] and Esseen [19458. Esseen , C. 1945 . Fourier analysis of distribution functions: A mathematical study of the Laplace–Gaussian law . Acta Mathematica , 77 ( 1 ) : 1 – 125 . [CrossRef] View all references. Fourier analysis of distribution functions: A mathematical study of the Laplace–Gaussian law. Acta Mathematica 77, no. 1: 1–125] to demonstrate how the distribution of the modified Corrado test statistic developed here asymptotically converges towards the normal distribution. This shows that describing the distributional properties of the sum of the ranks in terms of the normal distribution is highly problematic for small sample sizes and small event windows. In these circumstances, we show that a second-order Edgeworth expansion provides a good approximation to the actual probability distribution of the modified Corrado test statistic. The application of the modified Corrado test developed here is illustrated...

Assessing abnormal returns: the case of Chinese M&A acquiring firms

“…They also note that when cash offers do occur it is normally the case that acquiring firms raise debt from banks and/or other financial institutions so that they can finance their M&A activities through cash. Our study extends the sparse Chinese literature available in this area by i) conducting a more robust empirical analysis using recently developed nonparametric statistical techniques (Ataullah et al, 2011) and ii) examining M&A's that occur over the much longer time frame from 1990 until 2008, rather than just the one or two-year period that is typical of the pre-existing Chinese literature in the area. We also investigate whether the relative value of the acquiring firm's stock has any impact on the choice of the mode of consideration used to 7 finance the takeover and on the CAARs earned by the acquiring firm as a result of the takeover as suggested in the model developed by Hansen (1987).…”

“…Now the central question here is whether the AAR's and/or the CAAR's on any particular date are significantly different from zero in a statistical sense. Three statistics are used to make assessments of this hypothesis; namely the Patell (1976) "t" statistic, the Corrado (1989) "z" statistic and the modified Corrado "z" statistic of Ataullah et al (2011). Since the modified Corrado statistic had the most consistent record of detecting abnormal performance and yet, is the least known of the three statistics, we now provide a brief summary of the testing procedures on which this statistic is based.…”

“…(Section 9). Moreover, we use the newly developed Modified Corrado test of Ataullah et al (2011) to assess the significance of the economic benefits which accrue to Chinese acquirers. However, we also conduct robustness tests on the significance of economic benefits for Chinese acquirers by using the original Corrado (1989) test and the Patell (1976) test throughout the paper.…”

“…We now examine the impact that the mode of consideration has on the CAARs that accrue to shareholders of Chinese acquiring firms. Here Table 5 summarises the CAARs based on Dimson (1979) betas 20 and their associated Patell (1976) "t", Corrado (1989) "z" and modified Corrado (Ataullah et al, 2011) "z" scores for the 168 Chinese acquiring firms involved in pure-cash deals and the 45 deals where alternative modes of consideration were used.…”

The effects of multilateral trading systems on risk and return in equity markets

“…From a statistical point of view, nonnormality is addressed, but from the point of view of an investor, it is not adequate as it does not provide the magnitude of ARs. Ataullah et al (2011) argue that NPRT is valid when applied to skewed and/or leptokurtic distributions.…”