A modified Corrado test for assessing abnormal security returns

Event studies typically use the methodology developed by Fama et al. [1969. 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 [1989. 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 (1989). We also use the theorem of Berry [1941. 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 [1945. 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 using data for the purchase and sale by UK directors of shares in their own companies.