Detecting cumulative abnormal volume: a comparison of event study methods

Abstract

A growing body of research in accounting and finance examines the reaction of trading volume to new information. The typical ‘volume event study’ employs a single-index market model borrowed mutatis mutandis from abnormal returns event studies. In this article, several alternative event study test statistics are compared using Brown and Warner (1985) style simulations, i.e. random samples of securities are drawn from the data set provided by the Center for Research in Security Prices (CRSP) and the empirical distributions of alternative test statistics are compared. In contrast to the extant literature, these simulations show that estimated generalized least squares with first- and second-order autoregressive structures do not offer material improvement over ordinary least squares (OLS) regression. A first-order moving average structure also does not offer material improvement. These simulations also show that test statistics that are robust with regard to cross-sectional heteroskedasticity are essential for testing the hypothesis that the cross-sectional mean cumulative abnormal log turnover is zero.

Notes

¹Ajinkya and Jain (1989) state that ‘Although a well developed economic theory such as Capital Asset Pricing Model (CAPM) for returns does not seem to exist for trading volume, a number of theoretical papers linking trading volume to information releases can be used to motivate a trading volume market model.’ Tkac (1999) develops a theoretical model justifying the use of the trading volume market model.

²More precisely, in these simulations the null hypothesis is zero mean cumulative abnormal log turnover. However, ‘abnormal volume’ will be used as a shorthand expression for the preceding statement throughout this article.

³For a survey of abnormal returns event studies, see Binder (1998).

⁴Preliminary results (not reported) revealed that (as expected) the continuous trading constraint dictates that a truly random sample from the NYSE, AMEX and NASDAQ would be dominated by the NYSE and AMEX.

⁵Ajinkya and Jain (1989) and Chae (2005) show that although raw volume is highly nonnormal, the log transformation restores approximate normality.

⁶Richardson et al. (1986) may be the earliest example of a volume event study in which a positive constant is added to turnover. Ajinkya and Jain (1989) add 1 to volume.

⁷In their footnote 12, Ajinkya and Jain report no tangible benefit to an AR(2) or ARMA(1,1) model relative to an AR(1) model. Their table 5 on page 341, however, does show a clear benefit from the AR(1) model relative to OLS – a result not replicated here.

⁸This test was suggested by Greene (2003).

⁹The experimental design in this article is adapted from Karafiath (2009).

¹⁰The results in Table 1 are from a grid search by varying the MA(1) coefficient from 0.99 to − 0.99 in increments of 0.03; the end points (0.99 and − 0.99) were never optimal. A smaller, preliminary simulation with an increment of 0.01 did not reveal any advantage to the finer increment.

¹¹Following the usual convention, the ‘event’ date in the tables is designated as day 0 and the event window is time subscripted relative to the event date, e.g. the event window spans day − 15 to day + 15. The format of the tables is borrowed from Karafiath (1994).

¹²Chae (2005) draws a random sample and shows that cumulative log abnormal volume has a zero mean for a 30-day event window. This does not contradict the result in Table 1. Chae's result is that Equation 4(4) has zero mean; Table 1 shows that the test statistic (Equation 5(5)) has progressively thicker tails as the length of the event window increases. More detailed results (not reported) show that the empirical distribution of the test is roughly symmetric.

¹³For each random draw of 50 securities, each security has a unique event date; the event clustering scenario is not examined here.

¹⁴Sanders and Robins (1991) find that the Collins and Dent (1984) test has uniformly greater power than several other robust test statistics, including a test that is functionally identical to the Boehmer et al. (1991) test.

¹⁵Although not reported in the table, in this instance the χ² test is rejected in part because the size of the test is too small in the 20% cell.

¹⁶This is a sharp contrast to the results obtained by Cready and Ramanan (1991), who focus on the difference between additive and multiplicative changes in volume.

¹⁷A final caveat is in order: these simulations represent firm-specific events. There is no guarantee that the results will generalize to an event study in which all firms have a common event date.