Review of Quantitative Finance and Accounting, 23: 275–290, 2004
2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
Bootstrap Tests for Multivariate Event Studies
Department of Finance, National Central University, Chung Li, Taiwan 320, Tel.: 886-3-4227151, Ext. 6270;
Abstract. Statistical tests for multivariate event studies—exact or asymptotic—are derived based on multivariate
normality. As it has been previously documented that the performances of these tests are not satisfactory, because
stock returns are far from normally distributed (especially for daily returns), this paper proposes the use of
bootstrap methods, which are free from any speciﬁc distributional assumption, to provide better approximations
to the sampling distributions of test statistics in multivariate event studies. The Monte Carlo experiments based on
real daily returns data show that the bootstrap tests outperform the traditional tests by having close rejection rates
to the nominal signiﬁcance levels. The traditional tests, in contrast, tend to reject the null hypotheses too often.
Keywords: bootstrap, multivariate event studies, likelihood ratio test, Wald test, exact test
JEL Classiﬁcation: C13, C53, G14
Event studies have constituted a great proportion of empirical studies in the literature
of accounting and ﬁnance. Early event studies are primarily concerned with the impact
of ﬁrm-speciﬁc events on stock returns. The focus generally lies on how stock prices
adjust to the release of relevant information around certain events or announcements.
Average abnormal returns and cumulative average abnormal returns across stocks that
are exposed to the same event of interest (but at different calendar times) are calcu-
lated to see if the event has caused the stocks to signiﬁcantly deviate from some rela-
tionship suggested by a certain benchmark model (see, e.g., Fama et al., 1969; Brown
and Warner, 1980, 1985). While several review papers have been written, Binder (1998)
and MacKinlay (1997) provide an excellent survey of the literature on ﬁrm-speciﬁc event
Later developments of event study methodology extend to the investigation of regulatory
events (i.e., multivariate event studies). The methodology for testing regulatory events
has become a focus of researchers in accounting and ﬁnance since the 1980s, because
regulatory event studies provide a means through which the response of stock prices to the
announcements or enactments of regulations can be investigated. Thus, these studies also
provide evidence upon which the impact and effectiveness of regulations can be evaluated.
The attention is given primarily on the enactment and announcement of industry-related
regulations by which stocks of the same industry are affected simultaneously. Thus, the
cross-sectional correlations among stocks of the same industry have to be taken into account
for statistical inferences.