Ch. 1: Econometrics of Event Studies 17
empirical relation between volatility and size. Our qualitative results apply if ranking is
by firm size, soTable 3is not simply picking up measurement error in volatility.
3.6.4. Results
Figure 1shows how, for a sample comprised of securities of average risk and 10%
abnormal performance, the power to detect abnormal performance falls with horizon
length. This level of abnormal performance seems economically highly significant. If
the abnormal performance is concentrated entirely in one day (and the day in known
with certainty), a sample of only six stocks detects this level of abnormal performance
100% of the time. In contrast, if the same abnormal performance occurs over six months,
a sample size of 200 is required to detect the abnormal performance even 65% of the
time. These various rejection frequencies are lower than those using pre-1990 volatili-
ties (not reported), although this is not surprising.
Figure 2(a)–(c) show related results using a one-day horizon for samples whose indi-
vidual security standard deviations correspond to the average standard deviation for: the
lowest decile (Figure 2(a)); all firms (Figure 2(b)); and the highest decile (Figure 2(c)).
For decile 1 firms, with 1% abnormal performance a 90% rejection rate requires only
21 stocks. For firms in decile 10, even with 5% abnormal performance a 90% rejection
rate requires 60 stocks. These comparisons may distort the differences in actual power
if high variance firms are less closely followed and events are bigger surprises. When
the effect of events differs cross-sectionally, analysis of test properties (i.e., power and
specification) is more complicated.
Collectively, our results illustrate that power against alternative hypotheses can be
sensitive to calendar time period and sample firm characteristics, and highlight the im-
portance already recognized in the profession of studying test statistic properties for
Fig. 1. Power of event study test statistic when abnormal return is 10%.