32 S.P. Kothari and J.B. Warner
4.4.3. The bottom line
Despite positive developments in BHAR calibration methods, two general long-horizon
problems remain. The first concerns power.Jegadeesh and Karceski (2004)report that
their tests show no increase in power relative to that of the test employed in previous
research, which already had low power. For example, even with seemingly huge cumu-
lative abnormal performance (25% over 5 years) in a sample of 200 firms, the rejection
rate of the null is typically under 50% (see their Table 6).
Second, specification issues remain. For example, as discussed earlier (Section3.6),
events are generally likely to be associated with variance increases, which are equiv-
alent to abnormal returns varying across sample securities. Previous literature shows
that variance increases induce misspecification, and can cause the null hypothesis to be
rejected far too often. Thus, whether a high level of measured abnormal performance is
due to chance or mispricing (or a bad model) is still difficult to empirically determine,
unless the test statistic is adjusted downward to reflect the variance shift. Solutions to the
variance shift issue include such intuitive procedures as forming subsamples with com-
mon characteristics related to the level of abnormal performance (e.g., earnings increase
vs. decrease subsamples). With smaller subsamples, however, specification issues unre-
lated to variance shifts become more relevant. Moreover, the importance of examining
specification for nonrandom samples cannot be overemphasized.
Given the various power and specification issues, a challenge that remains for the
profession is to continue to refine long-horizon methods. Whether calendar time, BHAR
methods or some combination can best address long-horizon issues remains an open
question.
References
Baker, M., Talliaferro, R., Wurgler, J., 2006. Predicting returns with managerial decision variables: Is there a
large-sample bias? Journal of Finance, in press.
Baker, M., Talliaferro, R., Wurgler, J., 2004. Pseudo market timing and predictive regression. Working Paper
#10823, National Bureau of Economic Research.
Ball, R., Brown, P., 1968. An empirical evaluation of accounting income numbers. Journal of Accounting
Research 6, 159–177.
Ball, R., Kothari, S., 1989. Nonstationary expected returns: Implications for tests of market efficiency and
serial correlation in returns. Journal of Financial Economics 25, 51–74.
Ball, R., Kothari, S., Shanken, J., 1995. Problems in measuring portfolio performance: An application to
contrarian investment strategies. Journal of Financial Economics 38, 79–107.
Banz, R., 1981. The relationship between return and market value of common stocks. Journal of Financial
Economics 9, 3–18.
Barber, B., Lyon, J., 1996. Detecting abnormal operating performance: The empirical power and specification
of test statistics. Journal of Financial Economics 41, 359–399.
Barber, B., Lyon, J., 1997. Detecting long-run abnormal stock returns: The empirical power and specification
of test statistics. Journal of Financial Economics 43, 341–372.
Barberis, N., Shleifer, A., Vishny, R., 1998. A model of investor sentiment. Journal of Financial Eco-
nomics 49, 307–343.