Since the event dates are identical for all the firms in this study, the authors estimated the MVRM by forming the stocks into a portfolio and estimating a single regression equation on the portfolio returns (Thompson, 1985).
Unlike the MVRM method used for the first set of regressions in the study, the Sefcik-Thompson procedure does not account for cross-sectional heteroscedasticity and crosscorrelation of the residuals.
The authors tested the average stock-price reaction to each of the events using the multivariate regression model (MVRM) suggested by Schipper and Thompson (1983).
The MVRM technique finds a negative cumulative excess return like that of the CAR method.
Domestic Captives: The MVRM tests conducted on the domestic sample show that five out of 21 firms earn significant excess returns over some event sub-period.
In summary, the MVRM technique shows that the overwhelming majority of firms do not earn any significant excess return.
After relaxing the presumptions of market risk homogeneity and equity return normality, however, we switch to an MVRM as Equations (3) and (4) jointly illustrate.
But when we employ the risk-adjusted MVRM framework and account for conditional heteroscedasticity and cross-section dependence, neither of the two portfolios shows statistically significant AR for those three event dates.
We next attempt to explain the possible reasons for insignificant risk-adjusted MVRM results.
where A [R.sub.i] is firm i's abnormal return on the day of the actual share repurchase, estimated from Gibbons' (1982) MVRM; [QDUM.sub.i] is a dummy variable equal to 1 if Tobin's q is smaller than one, and 0 otherwise; [PSIZE.sub.i] is a dummy variable equal to 1 if the repurchase size is greater than the median over the past 12 months, and 0 otherwise; [Q.sub.i] x [PSIZE.sub.i] is the interaction of [QDUM.sub.i] and [PSIZE.sub.i]; and [TLAG.sub.i] is the log of the number of trading days since a prior announcement.
where [AR.sub.i] is the abnormal return on the announcement day of an actual share repurchase estimated from Gibbons' (1982) MVRM; [QDUM.sub.i] is a dummy variable equal to 1 if Tobin's q is smaller than 1, and 0 otherwise; PSIZE, is a dummy variable equal to 1 if the percentage of outstanding shares repurchased in an announcement is greater than the median over the previous 12 months, and 0 otherwise; [Q.sub.i] - PSIZE, is the product of [QDUM.sub.i] and [PSIZE.sub.i]; and [TLAG.sub.i] is the log of the number of trading days since a prior announcement.
To mitigate the clustering problem and to extend the studies of Rees (1996) and Zhang (2005), we apply a modified version of Gibbons' (1982) multivariate regression model (MVRM) to estimate abnormal returns and their standard errors.