Consistent with this interpretation, returns within this "Undefined Growth" subset are extremely low: 5-year buy-and-hold abnormal returns
(BHARs) have an average of -73% and a median of -93%.
Whereas the average of cumulative buy-and-hold abnormal returns
with N shares in period T is defined as:
Figure 5 illustrates the pattern of daily buy-and-hold abnormal returns
surrounding the replacement date (day 0).
Barber, Lyon and Tsai's (1997) procedure is more or less forced on them by their preference for using buy-and-hold abnormal returns
as opposed to cumulative abnormal returns (summed monthly returns) when reviewing long-horizon returns.
Abnormal stock performance is measured using buy-and-hold abnormal returns
(BHAR), the difference between the SEO firm's buy-and-hold return and the equally weighted return to the portfolio of the nonissuing firm's matched based on size, six-month momentum, and the lagged book-to-market ratio.
Those are the CAR, the buy-and-hold abnormal return
(BHAR), and the calendar time portfolio approaches.
Buy-and-hold abnormal returns
(BHARs) in Panel B represent size-MB matched firm abnormal returns.
Buy-and-Hold Abnormal Returns
14-month window [-1, 12] 38-month window [-1, 36] Raw Return Abnormal Raw Return Abnormal Return Return N 159 159 159 159 Mean 16.
We use buy-and-hold abnormal returns
(BHARs) as our primary means of comparison; however, we also calculate and report raw (unadjusted) returns as well as returns adjusted for the returns of the CRSP equally weighted market portfolio.
Columns (1)-(4) report results where the book-to-market and size-matched three-year buy-and-hold abnormal returns
are used as the dependent variable and regressed on the amount of potentially informed exercises along with the other firm and SEO characteristics described in Section III.
In panel B, BHAR(-100, -1) and BHAR(-60, -1) are the buy-and-hold abnormal returns
for days (-100, -1), and (-60, -1), respectively.
We compute buy-and-hold abnormal returns
as the one-year buy-and-hold return on the sample firm's stock, minus the buy-and-hold return to an equal weighted portfolio matched on size, book-to-market equity ratio, and prior one-year return (Lyon, Barber, and Tsai, 1999).