Shares Outstanding and Cross-Sectional Returns *

Transcription

1 Shares Outstanding and Cross-Sectional Returns * Jeffrey Pontiff Carroll School of Management Boston College 140 Commonwealth Avenue Chestnut Hill, MA pontiff@bc.edu Artemiza Woodgate University of Washington School of Business, Box Seattle, WA artemiza@u.washington.edu First Draft: November 2, 2003 Abstract We examine the cross-sectional relation between the twelve-month real change in shares outstanding and stock returns. During the post-1970 time period, change in shares outstanding exhibits a strong cross-sectional ability to predict stock returns. This predictive ability is typically stronger than the predictive ability of size, book-to-market, or momentum. Our finding is related to research that finds that long-run returns are associated with share repurchase announcements and seasoned equity offerings, although our finding is not attributed to this association. We also provide novel estimation of the share change relation in the pre-1970 time period and find no statistically significant predictive ability. * We thank participants at the Boston College brown bag workshop for useful comments.

2 I. Introduction Whether or not long-run stock returns following share repurchase announcements and seasoned equity offerings reflect mispricing has been debated by the finance literature. Loughran and Ritter (1995) have argued that long-run stock performance following seasoned equity offerings reflect negative abnormal returns, whereas Ikenberry, Lakonishok, and Vermaelen (1995, 2000) argue that share repurchase announcements precede positive abnormal returns. These studies have focused on returns with holding periods of three or more years. These and other long-run return studies have created detraction in the finance literature. Two major criticisms of long-run returns have emerged. First, calculation of a long-run abnormal return requires an asset pricing model. The magnitude of the abnormal returns is very sensitive to the model that the researcher uses to calculate expected returns. Because of this, inference is subject to Fama s (1976) joint hypothesis problem, a point that Loughran and Ritter (2000) re-emphasize. Brav, Geczy, and Gompers (2000) illustrate this point by showing that the extent of long-run SEO and IPO returns is drastically affected by the benchmarking. Second, inference from long-run studies is very sensitive to statistical specification issues. Mitchell and Stafford (2000) show that inference from some long-run return specifications are influenced by whether or not hetereoskedasticty and cross-sectional correlation are controlled for adequately. Schultz (2003) shows that if the decision to issue or repurchase shares is correlated with past-stock performance, a spurious estimation bias will produce average estimates of long-run returns that are similar in magnitude to the long-run literature, even if the returns are generated under the null hypothesis of zero abnormal performance. Motivated by the long-run repurchase and SEO debate, we examine the cross-sectional ability of the twelve-month change in shares outstanding to predict share returns. We focus on the real change in shares outstanding, which is computed by removing nominal share changes caused by splits and stock dividends. We expect that changes in shares outstanding will provide some of the same information that is associated with share repurchases and SEOs. The number of shares outstanding is drastically affected by both repurchases and

3 3 SEOs, although it also contains information associated with other events such as the exercise of employee stock options and the purchase of stock by the corporation for employee benefit programs. A major benefit of examining changes in shares outstanding is that we can compute this variable for all stocks included in the CRSP database over all time periods for which the stock trades. This enables us to utilize Fama-MacBeth (1973) regressions, which are remarkably robust to the statistical problems that have been levied against long-run return studies. Since this methodology discards information from monthly t-statistics, it is robust to hetereoskedasticty and cross-sectional correlation problems [Mitchell and Stafford (2000)]. The Fama-MacBeth (1973) estimation procedure is not used to study post-event long-run returns since it requires the occurrence of some events every period. SEOs and repurchases are clustered through time, such that some months have no events. 1 Our change in shares outstanding variable contains cross-sectional variation every period, enabling Fama-MacBeth estimation. Our goal is to simply identify whether changes in shares outstanding is instrumental in predicting stock returns. We do not address whether return predictability implies market inefficiency or the rational outcome of an asset pricing model. We leave this to papers that investigate rejectable mispricing hypotheses such as Pontiff and Schill (2003). Our study provides three interesting findings. First, we show that post-1970, the change in shares outstanding is strongly related to the future of cross-section of stock returns. Our results remain strong for all holding periods that we study. In fact, our results are generally stronger than other popular predictors of cross-sectional returns such as book-tomarket, size, and momentum. Although we do not address whether the source of this predictability is mispricing or a rational response to an asset pricing model, it appears doubtful that these results can be explained solely by a risk-based asset pricing model. Bookto-market, size, and momentum typically explain between two to 10 times of the crosssectional return variation that is explained by changes in shares outstanding. Thus, it does not appear that the change in shares outstanding proxies for a market-wide risk factor. It is possible that a non-risk based asset pricing, such as a transaction cost model may explain these results. 1 We examine data from between 1970 and 1999 in our SEO sample and data from between 1980 and 1999 in our repurchase sample (detailed in section 3). For 174 months of 360 months (48.3%), no SEOs occurred. For 24 of 240 months (10%), no repurchases were announced.

4 4 Second, whether or not we include post-seo returns and post repurchase returns in our estimation, has virtually no affect on the strength and the magnitude of our results. We interpret this finding as evidence that post-seo and post repurchase return performance is part of a broader change in shares outstanding effect. Third, using the pre-1970 data we can not reject the hypothesis that changes in shares outstanding and the cross-section of future stock returns are related. Since the long-run SEO and repurchase literature has focused on the post-1970 time period, our pre-1970 finding implies that the long-run literature may be sample specific. This interpretation of our results coincides with Gompers and Lerner (2003), who show that long-run initial public offering (IPO) returns before 1972 are generally insignificant, in stark contrast to the typical finding of long-run IPO underperformance in later samples. Two papers that examine return predictability with proxies similar to ours are Daniel and Titman (2003) and Richardson and Sloan (2003). Both papers confine their samples to recent periods where accounting variables are available. Again, our findings suggest that the findings of these papers that relate to equity financing may be sample specific. The next section reviews the cross-sectional equity change literature and compares the methods used in this literature to our methods. Section III discusses data and estimation procedures. Section IV presents estimation results for the 1970 to 2002 period. Section V presents out-sample estimation results using the pre-1970 data, and Section VI concludes. II. Review of cross-sectional equity change literature Our paper has some similarities to contemporaneous work by Daniel and Titman (2003) and Richardson and Sloan (2003). Both Daniel and Titman (2003) and Richardson and Sloan (2003) focus on information that is related to accounting numbers. Because of this, these studies focus on recent time periods for which accounting data is available. Using data that starts in 1968, Daniel and Titman decompose stock return variation into variation that is associated with accounting numbers and variation that is not associated with accounting numbers. They use both types of variation to forecast stock returns. In order to supplement their examination of return predictability with non-accounting variation, and in order to reconcile their results with Lakonishok, Shleifer, and Vishny (1994) they construct a share issuance measure. Their measure is almost identical to ours with two exceptions. First, their

5 5 measure spans 5 year changes whereas we measure twelve month changes, and second, they study the natural log of change, whereas we examine the percentage change. Our choice of using the twelve month change in change in shares outstanding was determined before we had knowledge of the Daniel and Titman result. In order to avoid data mining biases, the twelve month change has been the only frequency that we have examined. Richardson and Sloan (2003) show that changes in external financing are related to differences in future realized returns. Using data from 1971 and 2000, they form 10 rank portfolios based on measures of external financing, and they find statistical significant differences in portfolio returns between the two extreme rank portfolios. Various accounting decompositions of changes in financing are considered. The closest measure to ours that Richardson and Sloan use is the change in common equity divided by total assets. They investigate both a cash flow definition and a balance sheet definition of change in common equity, and show that both measures produce statistically significant differences for the top and bottom decile portfolios. They attribute their results not to capital structure changes, per se, rather to an accrual anomaly originally documented by Sloan (1996). III. Data and Estimation Sample. Our paper is motivated by the share repurchase and SEO long-run return studies that have used data between 1970 and the present, thus we chose this time period as the starting point of our study. Since our variable of interest, SHRCHG, does not rely on Compustat data, we are able to extend our results to a sample before We select each month only those firms that have a non-missing return entry in that month, and that have been in the CRSP database for at least six months, thus allowing us to compute their past 6-month returns. Our primary sample consists of all firm observations that are in the CRSP database starting 1/1/1970. This leaves us with 2,367,488 firm-month observations. We conduct an out-of-sample test of the explanatory power of the change in shares outstanding variable for the sample period 3/1/1927 to 12/1/1969. Our starting date of 3/1/1927 allows for the lagged change in shares outstanding variable to be constructed as detailed below. For this period we have 557,990 firm-month observations.

6 6 Share Change. For each company we obtain from CRSP the number of shares outstanding and the Factor to Adjust Shares Outstanding. We compute the number of real shares outstanding, which adjusts for distribution events such as splits and rights offerings as follows. We first compute a Total Factor at time t, which represents the cumulative product of the CRSP-provided factor f up to period t inclusive. TotalFactor = (1 + f ) t t i= 1 i We compute the number of shares outstanding adjusted for splits and other events as, Adjusted Shares = Shares outstanding / TotalFactor. We use this measure of Adjusted t t Shares to compute the change in shares outstanding at time t as, AdjustedShares t AdjustedSharest 12 SHRCHG = t, t 12. AdjustedSharest 12 This measure is identical to Stephens and Weisbach (1998), who show that repurchase announcements are associated with decreases in shares outstanding, and similar to Daniel and Titman (2003), who show that the change in three-year natural logarithm of shares outstanding can predict returns. Sometimes there appears a timing mismatch between shares outstanding and CRSP reported shares outstanding. From correspondence with CRSP, CRSP purchases shares outstanding data from a vendor who gathers information from public disclosures such as quarterly reports. It is CRSP s intention to report shares outstanding when the information is publicly disclosed. We compared the timing of CRSP shares outstanding with COMPUSTAT shares outstanding and found that in some instances CRSP data corresponded to the end of quarter date, and sometimes it corresponded to dates a month or two after the end of quarter date. In order to be conservative, and ensure that the shares outstanding numbers are available to investors, we only use share changes using 6-month old CRSP data to predict returns, thus current returns (at time 0) are predicted using SHRCHG -6,-17. Our decision is influenced by Fama and French (1992) who delay using book-value data until at least 6 months after fiscal year-end. Daniel and Titman (2003) also use a 6 month delayed share change variable. t

7 7 Book-to-market. We use the annual COMPUSTAT book value of common equity (data60) to construct the book-to-market variable. If the previous year s book value is unavailable, we use stale book value from two years ago. We follow the Fama-French (1992) procedure in constructing the natural log of the book-to-market ratio. Book value is divided by size, where size is constructed using the CRSP firm market value the end of June of the current year. This variable is used to forecast returns from July of the current year to June of the following year. When the book value of equity was unavailable or it was negative, the book value variable was assigned a value of 0 and the book value dummy variable was set equal to 0. Utilizing this dummy variable, allows us to use all stock returns regardless of whether the security has COMPUSTAT coverage, without affecting inference of the slope coefficient on book-to-market. Size. From CRSP, we construct the monthly market value of equity variable. We use the natural logarithm of the share price times the number of shares outstanding for that given month. SIZE from the month of June is used to predict returns from July of the current year until June of the following year. Momentum. The momentum proxy is the 6 months holding-period return of the stock between months -2 and months -8. The momentum variable was lagged by one month to avoid losing predictive ability due to positive autocorrelation attributable to bid-ask-bounce. Returns. The dependent variable in our regressions is stock return for holding periods of one month, three months, six months, and twelve months. If the return information was missing in CRSP for a given month, we construct the holding period return by replacing the missing stock return with the return of the equally weighted market portfolio with dividends re-invested (EWRETD). Most studies estimate holding period returns by ignoring missing returns. These studies holding period returns represent the return that one would receive from holding the stock, and once the stock delists, investing the remaining value in a zero interest riskless security. Our holding period return represents the return from holding the stock until delisting, and investing the remaining value in a CRSP equally weighted index.

8 8 We believe that our holding period computation is more realistic, although we do not expect that it will significantly affect our inference. Estimation. Our regression estimation will estimate linear relations between returns and our independent variables. We do not know what the true functional form of our independent variables should be. Because of our ignorance regarding the correct specification of the independent variables, our results are likely to be sensitive to extreme observations. In order to avoid giving any observations undue weight in the regression estimation, we winsorize all right hand side variables, by setting the smallest and largest 1% of the observations equal to the value of the observation at the respective 1% tail. We do not transform the holding period returns that are used as dependent variables. In the same vein as Fama-MacBeth (1973), using every month of data, we regress stock returns on our independent variables. We report the average slope coefficients, intercepts and adjusted-r 2 s. Using the same procedure of Pontiff and Schall (1998), t-statistics for the slope coefficients are calculated with autocorrelation consistent standard errors that consider the holding period overlap. This procedure estimates a regression using each month s slope estimate where the residuals of the process follow an n th -order autoregressive process, where n is one minus the length of the holding period (in months). The standard error of the intercept from this estimation is used as the overlap consistent standard error of our average slope-coefficient. IV. In-Sample Estimation Results The second panel of Table 1 describes the correlation structure of our in sample ( ) data. From the lead-lag structure of SHRCHG, SHRCHG tends to be persistent. If the real number of shares outstanding shrinks (expands), it continues to shrink (expand) in future periods. Also, the positive correlation between R -23,-12 and both SHRCHG -11,0 and SHRCHG 1,12, show that real shares outstanding tends to expand (shrink) after periods of high (low) returns. The positive correlation between SHRCHG -23,-12 and R -11,0 and R 1,12 is a precursor to our results changes in real shares outstanding predict returns. The correlations between future returns and BM, ME, and MOM are consistent with the literature on stock

9 9 return predictability [for example, Fama and French (1992) and Jegadeesh and Titman (1993)]. Our first goal is to assess the extent to which changes in shares outstanding (SHRCHG) proxies for SEO offerings and repurchase announcements. We gather this data from Thomson Financial s SDC Platinum. We select all SEOs from the US common stock database that involved some primary shares and were not involved in a spin-off. Repurchase announcements came from the domestic merger database. Our search yields 3,892 SEOs and 15,918 repurchase announcements. Table 2 conducts Fama-MacBeth regressions of SHRCHG of various lead and lag dummy variables for whether the firm had an SEO or announced a repurchase, as well as levels of BM, ME, and MOM, from the period directly before SHRCHG was calculated. Consistent with our expectations, as well as Stephens and Weisbach (1998) who show that repurchase announcements forecast decreases in the real number of shares outstanding, we find that the current period s annual SHRCHG is negatively related to whether a repurchase was announced last year or two years ago, and positively related to whether an SEO occurred last year or two years ago. The average slope coefficients are large and statistically strong. An SEO between months -24 to -11 corresponds to an increase our measure of real shares outstanding change of approximately 18-20%. A repurchase announcement between months -24 to -11 corresponds to a 4-7% decrease in our real shares outstanding measure. These slope coefficients illustrate the staleness associated with the CRSP shares outstanding measure. Both ME and MOM forecast future SHRCHG, although the magnitude of the effect is smaller than the impact of either a repurchase announcement or an SEO. Our test of return predictability in the 1970 to 2002 period is presented in Table 3. Four return holding periods are considered; one month, one quarter, six-month, and one year. Panel A presents the one-month estimation results. The first four rows present a horse race by considering separate estimation for book-to-market (BM), size (ME), momentum (MOM), and change in shares outstanding (SHRCHG). The sign of the slope coefficients on BM, ME, and MOM is consistent with previous literature. The slope coefficients on BM and MOM are

10 10 both positive and statistically significant, although the estimate of the slope coefficient on BM is smaller than that reported by Fama and French (1992). The size effect is less pronounced in our sample period. Although the coefficient on ME is negative, it is statistically insignificant. From the monthly holding period regressions SHRCHG has a slope of -0.96, implying that a 100% change in nominal shares outstanding is associated with a -0.96% decrease in monthly cross-sectional return. The t-statistic on this slope is -5.55, which is considerably stronger the than the t-statistics on BM, ME, and MOM. The second to last row considers all variables except SHRCHG, while the last row includes SHRCHG. Whether or not all variables are included, the slope coefficients are similar except the t-statistic on BM shrinks slightly towards zero, while the t-statistic on SHRCHG increases slightly. The longer-holding period results are broadly consistent with the one-month results. The signs of the slopes remain. The t-statistics on the BM slopes increase with holding period and the t-statistic on the MOM slope peaks at the 6-month holding period, which is roughly consistent with Jegadeesh and Titman (1993). The t-statistics on ME tend to increase with holding period, although they remain insignificant. The t-statistics on SHRCHG tend to decrease, although they remain strongly significant. From the sets of simple regressions, the t-statistics on SHRCHG are always stronger than BE, ME, and MOM, except for the 6-month holding period, in which the t-statistic for MOM is stronger. When all independent variables are considered jointly, SHRCHG has the strongest t-statistic for monthly and quarterly holding periods, whereas MOM has the strongest t-statistics for the 6-month and one-year holding periods. Overall, we interpret these results as showing that SHRCHG has an ability to predict cross-sectional returns during this time period that is as strong as or stronger than other popular variables. The average adjusted R 2 s reported on Table 3 show a clear pattern. Compared with all of the other variables, SHRCHG does not explain very much cross-sectional return variance. From the monthly regressions, SHRCHG only explains 0.18% of the average cross-sectional return variance. This explanatory power is under a half the power of BM, nearly and eighth the power of MOM, and a tenth the power of ME. This occurs despite the strength of the

11 11 average SHRCHG slope coefficient. Thus, SHRCHG tends to have a consistent positive slope in most periods, although variables such as size pick up broad effects that cause swings in the returns of large and small capitalization stocks. Although this paper avoids making inferences regarding whether or not the return predictability associated with SHRCHG is a manifestation of market inefficiency or an asset pricing model, its clear that compared with the size, value, and momentum effects, the SHRCHG effect is not a risk effect--the covariance that securities share does seem related to SHRCHG. This does not rule out the possibility that SHRCHG proxies for compensation from non-risk based asset pricing models, such as [for example, Amihud and Mendelson (1986)]. Removal of SEO and repurchase returns. Table 2 has shown that changes in shares outstanding are strongly related to whether or not the firm has had a SEO or has announced a repurchase. Since some long-run return studies have argued that anomalous long-run returns are evident post-seo and post-repurchase announcement, we explore the impact of these events on our results. We re-estimate the Fama-MacBeth regressions over the sample, eliminating firm returns for the three years following a repurchase announcement or an SEO. This reduces our sample to 2.00 million firm-month observations from the 2.35 million observations used to generate Table 3. The results from this estimation are presented in Table 4. Overall, Table 4 shows that the removal of returns associated with SEOs and repurchases has a minor, if any, impact on the Fama-MacBeth regressions. The major difference is that the one year slope coefficients on ME are now more negative and marginally significant. Otherwise, significance levels tend to fall slightly, as is expected given the decrease in the number or observations. Our interpretation of these results is that the returns associated with SEOs and repurchases are part of a broader predictability that includes SHRCHG. Thus, SEOs and repurchases are not driving the SHRCHG effect. Table 2 demonstrates that SEOs and repurchase announcements are strongly related to variation in SHRCHG, whereas MOM and ME are moderately related, and BM is essentially unrelated. This implies that SEO and repurchase returns are being driven primarily by SHRCHG, and to a lesser extent, by MOM and ME.

12 12 V. Out-of Sample Estimation Results The entire SEO and repurchase long-run return literature has focused on the post-1970 time period. Concerning similar current literature, Sloan and Richardson (2003) focus on the period of 1971 to the present, whereas Daniel and Titman (2003) focus on a sample that starts in July of In order to evaluate the performance of SHRCHG in another time period, we re-estimate the Table 2 results, using data from 1927 to This time period has overlap with neither Sloan and Richardson nor any of the SEO and repurchase studies. A small overlap with (17 months) is shared with Daniel and Titman. We eliminate BM from our out-of-sample estimation since COMPUSTAT coverage is limited or non-existent during this time period. Table 5 presents our results. For all regressions and all holding periods, ME exhibits a statistically significant, negative relation with returns. MOM exhibits positive slope coefficients for all regressions, although not all slope coefficients are significant. Specifically, none of the one- month MOM slopes coefficients are significant and the threemonth simple regression slope is no significant, whereas the remaining MOM slopes are significant. The SHRCHG results suffer the biggest impact from the pre-1970 estimation. All the coefficients are closer to zero than the in-sample coefficients and all the out-of-sample t-statistics are insignificant. These results are attributable to both an increase in standard errors as well as the shrinkage of the slope coefficients towards zero. If (as Table 4 shows) post-seo and share repurchase returns are part of general change in shares outstanding effect, our findings suggest that the results of the long-run SEO and repurchase literature and some of the results of Sloan and Richardson and Daniel and Titman may be sample-specific. Our finding is similar to Gompers and Lerner (2003), who claim that before 1972, firms that undertook an initial public offering (IPO) did not have anomalous post-offering returns. These results contradict other studies such as Ritter (1991) that claims that post-1974 IPOs exhibit strong underperformance.

13 13 VI. Conclusion. This paper considers changes in real shares outstanding. Real shares outstanding is shares outstanding minus nominal shares that are created by stock dividends and splits. Changes in real shares outstanding occur as the firm purchases or sells its own stock. For example, real shares outstanding goes up when employees exercise employee stock options and the corporation issues stock to the employees or when the firm sells additional stock during an SEO. Conversely, real shares outstanding goes down when the firm purchases its own stock for inclusion in its pension plan, when it self-tenders its own shares, or when it conducts an open-market share repurchase. Some participants in the long-run return debate have argued that post-seo long-run returns are abnormally low and that post-share repurchase long-run returns are abnormally high. We are motivated by this debate to examine whether changes in real shares outstanding can be used to cross-sectional forecast stock returns. We show that the change in real shares outstanding is closely related to both announced repurchases and SEOs. During the post-1970 time period in which most long-run studies have been conducted, we find that changes in real shares outstanding is strongly related to future returns. In fact, our findings are as strong, if not stronger, than previous documented predictability attributed to book-to-market, size, and momentum. The source of this predictability is neither post-seo returns nor post-repurchase announcement returns. Thus, we interpret the long-run returns associated with SEOs and repurchases as being part of a broader change in shares outstanding effect. This effect does not appear to the manifestation of risk-based asset pricing, or at least not of the magnitude associated with the book-to-market, size effect, or momentum. The typical monthly explained return variation from these effects is several times greater than the explained variation attributed to changes in real shares outstanding. Last, we show that before 1970, the ability of changes in real shares outstanding to predict stock returns is statistically insignificant. This sample is interesting because it is outof-sample relative to the data used by the SEO and repurchase literature, as well as the recent literature on changes in real shares outstanding. This finding indicates that predictability associated with changes in shares outstanding is sample specific; implying that the long-run returns attributably to SEOs and repurchase announcements may also be sample specific.

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17 Table 1 Descriptive statistics Panel A: Simple Statistics. The variables used are: the natural logarithm of the ratio of book value of equity to market value of equity measured at the end of December t-1, BM, the natural logarithm of market equity measured at the end of the previous June, ME, the past six month s stock return as a proxy for momentum, MOM, the percentage change in the number of shares outstanding adjusted for splits to capture the effect of share repurchases and SEO s, SHRCHG = [(shares outstanding, t) (shares outstanding, t-12) ]/ (shares outstanding, t-12), the one year return R 0,-12 contemporaneous with the SHRCHG variable. The variables are measured at the end of December for the period between 1970 and Shares associated with splits and stock dividends are not included in the computation of shares outstanding. The sample consists out of 103,932 observations for each variable. Panel B: Correlations. Correlations between the variables defined in Panel A, SHRCHG, BM, ME MOM and R 0,-12, as well as the 12 month lead and lag of the change in shares outstanding variable, SHRCHG -23,-12 and SHRCHG 1, 12, and the 12 month lead and lag of the one-year return, R -23, -12 and R 1, 12. Panel A: Simple Statistics Variable Mean 25 th Quartile Median 75 th Quartile Standard Deviation SHRCHG -11, BM ME MOM R -11, Panel B: Correlations Variable SHRCHG -23,-12 SHRCHG -11, 0 SHRCHG 1, 12 BM ME MOM R -23, -12 R -11, 0 SHRCHG -11, SHRCHG 1, BM ME MOM R -23, R -11, R 1,

18 Table 2 Fama-MacBeth cross-sectional regressions with the change in shares outstanding as the dependent variable. The dependent variable is the percentage change in the number of shares outstanding adjusted for splits to capture the effect of share repurchases and SEO s, SHRCHG = [(shares outstanding, t) (shares outstanding, t-12) ]/ (shares outstanding, t-12). The rest of the variables are all lagged by 12 months. The variables are: the natural logarithm of the ratio of book value of equity to market value of equity from December t-1, BM, a book-to-market dummy variable which is 0 if BM is missing, BM Dum., the natural logarithm of market equity from June t-1, ME, the natural logarithm of the market value of the firm as of June t, the past six month s stock return as a proxy for momentum, MOM, and dummy variables for whether there was an SEO or a repurchase between various intervals, [-24,- 12], [-11,0], [1,12]. Shares associated with splits and stock dividends are not included in the computation of shares outstanding. The Average R 2 is the average of the adjusted R 2 obtained from the cross-sectional regressions, in percent. The results presented in the table are the regression coefficients and the t-statistics in brackets. Multi-month holding period results utilize overlap consistent t-statistics. These regressions are for 242 months where all variables are identified, from 1/1/1980 to 12/1/2002, with a total of 1,476,012 firm-observations. Coefficients with significant t-statistics are bolded and all coefficients are in percent. Intercept REP -24,-12 REP -11,0 REP 1,12 SEO -24,-12 SEO -11,0 SEO 1,12 SEO 1,12 BM BM Dum ME MOM Avg. R (13.80) (-18.10) (15.74) (19.30) (15.04) (-18.08) (18.54) (12.65) (-12.63) (-15.52) (-1.85) (15.49) (20.41) (1.47) (-0.41) (-0.41) (13.72) (-11.77) (-14.59) (-2.74) (19.17) (1.68) (-0.49) (-0.49) (7.76) (-1.00) (-0.22) (-6.68) (7.11) (7.58) (-10.51) (10.19) (-0.85) (-0.30) (-6.47) (5.09) (7.39) (-9.25) (-9.03) 0.03 (0.14) (10.47) 1.98 (2.63) 0.45 (0.35) 0.45 (0.35) (-0.71) (-0.30) 1.06 (-6.11) 3.12 (4.98) 4.56

19 Table 3 Fama-MacBeth cross-sectional regressions Fama-MacBeth cross-sectional regressions results are computed for stock returns of various holding periods (each panel gives the appropriate holding period), on the following variables: the natural logarithm of the ratio of book value of equity to market value of equity measured at the end of December t-1, BM, a book-to-market dummy variable which is 0 if BM is missing, BM Dum., the natural logarithm of market equity measured at the end of June, ME, the past six month s stock return as a proxy for momentum, MOM, and the percentage change in the number of shares outstanding adjusted for splits to capture the effect of share repurchases and SEO s. SHRCHG = [(shares outstanding, t-6) (shares outstanding, t-18) ]/ (shares outstanding, t-18). The Average R 2 is the average of the adjusted R 2 obtained from the cross-sectional regressions, in percent. Shares associated with splits and stock dividends are not included in the computation of shares outstanding. The results presented in the table are the regression coefficients and the t-statistics in brackets. These regressions are for 384 months from 1/1/1970 to 12/1/2002, with a total of 2,347,680 firm-observations. Multi-month holding period results utilize overlap consistent t-statistics. Coefficients with significant t-statistics are bolded and all coefficients are in percent. Panel A: Dependent variable is the one month stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (4.94) 0.10 (3.03) (-1.01) (1.97) (-0.84) (3.76) 0.84 (2.29) (4.09) (-5.55) (2.26) 0.07 (2.26) (-0.43) (-0.84) 0.86 (2.69) (2.34) 0.07 (2.11) (-0.42) (-0.86) 0.83 (2.61) (-5.71) 3.33 Panel B: Dependent variable is the one quarter stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (4.09) 0.33 (3.01) (-0.99) (2.12) (-1.10) (3.94) 3.34 (4.18) (4.06) (-5.88) (2.37) 0.22 (1.77) (-0.10) (-1.14) 3.43 (4.56) (2.44) (-0.13) 1.13 (1.60) (-1.15) 3.33 (4.44) (-5.21) 4.02

20 Table 3--Continued Fama-MacBeth cross-sectional regressions Panel C: Dependent variable is the six month stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (5.26) 0.71 (3.77) (-0.83) (3.05) (-1.75) (4.88) 7.78 (6.02) (5.08) (-5.12) (3.36) 0.46 (2.34) 0.19 (0.23) (-1.81) 7.69 (6.32) (3.45) 0.43 (2.24) 0.18 (0.23) (-1.83) 7.50 (6.18) (-4.55) 3.93 Panel D: Dependent variable is the one year stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (6.44) 1.38 (3.40) (-0.19) (3.02) (-1.57) (6.97) 8.05 (3.47) (7.03) (-3.64) (3.27) 0.91 (2.89) 1.37 (0.92) (-1.69) 7.93 (4.15) (3.35) 0.86 (2.75) 1.36 (0.92) (-1.71) 7.62 (3.93) (-3.26) 2.86

21 Table 4 Fama-MacBeth cross-sectional regressions with SEO and share repurchase removed Fama-MacBeth cross-sectional regressions results are computed for stock returns of various holding periods (each panel gives the appropriate holding period). All firm observations for three years after an SEO or repurchase announcement have been removed. The following are independent variables: the natural logarithm of the ratio of book value of equity to market value of equity from December t-1, BM, a book-to-market dummy variable which is 0 if BM is missing, BM Dum., the natural logarithm of market equity from June t-1, ME, the natural logarithm of the market value of the firm as of June t, the past six month s stock return as a proxy for momentum, MOM, and the percentage change in the number of shares outstanding adjusted for splits to capture the effect of share repurchases and SEO s, SHRCHG = [(shares outstanding, t-6) (shares outstanding, t-18) ]/ (shares outstanding, t-18). Shares associated with splits and stock dividends are not included in the computation of shares outstanding. The Average R 2 is the average of the adjusted R 2 obtained from the cross-sectional regressions, in percent. The results presented in the table are the regression coefficients and the t-statistics in brackets. Multi-month holding period results utilize overlap consistent t-statistics. These regressions are for 384 months from 1/1/1970 to 12/1/2002, with a total of 1,996,722 firm-observations. Coefficients with significant t-statistics are bolded and all coefficients are in percent. Panel A: Dependent variable is the one month stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (4.70) 0.09 (2.88) (-0.96) (2.03) (-1.04) (3.58) 0.79 (2.14) (3.90) (-5.06) (2.34) 0.07 (2.08) (-0.24) (-1.08) 0.83 (2.55) (2.42) 0.06 (1.92) (-0.25) (-1.09) 0.79 (2.46) (-5.24) 3.29 Panel B: Dependent variable is the one quarter stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (3.92) 0.29 (2.87) (-0.36) (2.16) (-1.28) (3.76) 3.24 (4.05) (3.86) (-4.91) (2.44) 0.18 (1.59) (-0.62) (-1.36) 3.38 (4.50) (2.52) 0.17 (1.49) (-0.02) (-1.37) 3.27 (4.39) (-4.37) 3.97

22 Table 4--continued Fama-MacBeth cross-sectional regressions with SEO and share repurchase removed Panel C: Dependent variable is the six month stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (5.01) 0.64 (3.73) (-0.72) (3.15) (-2.02) (4.64) 7.57 (5.76) (4.83) (-4.66) (3.52) 0.39 (2.15) (-0.41) (-2.14) 7.56 (6.13) (3.61) 0.36 (2.05) (-0.40) (-2.16) 7.38 (6.00) (-4.10) 3.85 Panel D: Dependent variable is the one year stock return. Intercept BM BM Dum. ME MOM SHRCHG Avg. R (6.18) 1.26 (3.37) (-0.12) (3.14) (-1.80) (6.67) 7.68 (3.08) (6.71) (-3.30) (3.42) 0.78 (2.76) 0.52 (0.35) (-1.96) 7.67 (3.70) (3.49) 0.73 (2.61) 0.16 (1.09) (-1.98) 7.36 (3.50) (-2.93) 2.78

23 Table 5 Out-of-sample Fama-MacBeth cross-sectional regressions Fama-MacBeth cross-sectional regressions results are computed for stock returns of various holding periods (each panel gives the appropriate holding period), on the following variables: the natural logarithm of market equity measured at the end of June, ME, the natural logarithm of the past six month s stock return as a proxy for momentum, MOM, and the 6-months lagged percentage change in the number of shares outstanding adjusted for splits to capture the effect of share repurchases and SEO s, Shrchg = [(shares outstanding, t-6) (shares outstanding, t-18) ]/ (shares outstanding, t-18). The Average R 2 is the average of the adjusted R 2 obtained from the cross-sectional regressions, in percent. Shares associated with splits and stock dividends are not included in the computation of shares outstanding. The results presented in the table are the regression coefficients and the t-statistics in brackets. Multi-month holding period results utilize overlap consistent t-statistics. These regressions are for 480 months from 3/1/1927 (to ensure the existence of shares outstanding) to 12/1/1969, with a total of 557,990 firm-observations. Coefficients with significant t-statistics are bolded and all coefficients are in percent. Panel A: Dependent variable is the one month stock return. Intercept ME MOM SHRCHG Avg. R (3.63) (-3.21) (3.35) 0.74 (1.36) (3.63) (-0.72) (3.71) (-3.32) 0.85 (1.82) (3.71) (-3.31) 0.86 (1.84) (-0.81) 4.85 Panel B: Dependent variable is the one quarter stock return. Intercept ME MOM SHRCHG Avg. R (3.03) (-2.62) (2.79) 2.41 (1.85) (3.35) (-0.79) (2.92) (-2.7) 2.64 (2.23) (2.92) (-2.69) 2.65 (2.23) (-0.81) 6.01

24 Table 5--Continued Out-of-sample Fama-MacBeth cross-sectional regressions Panel C: Dependent variable is the six month stock return. Intercept ME MOM SHRCHG Avg. R (2.95) (-2.64) (2.89) 6.93 (4.66) (3.1) (-1.01) (2.86) (-2.66) 6.95 (5.22) (2.86) (-2.66) 6.97 (5.26) (-0.95) 5.74 Panel D: Dependent variable is the one year stock return. Intercept ME MOM SHRCHG Avg. R (2.94) (-2.2) (4.84) 5.68 (2.5) (4.07) (-1.3) (3.02) (-2.21) 5.91 (2.94) (3.02) (-2.19) 5.92 (2.93) (-1.16) 4.92