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Takeovers and the size effect.

Empirical evidence suggests takeovers play an important role in the cross-section of stock returns. I study the influence of takeover activity on common factors, size and book-to-market. After controlling for takeovers, I find that the size effect is reduced by over 40% and is no longer an anomaly. Specifically, the CAPM cannot be rejected relative to portfolios sorted on size. I do not find that takeovers have any impact on book-to-market. Furthermore, takeovers impact the alpha of small size portfolios but do not affect their risk profile.

Introduction

Corporate finance literature has documented large abnormal returns surrounding takeover events. Empirical evidence from Cremers et al. (2009) suggests that takeovers play an important role in the cross-section of stock returns; specifically, they find that firms with a higher likelihood of becoming takeover targets have higher expected returns. I examine how takeovers impact commonly used factors of size and book-to-market. I find that the premium related to the size effect is in large part driven by takeover activity, while takeovers have no real affect on the premium related to book-to-market. While the actual size effect remains unchanged, these results give clarification and context to the mechanism that drives the anomaly.

The size effect was first documented by Banz (1981) and Reinganum (1981). Since that time, much research in the literature has been dedicated to understanding its cause and interpreting its meaning in both efficient market and behavioral frameworks. The standard explanation for the size effect, which was promoted by Fama and French (1992, 1993 and 1996), is that size is a proxy for a systematic risk factor related to distress. Other explanations, including Berk (1995), demonstrate a mechanical explanation of the size effect, and other studies connect the size effect to calendar effects and other phenomena.

I borrow from results in the corporate finance literature to formulate an acquisition-based explanation of the size effect. The evidence around mergers and acquisitions is established in Bradley et al. (1988), which shows that target firms receive an abnormal announcement return of 31.77%; Kaplan and Weisbach (1992), who find an abnormal return of 26.90%; and Andrade et al. (2001), who find that abnormal announcement returns from 1973-1999 are 16.0%. Andrade et al. (2001) also show that the median relative size of targets to acquirers is 11.7%, which provides anecdotal evidence that smaller firms are more likely to be the target of takeovers than larger firms who are the acquirers. This series of results indicates that there are large abnormal returns, which appear to be concentrated in the smaller firms. Cremers et al. (2009) use a probit model to determine the probability of a firm being taken over. In their model, they find that market capitalization has a negative and statistically significant coefficient, implying that smaller firms have a higher probability of being taken over.

Knez and Ready (1997) study the size effect and find that by trimming the most extreme outliers, the size effect disappears. They point out that merger and acquisition activity could lead to their statistical findings but fail to find evidence to support this hypothesis. While they find that the extreme observations they document are not caused by takeover activity, they fail to examine the overall impact of mergers and acquisitions on the returns to size-sorted portfolios and cannot make a statement on the total effect.

I find that after controlling for the impact of takeovers, the size effect is diminished over the entire sample period. These results do not imply the non-existence of the size effect but, rather, give context to why the size effect occurs. I find that the size effect occurs because firms in small capitalization portfolios are more likely to be acquired than firms in the big capitalization portfolios. Not only are smaller firms more likely to become takeover targets, but the abnormal announcement returns to smaller firms are greater than those for the larger capitalization firms. Further, I find that takeovers impact the alpha of the small size portfolios but do little to affect their risk profile.

Cremers et al. (2009) argue that takeover risk is systematic; hence, it should be and is priced in the cross-section of stock returns. I provide a further investigation into the link between takeovers and the size effect and find that most of the premium related to size comes from smaller firm's exposure to takeovers. The takeover factor created in Cremers et al. (2009) does not explain away the size premium. Their factor only accounts for a firm's propensity to become a takeover target and does not also account for the larger takeover premium paid to small firms relative to large firms. I decompose the returns of firms in all size deciles into returns that are and are not related to takeover activity. This allows me to account for the total impact of takeovers on the portfolios sorted on size and book-to-market.

Data

To test the implications of takeovers on the size effect, my sample includes all NYSE, AMEX and Nasdaq common stocks from July 1963 through June 2008. Each year in June breakpoints are created based on NYSE firm market capitalization. When I form portfolios based on book-to-market or double sorted on size and book-to-market, I only examine firms that exist in the intersection of CRSP and Compustat. Following Fama and French (1992), I match CRSP stock return data from July of year t to June of year t+1 with Compustat accounting information for the fiscal year ending in year t-1. I use the following variable definitions. Size is the number of shares outstanding multiplied by the stock price at the end of June of year t. Book equity is Compustat stockholder's equity, plus deferred taxes and investment tax credit, minus the book value of preferred stock. All portfolios sorted on size or book-to-market are sorted into 10 portfolios with decile breakpoints based on only NYSE firms. Portfolios formed on the double sort of size and book-to-market are sorted into 25 portfolios with five quintile breakpoints for both variables. All other data related to excess market returns, the risk-free interest rate and the Fama-French factors are from Ken French's website. (1)

The SDC mergers and acquisitions database available from Thomson Reuters is often used in takeover research. The data are limited in that the database only has acquisitions back to 1981, while the size effect is documented much earlier. To overcome this limitation, I use CRSP delisting codes to identify acquired firms. Firms with delisting codes between 200 and 399 are considered to have been acquired as in Knez and Ready (1997).

Measuring the Impact of Acquisitions

While the majority of abnormal takeover returns occur at deal announcement, the risk arbitrage literature, such as Baker and Savasoglu (2002), documents abnormal returns to targets between takeover announcements and final deal completion. It has also been documented by Bradley et al. (1988) and Andrade et al. (2001) that there is a return run-up prior to takeover announcements. This evidence suggests that returns to takeover targets are impacted over an extended period of time prior to delisting. To control for the impact of takeovers on stock returns, the entire takeover period must be accounted for. For this reason, I use data from the SDC mergers and acquisitions database to determine the standard length of time between takeover announcements and deal completion.

Using SDC data between 1981 and 2008, I estimate the duration of time between merger announcement and completion. Table 1 shows the distribution of deal duration over the sample period. In order to maximize the percentage of takeover announcements captured in the takeover window, while minimizing the size of the window, I use the 10 months prior to delisting as the window for returns to be impacted by acquisitions. (2) Examining all SDC merger data from 1981 through 2008, I find that 95% of deals are completed within 10.6 months of announcement. Table 1 shows that 75% of deals are complete within 5.7 months, but to capture 99% of deals, the announcement window would need to be longer than 18 months.

To measure the impact of acquisitions, I recreate the various size-based portfolios and remove returns to target firms 10 months prior to their delisting. This has the result of delisting firms earlier than their actual delisting in an attempt to remove returns that are impacted by the takeover process. This allows me to compare the returns of various size and book-to-market sorted portfolios that are not affected by takeover activity to the overall portfolios. Also, by delisting the firms earlier, I am effectively replacing their returns with the average returns to their portfolio. I perform sensitivity analysis on the length of the 10-month takeover measurement window. The results are robust to small changes in the window length.

Three main factors suggest that analyzing target returns in the 10 months prior to delisting to measure the impact of takeovers is conservative. First, I only examine deals where targets are delisted. Many deals that do not result in 100% ownership by the acquiring firm are completed, and the target is never delisted. Those deals are not included in my sample. The second item is that I only measure the impact of takeovers on targets. While the results of measuring returns to acquirers has generally been inconclusive, Moeller et al. (2004) find that larger acquirers tend to have the worst stock reaction upon merger announcements. This is significant because while I show that takeovers result in an increase in returns to small size portfolios, the results of Moeller et al. (2004) suggest that acquisitions would decrease the returns to the large size portfolios. The final issue is the use of a 10-month window. By using a window of this length, I do not capture all announcements, the run-up prior to announcements at the end of the window or the impact of multiple bids that could be extended over a larger time period. Consequentially, my results will be an underestimate of the impact of takeovers on the size and book-to-market effects.

The percentage of firms acquired and the returns to firms in the takeover window are shown in Table 2 for each size-based portfolio. By sorting firms on size, two different effects related to takeovers are shown. Panel A shows that smaller firms receive higher returns during the takeover period, and Panel B shows that smaller firms are more likely to be acquired than firms in the larger capitalization portfolios. The double effect of higher takeover returns and higher probability of takeovers causes a sort of firms on size to have a bigger impact on acquisitions than sorting on other variables that are related only to the probability of takeover.

Figure 1 shows the average impact of takeovers for the small and big size portfolios over time as measured by the difference between returns to size-sorted portfolios and the same portfolios with target firms removed during the takeover window. While both are consistently positive, the average small portfolio impact is nearly uniformly greater than the average impact on the big portfolio. Further, the impact on the small portfolio can be seen as loosely consistent with merger waves, while the impact on the big portfolio is more ambiguous. The main exception to this is the late 1960s, which is known for its conglomerate mergers of large companies. The economic significance of this difference is demonstrated in Figure 2, which shows the cumulative returns to the small and big portfolios with the impact of takeovers measured.

Time Series Analysis of the Size Effect

The average returns to the value-weighted size decile portfolios are shown in Table 3. The impact of takeovers on the small portfolio returns is 0.12% per month larger than the impact on the big portfolio. The impact of takeovers is very consistent over time, which is shown by the standard deviation of returns being nearly unchanged when comparing the raw returns and the returns adjusted for the impact of acquisitions. Also, the time-series correlation of the raw excess returns with the returns adjusted for takeovers is greater than .99 for all size deciles. This confirms that even with the presence of merger waves, takeovers primarily impact the mean returns over time of the sorted portfolios but not their risk profile. This is because the variance induced by merger waves is dominated by the original return variance.

The size effect was first documented as an anomaly that contradicted the validity of the CAPM. I use the CAPM as a benchmark model to test the impact of takeovers as a result. Table 4 shows the time-series regression results for the CAPM for portfolios of both size-sorted portfolios that include all firms and the portfolios that remove target firms. Panel A shows the results for value-weighted portfolios, while Panel B presents the results for equal-weighted portfolios. Once I control for the effect of takeovers, there is an over 40% reduction in the spread alphas ([alpha]small--[alpha]big) from 27 basis points per month to 15 for the value-weighted portfolios. Once targets are removed, I no longer find the size effect to be significant.

Panel B shows the same tests as Panel A but gives the results for equal-weighted portfolios. In the equal-weighted portfolios, there is still evidence that the size effect exists even after controlling for takeovers. By looking at the alphas for all portfolios other than the small portfolio, we can see that this is due solely to the small portfolio. This indicates that even after controlling for takeovers there is still some evidence for the size effect in the very smallest firms, given that they receive more weight in the equal-weighted portfolios. This implies that there is still evidence of a size effect within the very smallest firms. These are the firms most likely to be affected by other explanations for the size effect, like liquidity and information costs.

Implications for Book-to-Market

The book-to-market effect is the other significant effect documented relative to the Fama-French three-factor model. For robustness, I test the impact of takeovers on portfolios sorted on book-to-market values of equity. There is some evidence that takeovers might impact the book-to-market effect given that Q is a significant factor in the Cremers et al. (2009) probit model for the probability of a firm being taken over. Table 5 shows a CAPM model test of the size effect on time-series portfolios. Given the magnitude of the book-to-market effect, takeovers contribute at best marginally to the effect of increasing the alpha spread ([alpha]high--[alpha]low) by roughly 10% in the value-weighted portfolios and 3% in the equal-weighted portfolios. The significance of the book-to-market effect is completely unaffected by removing the targets.

These results show that the takeovers are specifically a driving force behind the size effect while the book-to-market effect remains essentially unchanged. Figure 3 demonstrates the impact of acquisitions on portfolios sorted by size and book-to-market. The average difference between size-and book-to-market-sorted returns and the same portfolios adjusted for takeovers is shown. Across the book-to-market axis, there is no clear relation between book-to-market and the impact of takeovers, but across the size axis there is a clear increasing impact of acquisitions as firms get smaller.

Takeovers and Portfolio Correlations

Table 6 shows the time-series correlations of market returns, SMB, HML, momentum and takeover factors from January 1981 to December 3 2004. (3) The takeover factor is defined in Cremers, Nair and John (2009). SMB is the small minus big size return factor, and HML is the high minus low book-to-market return factor. Both SMB and HML are defined in Fama and French (1996). UMD is the momentum return factor defined in Carhart (1997). It also shows the correlations with duplicate SMB and HML factors that remove the impact of takeovers by removing target firms in the 10 months prior to their delisting due to takeovers. SMB and HML are almost perfectly correlated with the duplicate factors. This is more evidence that takeovers do not affect the risk structure of the portfolios.

Interestingly, the SMB factor and the SMB factor controlled for takeovers have extremely low correlations with the Takeover Factor of Cremer et al. (2009). Again, this comes from the return variance in the size-sorted portfolios dominating the merger-induced variance. These results do not imply that SMB should be replaced by the takeover factor, because they are fundamentally different things. The takeover factor was created under the assumption that firms with high probability of being taken over have different characteristics from protected firms, while the size effect is simply the effect of having a larger concentration of firms that are taken over with higher takeover premiums in the small portfolios. These results call into question the standard risk interpretation of the size effect.

Conclusions

Evidence from Cremers et al. (2009) suggests that takeovers play an important role in the cross-section of stock returns; specifically, they find that firms with a higher likelihood of becoming takeover targets have higher expected returns. I examine how takeovers impact commonly used factors of size and book-to-market. I find that the premium related to the size effect is in large part driven by takeover activity, while takeovers have no real effect on the premium related to book-to-market. While the actual size effect remains unchanged, these results give clarification and context to the mechanism that drives the anomaly.

The size effect has been researched for decades. The empirical findings have provided information related to the seasonality and consistency of the size effect but have yet to provide a grounded reason for its existence. I find that controlling for the impact of takeovers, the size effect is diminished over the entire sample period by over 40% and that it is significantly dampened during the time period when the size effect was originally discovered. These results do not imply the non-existence of the size effect but, rather, give context to why the size effect occurs. I find that the size effect occurs because firms in small capitalization portfolios are more likely to be acquired than firms in the big capitalization portfolios. Not only are smaller firms more likely to become takeover targets, but the abnormal announcement returns to smaller firms are greater than for the larger capitalization firms. Further, I find that takeovers impact the alpha of the small size portfolios but do little to affect their risk profile.

The desire for an explanation of the size effect comes from the lack of a theoretical foundation as to why it even exists. I find that the premium related to size is not due to distress risk but is instead due to the impact of takeovers, specifically, that smaller firms are more likely to be taken over with a higher takeover premium than larger firms. In the original findings related to the size effect, Banz (1981) says:

   The size effect exists but it is not at all clear why it exists.
   Until we find an answer, it should be interpreted with caution. It
   might be tempting to use the size effect, e.g., as the basis for a
   theory of mergers--large firms are able to pay a premium for the
   stock of small firms since they will be able to discount the same
   cash flows at a smaller discount rate. Naturally, this might turn
   out to be complete nonsense if size were to be shown to be just a
   proxy.


This suggests that the size effect could be related to mergers, but I have found no previous evidence to support this conjecture. There have been two different questions in the literature. What is this size effect, and why do managers pay large takeover premiums? I believe that these questions are just two sides of the same coin.

Current asset pricing models see the world through the viewpoint of investors maximizing some objective function, but more thought should be given to the roles of takeovers in these models. If managers are able, as Banz (1981) suggested, to use a different discount rate or gain value not only from the cash flows but also from the control rights of a firm, then they would value assets differently than other investors. Corporate finance models suggest that managers may value both the cash flows and control rights to a firm separately. These types of models may need to be incorporated in asset pricing theory.

A takeover explanation of the size effect is also not inconsistent with Berk's (1995) work that suggests the size effect is simply mechanical. If two firms have an equal true value that is unknown to the market and unequal market values, the firm with the smaller initial market capitalization should have higher returns as information is revealed to the market. As acquirers attempt to identify undervalued takeover targets, they would simply be increasing the information revelation process described by Berk (1995).

In this paper, I study the influence of takeover activity on the size effect. Having controlled for the impact of takeovers, I find that the size effect is no longer an anomaly. Specifically, the CAPM cannot be rejected relative to portfolios sorted on size. This implies that the premium related to the size effect is unrelated to distress or systematic risk but, rather, it is driven by takeover premiums.

BRADLEY A. GOLDIE

Miami University (Ohio)

References

Andrade, Gregor, Mark Mitchell, and Erik Stafford. "New Evidence and Perspectives on Mergers." Journal of Economic Perspectives 15.2(2001): 103-20.

Baker, Malcom and Serkan Savasoglu. "Limited Arbitrage in Mergers and Acquisitions." Journal of Financial Economics 64.1(2002): 91-115.

Banz, Rolf W. "The Relationship between Return and Market Value of Common Stocks." Journal of Financial Economics 9.1(1981): 3-18.

Berk, Jonathan B. "A Critique of Size-Related Anomalies." Review of Financial Studies 8.2(1995): 275-86.

Bradley, Michael, Anand Desai, and E. Han Kim. "Synergistic Gains from Corporate Acquisitions and Their Division between the Stockholders of Target and Acquiring Firms." Journal of Financial Economics 21.1(1988): 3-40.

Carhart, Mark, M. "On Persistence in Mutual Fund Performance." Journal of Finance 52.1(1997): 57-82

Cremers, K. J. Martijn, Vinay B. Nair, and Kose John. "Takeovers and the Cross-Section of Returns." Review of Financial Studies 22.4(2009): 1409-46.

Dichev, Ilia D. "Is the Risk of Bankruptcy a Systematic Risk?" Journal of Finance 53.3(1998): 1131-47.

Fama, Eugene R, and Kenneth R. French. "The Cross-Section of Expected Stock Returns." Journal of Finance 47.2(1992): 427-65.

--. "Common Risk Factors in the Returns of Stocks and Bonds." Journal of Financial Economics 33.1(1993): 3-56.

--. "Multifactor Explanations of Asset Pricing Anomalies." Journal of Finance 51.1(1996): 55-84.

Gibbons, Michael R., Stephen A. Ross, and Jay Shanken. "A Test of the Efficiency of a Given Portfolio." Econometrica 57.5(1989): 1121-52.

Horowitz, Joel L, Tim Loughran, and N.E. Savin. "Three Analyses of the Firm Size Premium." Journal of Empirical Finance 7.2(2000): 143-53.

Kaplan, Steven, and Michael Weisbach. "The Success of Acquisitions: Evidence from Divestitures." Journal of Finance 47.1(1992): 107-38.

Knez, Peter J., and Mark J. Ready. "On the Robustness of Size and Book-to-Market in Cross-Sectional Regressions." Journal of Finance 52.4(1997): 1355-82.

Moeller, Sara B., Frederik P. Schlingemann, and Rene M. Stulz. "Firm Size and the Gains from Acquisitions." Journal of Financial Economics 73.2(2004): 201-28.

Reinganum, Marc R. "Misspecification of Capital Asset Pricing." Journal of Financial Economics 9.1(1981): 19-46.

Van Dijk, Mathijs A. "Is Size Dead? A Review of the Size Effect in Equity Returns." Journal of Banking and Finance 35.12(2011): 3263-74.

(1) http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html

(2) The results are robust to use of a window of 6-18 months

(3) I would like to thank Martijn Cremers for providing me with the takeover factor created in Cremers et al. (2009).

TABLE 1
Announcement to Completion Duration

This table presents the length of time between deal announcement
and deal completion for all completed deals in the SDC database
between 1981 and 2008. All target firms are listed on NYSE, AMEX
or Nasdaq. The count is the number of deals completed in each
time period, with the other variables representing the number of
months between announcement and completion.

Time                                    75th
Period      Count    Mean   Median   Percentile

1981-1985     589    3.5     2.5        5.1
1986-1990   1,324    5.1     3.9        6.6
1991-1995   1,322    5.1     4.5        6.8
1996-2000   2,833    4.2     3.6        5.3
2001-2005   1,807    4.1     3.4        5.3
2006-2008     977    3.9     3.4        5.0
1981-2008   8,852    4.4     3.6        5.7

Time           95th         99th
Period      Percentile   Percentile   Maximum

1981-1985     10.5          18.4       29.4
1986-1990     13.4          22.8       68.4
1991-1995     12.1          22.6       38.1
1996-2000      9.6          15.6       35.0
2001-2005      9.4          16.3       52.3
2006-2008      8.6          15.8       25.7
1981-2008     10.6          18.3       68.4

TABLE 2
Average Takeover Returns and the Percentage of Firms Acquired

The sample includes all common stocks listed on NYSE, AMEX or
Nasdaq listed on the CRSP database. Size deciles are sorted on
NYSE breakpoints. Target firms are identified as firms that have
a CRSP delisting code of 200-399. Average returns in percentages
are measured during the 10 months prior to firm delisting. The
percentage for firms that are acquired is the total number of
takeovers in a size decile each year divided by the total number
of firms in the decile.

Panel A: Average Returns to Acquired Firms during 10 Months Prior
to Delisting

Time
Period    Small   2    3    4    5    6    7    8    9   Big  Total

1963:07-   4.3   4.0  3.8  4.0  4.2  4.6  3.1  2.8  2.3  3.3   4.0
1968:06

1968:07-   3.3   2.4  1.8  1.6  2.0  2.6  3.3  2.8  4.6  4.2   2.7
1973:06

1973:07-   6.1   5.2  3.8  6.3  5.0  3.5  5.0  4.1  4.2  0.7   5.6
1978:06

1978:07-   5.8   6.4  5.7  5.5  6.3  4.8  5.9  4.5  4.8  3.3   5.8
1983:06

1983:07-   3.5   4.3  4.1  4.4  4.1  3.4  4.8  4.6  4.3  4.4   3.9
1988:06

1988:07-   4.2   4.1  4.6  4.1  3.8  3.1  3.5  3.5  3.9  6.1   4.1
1993:06

1993:07-   5.2   4.7  4.1  4.1  4.2  3.3  3.2  3.1  4.3  3.3   4.6
1998:06

1998:07-   5.7   3.7  3.5  3.6  4.2  3.8  3.3  2.5  3.0  2.0   4.5
2003:06

2003:07-   3.9   3.7  3.5  4.0  3.3  3.5  3.3  2.6  1.3  3.2   3.7
2008:06

1963:07-   4.8   4.3  4.0  4.2  4.1  3.6  3.8  3.1  3.3  3.1   4.4
2008:06

Panel B: The Percentage of Firms in Each Portfolio that Is Acquired

Time
Period    Small   2    3    4    5    6    7    8    9   Big  Total

1963:07-   16%   23%  22%  26%  19%  18%  16%   7%   4%   2%   18%
1968:06

1968:07-   14%   11%  15%  16%  21%  11%  10%  11%   3%   2%   14%
1973:06

1973:07-   14%   19%  19%  14%  14%  14%   7%   4%   2%   2%   15%
1978:06

1978:07-   20%   25%  32%  26%  18%  22%  22%  16%  14%  10%   24%
1983:06

1983:07-   20%   33%  29%  31%  40%  32%  28%  20%  16%  13%   27%
1988:06

1988:07-   15%   24%  21%  24%  32%  20%  19%  15%   9%   7%   20%
1993:06

1993:07-   24%   35%  37%  20%  31%  26%  34%  18%  19%  14%   30%
1998:06

1998:07-   33%   46%  39%  43%  42%  35%  45%  42%  31%  26%   41%
2003:06

2003:07-   33%   32%  36%  29%  37%  30%  29%  28%  24%  14%   35%
2008:06

1963:07-   22%   31%  30%  28%  30%  25%  25%  19%  15%  11%   24%
2008:06

TABLE 3
The Impact of Takeover on Excess Returns

The sample includes all common stocks listed on NYSE, AMEX or
Nasdaq listed on the CRSP database. Size deciles are sorted on
NYSE breakpoints. All returns reported are in excess of the risk
free rate. Target firms are identified as firms that have a CRSP
delisting code of 200-399. Target firms are removed 10 months
prior to delisting due to acquisition to account for returns
during the takeover period. Excess returns are in excess of the
riskfree rate. ***, ** and * represent significance at the 1%, 5%
and 10% levels, respectively.

                                 Small       2         3         4

Size Decile: All Firms
Mean Excess Returns               0.73      0.64      0.69      0.67
Standard Deviation                6.40      6.28      5.96      5.80

Size Decile: Takeovers Removed
Mean Excess Returns               0.59      0.51      0.57      0.55
Standard Deviation                6.49      6.36      6.01      5.84
Returns Due to Takeovers          0.14      0.13      0.12      0.12
t-Statistic                     5.70 ***  5.40 ***  4.63 ***  4.81 ***
Correlation                      0.9997    0.9996    0.9995    0.9993

                                   5         6         7        8

Size Decile: All Firms
Mean Excess Returns               0.69      0.60      0.62     0.58
Standard Deviation                5.51      5.20      5.09     4.97

Size Decile: Takeovers Removed
Mean Excess Returns               0.58      0.51      0.53     0.53
Standard Deviation                5.56      5.23      5.13     4.99
Returns Due to Takeovers          0.11      0.09      0.09     0.05
t-Statistic                     4.40 ***  3.22 ***  3.19 ***  1.94 *
Correlation                      0.9993    0.9992    0.9993   0.9995

                                                 Small-
                                  9      Big      Big

Size Decile: All Firms
Mean Excess Returns              0.52    0.38     0.35
Standard Deviation               4.51    4.20     5.03

Size Decile: Takeovers Removed
Mean Excess Returns              0.48    0.36     0.23
Standard Deviation               4.53    4.21     5.10
Returns Due to Takeovers         0.04    0.02     0.12
t-Statistic                      1.49    0.54   4.45 ***
Correlation                     0.9995  0.9998

TABLE 4
Time Series Analysis of the Size Effect and Takeovers

This table presents the results of time series CAPM style
regressions of excess portfolio returns of size sorted portfolios
on the excess market return, which is measured as the CRSP
value-weighted market return. The F-statistic for the joint
hypothesis that all alphas are equal to zero is the Gibbons, Ross
and Shanken (1989) test statistic. The sample includes all common
stocks listed on NYSE, AMEX and Nasdaq on the CRSP database. Size
deciles are sorted on NYSE breakpoints. Target firms are
identified as firms that have a CRSP delisting code of 200-399.
Target firms are removed 10 months prior to delisting due to
acquisition to account for returns during the takeover period.
***, ** and * represent significance at the 1%, 5% and 10%
levels, respectively.

Panel A: Value Weighted

                     Small      2        3        4        5

Size Deciles: All Firms

[alpha]               0.23%    0.10%    0.15%    0.15%    0.18%
t([alpha])            1.27     0.68     1.24     1.28     1.84
[beta]                1.11     1.21     1.20     1.18     1.16
Adj. [R.sup.2]        0.58     0.71     0.77     0.78     0.84

Size Deciles: Removing Targets

[alpha]               0.09%   -0.04%    0.04%    0.02%    0.06%
t([alpha])            0.47    -0.24     0.28     0.21     0.60
[beta]                1.13     1.22     1.21     1.19     1.17
Adj. [R.sup.2]        0.57     0.70     0.76     0.78     0.84
[[alpha].sub.all]-    0.14%    0.14%    0.12%    0.12%    0.12%
[[alpha].sub.rem]

                       6        7        8        9       Big

Size Deciles: All Firms

[alpha]               0.10%    0.12%    0.09%    0.07%   -0.04%
t([alpha])            1.22     1.82     1.50     1.64    -0.91
[beta]                1.11     1.11     1.09     1.01     0.93
Adj. [R.sup.2]        0.87     0.91     0.92     0.95     0.94

Size Deciles: Removing Targets

[alpha]               0.01%    0.03%    0.03%    0.03%   -0.06%
t([alpha])            0.13     0.49     0.57     0.64    -1.29
[beta]                1.12     1.12     1.10     1.01     0.94
Adj. [R.sup.2]        0.87     0.90     0.92     0.95     0.94
[[alpha].sub.all]-    0.09%    0.09%    0.06%    0.04%    0.02%
[[alpha].sub.rem]

                                                       Total

Size Deciles: All Firms         [H.sub.0]: [[alpha].sub.small] =
                                  [[alpha].sub.big]

[alpha]                         t-stat: 1.79 *
t([alpha])                      p: 0.07
[beta]
Adj. [R.sup.2]

Size Deciles: Removing Targets  [H.sub.0]: [[alpha].sub.small] =
                                  [[alpha].sub.big]

[alpha]                         t-stat: 0.94
t([alpha])                      p: 0.35
[beta]
Adj. [R.sup.2]
[[alpha].sub.all]-
[[alpha].sub.rem]

Panel B: Equal Weighted

                     Small      2        3        4        5

Size Deciles: All Firms

[alpha]               0.54%    0.06%    0.11%    0.10%    0.13%
t([alpha])            2.65     0.39     0.82     0.88     1.31
[beta]                1.08     1.22     1.22     1.21     1.19
Adj. [R.sup.2]        0.50     0.71     0.79     0.79     0.83

Size Deciles: Removing Targets

[alpha]               0.41%   -0.09%   -0.02%   -0.03%    0.01%
t([alpha])            2.02    -0.58    -0.14    -0.22     0.08
[beta]                1.08     1.23     1.23     1.21     1.20
Adj. [R.sup.2]        0.50     0.71     0.76     0.79     0.83
[[alpha].sub.all]-    0.12%    0.14%    0.12%    0.13%    0.13%
[[alpha].sub.rem]

                       6        7        8        9       Big

Size Deciles: All Firms

[alpha]               0.09%    0.10%    0.06%    0.06%   -0.05%
t([alpha])            0.98     1.45     0.91     1.14    -0.95
[beta]                1.15     1.14     1.12     1.04     1.00
Adj. [R.sup.2]        0.86     0.90     0.91     0.93     0.94

Size Deciles: Removing Targets

[alpha]               0.00%    0.01%    0.00%    0.02%   -0.08%
t([alpha])           -0.05     0.20     0.01     0.30    -1.57
[beta]                1.15     1.14     1.12     1.04     1.00
Adj. [R.sup.2]        0.86     0.90     0.91     0.93     0.94
[[alpha].sub.all]-    0.09%    0.09%    0.06%    0.05%    0.03%
[[alpha].sub.rem]

                                                       Total

Size Deciles: All Firms         [H.sub.0]: all = [[alpha].sub.0]

[alpha]                         t-stat: 3.15 ***
t([alpha])                      p: 0.00
[beta]
Adj. [R.sup.2]

Size Deciles: Removing Targets  [H.sub.0]: [[alpha].sub.small] =
                                  [[alpha].sub.big]

[alpha]                         t-stat: 2.62 ***
t([alpha])                      p: 0.01
[beta]
Adj. [R.sup.2]
[[alpha].sub.all]-
[[alpha].sub.rem]

TABLE 5
Time Series Analysis of the Book-to-Market Effect and Takeovers

This table presents the results of time series CAPM style
regressions of excess portfolio returns of book-to-market sorted
portfolios on the excess market return, which is measured as the
CRSP value-weighted market return. The F-statistic for the joint
hypothesis that all alphas are equal to zero is the Gibbons, Ross
and Shanken (1989) test statistic. The sample includes all common
stocks listed on NYSE, AMEX and Nasdaq on the intersection of
CRSP and Compustat. Book-to-market deciles are sorted on NYSE
breakpoints. Target firms are removed 10 months prior to
delisting due to acquisition to account for returns during the
takeover period. ***, ** and * represent significance at the 1%,
5% and 10% levels, respectively

Panel A: Value Weighted

                      Low       2        3        4       5

Book-to-Market Deciles: All Firms

[alpha]              -0.17%    0.02%   -0.03%   0.06%   0.04%
t ([alpha])          -2.16     0.36    -0.42    0.81    0.44
[beta]                1.08     1.04     0.99    0.95    0.93
Adj. [R.sup.2]        0.86     0.92     0.90    0.85    0.82

Book-to-Market Deciles: Removing Targets

[alpha]              -0.19%    0.00%   -0.06%   0.02%   0.00%
t ([alpha])          -2.32     0.04    -0.92    0.26    0.00
[beta]                1.08     1.04     0.99    0.96    0.93
Adj. [R.sup.2]        0.86     0.92     0.90    0.84    0.83
[[alpha].sub.all]-    0.01%    0.02%    0.03%   0.04%   0.04%
[[alpha].sub.rem]

                       6       7       8       9     High

Book-to-Market Deciles: All Firms

[alpha]              0.22%   0.29%   0.34%   0.34%   0.38%
t ([alpha])          2.57    3.22    3.35    3.09    2.72
[beta]               0.87    0.87    0.87    0.93    0.97
Adj. [R.sup.2]       0.79    0.77    0.73    0.71    0.64

Book-to-Market Deciles: Removing Targets

[alpha]              0.18%   0.25%   0.31%   0.30%   0.30%
t ([alpha])          2.11    2.73    3.05    2.69    2.15
[beta]               0.87    0.87    0.87    0.93    0.98
Adj. [R.sup.2]       0.78    0.76    0.73    0.71    0.64
[[alpha].sub.all]-   0.04%   0.04%   0.03%   0.04%   0.08%
[[alpha].sub.rem]

                                         Total

Book-to-Market Deciles: All Firms        [H.sub.0]:[[alpha].sub.low] =
                                           [[alpha].sub.high]
[alpha]                                  t-stat: -4.50 ***
t ([alpha])                              p: 0.00
[beta]
Adj. [R.sup.2]

Book-to-Market Deciles: Removing Targets [H.sub.0]:[[alpha].sub.low] =
                                           [[alpha].sub.high]
[alpha]                                  t-stat: -3.96 ***
t ([alpha])                              p: 0.00
[beta]
Adj. [R.sup.2]
[[alpha].sub.all]-
[[alpha].sub.rem]

Panel B: Equal Weighted

                      Low       2        3        4       5

Book-to-Market Deciles: All Firms

[alpha]              -0.35%   -0.01%    0.12%   0.23%   0.33%
t ([alpha])          -2.28    -0.04     1.01    2.01    2.83
[beta]                1.40     1.24     1.16    1.09    1.04
Adj. [R.sup.2]        0.74     0.77     0.77    0.76    0.74

Book-to-Market Deciles: Removing Targets

[alpha]              -0.41%   -0.07%    0.05%   0.16%   0.25%
t ([alpha])          -2.62    -0.57     0.41    1.34    2.18
[beta]               -1.40     1.24     1.17    1.09    1.04
Adj. [R.sup.2]        0.74     0.77     0.77    0.76    0.74
[[alpha].sub.all]-    0.05%    0.07%    0.07%   0.08%   0.07%
[[alpha].sub.rem]

                       6       7       8       9     High

Book-to-Market Deciles: All Firms

[alpha]              0.47%   0.57%   0.64%   0.77%   0.96%
t ([alpha])          3.99    4.57    4.80    5.11    5.07
[beta]               1.01    0.98    0.96    1.00    1.01
Adj. [R.sup.2]       0.72    0.69    0.65    0.61    0.50

Book-to-Market Deciles: Removing Targets

[alpha]              0.39%   0.49%   0.56%   0.68%   0.88%
t ([alpha])          3.30    3.90    4.21    4.52    4.59
[beta]               1.01    0.99    0.97    1.00    1.01
Adj. [R.sup.2]       0.72    0.69    0.65    0.61    0.50
[[alpha].sub.all]-   0.08%   0.08%   0.08%   0.09%   0.08%
[[alpha].sub.rem]

                                         Total

Book-to-Market Deciles: All Firms        [H.sub.0]:[[alpha].sub.low] =
                                           [[alpha].sub.high]
[alpha]                                  t-stat: -4.36 ***
t ([alpha])                              p: 0.00
[beta]
Adj. [R.sup.2]

Book-to-Market Deciles: Removing Targets [H.sub.0]:[[alpha].sub.low] =
                                           [[alpha].sub.high]
[alpha]                                  t-stat: -4.23 ***
t ([alpha])                              p: 0.00
[beta]
Adj. [R.sup.2]
[[alpha].sub.all]-
[[alpha].sub.rem]

TABLE 6
Takeovers and Factor Correlations

This table reports the correlation matrix for various return
factors at a monthly frequency. The takeover factor is defined in
Cremers, Nair and John (2009). SMB is the small minus big size
return factor, and HML is the high minus low book-to-market
return factor. Both SMB and HML are defined in Fama and French
(1996). UMD is the momentum return factor defined in Carhart
(1997). The control factors are a recreation of SMB and HML that
have controlled for takeovers by removing target returns 10
months prior to delisting. Target firms are identified as firms
that have a CRSP delisting code of 200-399.

Time-series Correlation of the Factors

                                                               SMB
              Market    SMB      HML      UMD     Takeover   Control

SMB            18.2%
HML           -52.2%   -42.1%
UMD            -9.0%    11.1%    -9.6%
Takeover      -32.0%   -10.0%    50.3%   -31.8%
SMB Control    18.2%    99.7%   -42.4%    12.9%   -10.5%
HML Control   -51.5%   -41.8%    98.8%   -10.8%    51.3%     -42.8%
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Author:Goldie, Bradley A.
Publication:Quarterly Journal of Finance and Accounting
Date:Dec 22, 2014
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