Abstract
We employ an event study analysis to examine the market reaction to
congressional agreement on the passage of the Sarbanes-Oxley Act of
2002. We find that as firm size increases, the negative impact of
Sarbanes-Oxley's passage decreases. The results show that the
difference in abnormal returns between the smallest and largest firms is
3.91%.
The Corporate Context of Sarbanes-Oxley
In a volatile world, burdened by corporate scandals and a decline
in investors' confidence, lawmakers crafted the Sarbanes-Oxley Act
of 2002 (hereafter abbreviated as SOX) with an enthusiastic desire for
corrective action. Passed by Congress as a reaction to financial
scandals such as Enron, WorldCom, Adelphia, Global Crossing, and Tyco,
SOX enhanced standards for corporate accountability and penalties for
corporate wrongdoing. SOX contains 11 extensive titles, ranging from
extra responsibilities for audit committees to tougher criminal
penalties for white-collar crimes such as securities fraud. In plain
English, the objective of the law was to make financial reporting more
transparent and executives more accountable, changes that were
ultimately planned to restore investors' confidence in financial
markets and enhance corporate governance.
SOX requires executives, boards of directors, and independent
auditors to take specific actions that are intended to produce more
reliable, timely, and useful financial information to the public.
Greater transparency and more reliability in corporate reporting means
that companies function in a moral and ethical environment that enhances
their credibility. This is a key benefit that should lower the
firm's cost of capital, which may improve growth. Thus, at least
theoretically, SOX could provide a win-win situation for both companies
and investors.
Although many agreed that the changes to the corporate governance
system in the U.S. were necessary, some now believe that SOX has imposed
an unnecessary burden on companies because of its high compliance costs.
A challenging issue is Section 404 of SOX, Management Assessment of
Internal Controls, which requires publicly held firms to identify
financial reporting risks, establish related controls, assess their
effectiveness, fix any material control deficiencies, and then re-test
and re-document all of the above. A March 2005 survey by Financial
Executives International shows that the first year compliance costs on
section 404 of SOX alone averaged $4.36 million per company, and large
companies with more than $5 billion in revenues spent more than $10
million per company.
Critics argue that for many firms, the costs of complying with SOX
outweigh the benefits. For example, these costs are unreasonably high
for small firms. If the compliance costs are at least in part fixed,
small firms may bear a disproportionate burden. The American Electronics
Association (AeA) claims that Section 404 compliance costs serve as a
"regressive tax on small business." The purpose of this study
is to examine the market impact of the enactment of SOX, in an effort to
determine the market's reaction to the passage of this regulation
with respect to firm size.
While the true costs of SOX compliance are not easy to measure, the
benefits are even more difficult to estimate. The promised benefits of
SOX, which include more transparent disclosure, improved corporate
governance, and enhanced investor confidence, are difficult to measure
in the short run. Thus, to investigate the impact of SOX on firms of
different sizes, we use an event study analysis. Using an event study
methodology allows us to gauge, in a single framework, the market's
perspective of the benefits versus the costs of SOX. In particular, we
find that small firms experienced a much larger negative abnormal return
on the day that Congress agreed on the passage of SOX than did large
firms. We find an almost monotonic relationship between firm size and
adverse impact of SOX. In the next section, we discuss the major
provisions of SOX, and we detail some of the provisions that have
resulted in the highest compliance costs. In addition, we discuss how
these costs are disproportionately burdensome to small firms.
SOX Provisions and Compliance Costs
Exhibit 1 includes the major titles of the Sarbanes-Oxley Act (SOX)
of 2002. SOX addresses financial reporting, CEO and CFO certifications,
internal controls, risk management, the composition of audit committees,
corporate codes of ethics, whistleblower protection and attorney
conduct.
Some of the most costly provisions include:
* Section 302, which requires the CEO and CFO to certify each
annual or quarterly report filed;
* Section 906, which provides criminal penalties for the CEOs or
CFOs who certify the reports knowing that they do not comply with
requirements of the Security Exchange Act of 1934;
* Section 401, which requires that annual and quarterly reports
disclose all material off-balance-sheet transactions and arrangements,
and that pro forma financial information be presented appropriately.
However, according to many studies, the most costly provision of
SOX is Section 404, which requires management oversight of the internal
control structure of the firm, and requires an annual assessment of this
control structure. The costs related to the fact that the CEO and CFO
must certify the accuracy of financial statements are expected to ripple
through the entire corporation, leading to increased monitoring by the
audit committees.
Other costs are those related to increased audit fees and insurance
premiums, larger expenses on internal control software, and higher
consulting-related fees. These costs are extremely difficult to measure
directly because firms may not have a direct method to measure the
monitoring costs.
By many estimates, however, Sarbanes-Oxley's compliance costs
have been much higher than expected, especially for smaller firms.
Compliance costs for Section 404 alone have mounted to more than $35
billion, 20 times higher than regulators originally estimated. In
Exhibit 2, three SOX cost-compliance studies are summarized. An AeA
report entitled "The Sarbanes-Oxley Section 404: The
'Section' of Unintended Consequences and its Impact on Small
Business" shows that Section 404 compliance costs for firms with
$100 million or less in revenues amount to 2.55% of total revenues,
while larger firm costs are lower (0.27% for firms $500-999 million;
0.16% for firms $1-4.9 billion; and 0.06% over $5 billion). In addition,
Carney [5] and a Financial Executives International survey [8] both
present evidence of mounting SOX compliance costs.
In addition to the explicit costs presented in Exhibit 1, several
academic studies have examined the implicit cost of SOX compliance. For
example, Engel et al. [7] find that the increased financial reporting
and internal control requirements introduced by SOX are principal
motives for companies in choosing to "go dark" or "go
private." In a study using a comprehensive sample of 400 companies,
Leuz et al. [9] note that on average, there is a large negative market
reaction of approximately -10% to firms' decisions to go dark, the
abnormal return at the announcement date being particularly negative for
smaller firms. Investors anticipate that by deregistering, companies
have lower-than-expected growth opportunities, lower profitability, and
potential internal control problems. These results are in line with our
conclusion that smaller companies are damaged more than large companies
by the passage of SOX.
Block [3] notes that for some firms, the cost of remaining public
more than doubled after the passage of SOX. This increase in costs is
due to higher audit costs, increased insurance premiums, and outside
director fees. Ribstein [14] finds that due to increased costs
associated with passage of SOX, particularly in personal liability,
executives may become more risk-adverse in the post-SOX environment. As
a result, companies will tackle less-risky projects, which may reduce
the value of their firms. Thus, even though in the short run the
cost-saving rationale makes sense, in the long run, this decision to
avoid risky projects will not only suppress creativity, but also have a
negative impact on overall economic growth. Zhu and Small [17] find that
American Depository Receipts (ADR) listings from foreign issuers
decreased, and ADR delistings increase, after the passage of SOX. The
increased cost of regulation has, in effect, discouraged foreign firms
from being listed on the U.S. security exchanges.
Zhang [16] investigates the private cost and benefits of SOX by
examining changes of the market index around the most significant
legislative events. He finds that the cumulative abnormal returns around
the events leading to the passage of SOX are significantly negative.
Although the total market value loss of NYSE, AMEX and NASDAQ around the
most significant three events amounts to $1.4 trillion, this loss is not
directly attributed only to SOX. Li et al. [11] consider market
reactions to the events by estimating the deviation of the market
returns from the average raw returns of nonevent days in 2002. They find
evidence of a positive association between stock returns and the extent
of earnings management, suggesting that investors viewed SOX as
beneficial. Chhaochharia and Grinstein [6] and Rezaee and Jain [13],
using the same event-study methodology, also find that SOX is
value-increasing. In the next section we detail our event-study
analysis, and we reconcile possible reasons for the contradictory
results of previous event study analyses of the passage of SOX.
Data and Empirical Method
Because our primary objective is to examine the impact of SOX on
different-sized firms, we create size-based quintiles and deciles by
partitioning our sample in two ways. First, we create a
market-capitalization-based sample. We take all firms listed in the
Center for Research in Security Prices (CRSP) database and remove all
ADRs, all warrants, and all non-ordinary shares. We calculate the market
capitalization of each firm on the last trading day in July 2002. Using
this market capitalization value, we partition the sample into five
quintiles based on the market capitalization for each security. After
applying the sample filters, there are 5,395 firms in the final market
capitalization-based sample. Second, we create an asset-based sample by
taking all firms listed in the annual COMPUSTAT database, again deleting
all non-ordinary shares, ADRs and non-U.S. listed securities, and
partition them based on their total assets. After filtering the data,
4,303 firms remain in the asset-based sample, which we partition into
five-asset-based quintiles. In a subsequent section, to examine further
the firm size relationship, we break the asset-based sample into ten
deciles.
We calculate abnormal returns for the entire sample using the
market-adjusted approach (Brown-Warner 1980). Abnormal returns are
calculated as: A[R.sub.it] = [R.sub.it] - [^.[alpha].sub.i] -
[^.[beta].sub.i][R.sub.mt] where [R.sub.it] is the return to firm i on
day t, [^.[alpha].sub.i] is an intercept term estimated using the 225
trading days returns 90 days prior to July 24, 2002, [^.[beta].sub.i] is
the market beta for the ith firm estimated using the using the 225
trading days returns prior to July 24, 2002, [R.sub.mt] and is the
market return on day t. We use the CRSP value-weighted market index as a
proxy for the market return. We focus our event study analysis around
July 24, 2002, because this is the day that the House and Senate reached
an agreement on the final regulation. We use this day as the event day
because much of the reaction should occur on the day that the rule was
agreed upon, not the day that it was signed into law by the President.
Cumulative abnormal returns (CARs) are the sum of the one-day
abnormal return estimates, and we calculate CARs for a window of one day
before and the day of the announcement (-1, 0) and for one day before,
the day of, and one day after the announcement (-1, 0, 1). Using these
specifications allows our event study to capture anticipation of
agreement (day -1) and any post-announcement stock price movement (day
1). We obtain the stock price and returns date for the event study
analysis from the CRSP database. After estimating the abnormal returns
for each firm, we average them within their quintile/decile rank, which
allows us to assess the economic impact the passage of SOX had on firms
of different sizes. We discuss the results of this analysis in the next
section.
Firm Size and the Impact of the Passage of SOX
Exhibit 3 contains the abnormal returns for the market
capitalization and asset-based quintile samples. Firms in the smallest
market capitalization quintile have market capitalizations less than
$22.14 million, and firms in the largest quintile have market
capitalizations over $2.45 billion. As a reference, firms in quintile 3
have market capitalizations between $70.9 million and $227 million. As
can be seen in Exhibit 3, firms in the two smallest market
capitalization quintiles experienced the largest negative abnormal
returns (i.e., the largest adverse economic impact), while firms in the
largest-volume quintile experienced slightly positive abnormal returns.
This indicates that small firms lost 3% of their value, while large
firms actually experienced a very small increase in value, while
controlling for general market movements on the day that the House and
Senate agreed on the final SOX legislation. These negative abnormal
returns for small firms are both economically and statistically
significant, and provide evidence of an uneven burden borne by small
firms.
Because market-capitalization quintiles may not be robust enough to
measure a size factor, we repeat the analysis using an asset-based
sample. Again we break the sample into five quintiles based on total
assets. Firms in the smallest asset-based quintile had assets worth less
than $51.9 million, and firms in the largest quintile had assets worth
more than $1.88 billion. As a reference, firms in quintile 3 had assets
between $183 million and $525 million. As can be seen in Exhibit 3, the
asset-based quintiles exhibited a similar monotonic increase in adverse
impact as firm size decreases. Again, however, the second to the
smallest quintile has the largest negative abnormal returns.
To further examine the relationship between firm size and SOX, we
break the sample into ten deciles to see if negative abnormal returns
are decreasing in size on a finer scale. In addition, we estimate
multiple-day abnormal returns for the asset-based deciles to assure the
robustness of the analysis. Exhibit 4 contains the estimates from these
specifications and we graph the results from the one-day abnormal return
model in Diagram 1.
Again, the almost monotonic increase in adverse impact to small
firms is evident. However, we note that the third decile has the largest
negative abnormal returns in all specifications, but the increasing
adverse impact is undeniable. This pattern holds across specifications
of different size-based proxies, and when we consider the
pre-announcement expectation, announcement day, and post-announcement
drift (-1,0,1); and the pre-announcement expectation, announcement day
(-1,0) specifications. In each of these specifications, smaller firms
faired poorly versus larger firms.
The true relationship between firm size and economic impact of SOX
is not apparent if one only looks at the average one-day negative
abnormal return of -1.79% (-1.93%) for the aggregated asset-based
(market capitalization-based) sample. The difference in abnormal returns
for firms in the largest asset-based decile and the smallest decile is
around -4% when considering the one-day abnormal specification. Only
after examining the abnormal returns in decile and quintile forms does
the true disproportional economic impact on firms of different sizes
become apparent.
Future Research
While our article details the differential impact associated with
the passage of SOX, our results should be taken in context of the
limited amount of time that has passed since the regulation has taken
effect. Further research is needed to gauge the long term impact of SOX
on publicly listed firms. It is possible that the costs associated with
compliance will decrease as the auditing industry adjusts to the new
methods and regulatory requirements. But further research is needed to
examine how firms have coped with the increased costs. For example, have
the costs been absorbed by the firms or passed on to consumers? In
addition, have the costs decreased since the enactment of SOX? It is
likely that the regulatory burden associated with compliance will
decrease as firms adjust to the process. A larger question is: What has
happened to the firms that have chosen to de-list from their primary
exchanges (i.e., go dark)? Do they remain private or do they, at a later
date, decide to re-list; or do they choose other financing alternatives
such as private placements?
Prior to the enactment of SOX, many firms had internal control
systems that were similar to those imposed by SOX. Of particular
interest to corporate governance researchers is an analysis of the
compliance cost differential between firms that had adequate compliance
procedures in place before the passage of SOX, and those that did not.
This would provide additional insight into the benefits of establishing
and maintaining adequate governance oversight and control mechanisms. In
addition, the reaction of the announcement of the passage of SOX would
differ between the two sets of firms. Firms with inadequate control
systems would experience lower abnormal returns than the firms that had
adequate control systems in place. Instead of our research providing a
definitive answer to the impact of SOX, we hope our research opens to
door to future study in this area.
Conclusion
More reliable financial statements, effective internal control
mechanisms, and improved ethical culture may lead to improved long-term
performance. However, at what cost? The actual compliance costs of SOX
are difficult to measure directly. Firms have an incentive to
over-report the costs of SOX in hopes of having the law repealed or
changed. In addition, the benefits of SOX are difficult to measure in
the short run. Thus, we chose to employ an event study analysis to
examine the abnormal market reaction to the passage of SOX, which
allowed us to gauge non-linearity in the benefits-cost structure of SOX.
We show that small firms experienced larger negative abnormal returns
associated with the passage of SOX than did large firms. The
relationship between firm size and negative abnormal returns was almost
monotonic; that is to say, the negative returns associated with SOX
decreased as firm size increased. The results of our study should lead
to further consideration of the burdens associated with SOX compliance,
and we hope more effort is placed on determining the impact that this
regulation has imposed on small firms.
References
1. American Electronics Association (AeA). "Sarbanes-Oxley
Section 404: The 'Section' of Unintended Consequences and its
Impact on Small Business," 2005.
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Andersen, and Sarbanes-Oxley on the Market for Audit Services,"
SSRN Working Paper, 2004.
3. Block, S. B. "The Latest Movement to Going Private: An
Empirical Study," Journal of Applied Finance, 2004, 36-37.
4. Brown, S. and Warner, J. "Measuring Security Price
Performance," Journal of Financial Economics 8, 1980, 205-258.
5. Carney, W. J. "The Costs of Being Public After
Sarbanes-Oxley: The Irony of 'Going Private'," Emory Law
and Economics Research Paper, 2005.
6. Chhaochhaira, V. and Grinstein, Y. "Corporate Governance
and Firm Value--the Impact of the 2002 Governance Rules," Cornell
University Working Paper, 2004.
7. Engel, E., Hayes, R. M., and Wang, X. "The Sarbanes-Oxley
Act and Firms' Going-Private Decisions," SSRN Working Paper,
2004.
8. Financial Executives International. "Sarbanes-Oxley
Compliance Costs Exceed Estimates," Press Release, 2005.
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Dark? Causes and Economic Consequences of Voluntary SEC
Deregistrations," AFA 2006 Boston Meetings Paper, 2004.
10. Levitin, M. J. and Snider, S. "Looking Ahead: The Market
for Buyouts of Public Companies, Part II, Buyouts," LexisNexis
Academic, 2002.
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Events Surrounding the Sarbanes-Oxley Act of 2002," SSRN Working
Paper, 2004.
12. Linck, J. S., Netter, J. M. and Yang, T. "Effects and
Unintended Consequences of the Sarbanes-Oxley Act on Corporate
Boards," AFA 2006 Boston Meetings Paper, 2006.
13. Rezaee, Z. and Jain, P.K. "The Sarbanes-Oxley Act of 2002
and Security Market Behavior: Early Evidence," SSRN Working Paper,
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14. Ribstein, L. E. "Sarbanes-Oxley After Three Years,"
University of Illinois Law & Economics Research Paper, 2005.
15. Romano, R. "The Sarbanes-Oxley Act and the Making of Quack
Corporate Governance," SSRN Working Paper, 2004.
16. Zhang, I.X. "Economic Consequences of the Sarbanes-Oxley
Act of 2002," University of Rochester, Working Paper, 2005
17. Zhu, H. and Small, K. "Has Sarbanes-Oxley Led to a
Chilling in the U.S. Cross-listing Market?" Loyola College,
Forthcoming CFA Journal.
Ken Small, Coastal Carolina University
Octavian Ionici, Loyola College in Maryland
Hong Zhu, Loyola College in Maryland
Exhibit 1: MAJOR PROVISIONS of SARBANES-OXLEY ACT OF 2002
Title
I. Public Company Accounting Oversight Board (Sections 101-109)
II. Auditor Independence (Sections 201-209)
Section 201 Prohibits auditor from providing certain non-audit-
related services
Section 203 Requires rotation of the senior audit officials
Section 204 Requires the firm's auditor to communicate with the
audit committee
Section 206 Addresses conflicts of interest that may arise if
management were employed by the auditor
III. Corporate Responsibility (Sections 301-308)
Section 301 Requires audit committee members be independent
board members
Section 302 Requires CEO/CFO certification of the firm's
financial statements
Section 303 Addresses improper influence of audits
IV. Enhanced Financial Disclosures (Sections 401-409)
Section 401 Requires periodic reports including off-balance
sheet transaction
Section 403 Requires disclosure of transactions involving
management and principal stockholders
Section 404 Addresses management's assessment of internal
controls
Section 407 Requires audit committee contain one financial
expert
V. Analyst Conflicts of Interest (Section 501)
VI. Commission Resources and Authority (Sections 601-604)
VII. Studies and Reports (Sections 701-705)
VIII. Corporate and Criminal Fraud Accountability (Sections 801-807)
Section 802 Imposes criminal penalties for altering documents
Section 803 Makes debts non-dischargeable if incurred in
violation of securities fraud laws.
Section 806 Provides protection for employees of publicly
traded companies who provide evidence of fraud
Section 807 Provides criminal penalties for defrauding
shareholders of publicly traded companies.
IX. White-Collar Crime Penalty Enhancements (Sections 901-906)
Section 906 Imposes corporate responsibility for financial
reports
X. Corporate Tax Returns (Section 1001)
XI. Corporate Fraud and Accountability (Section 1101-1107)
Section 1102 Covers tampering with a record or otherwise
impeding an official proceeding
Section 1106 Increases criminal penalties under Securities
Exchange Act of 1934
Section 1107 Addresses retaliation against informants
Exhibit 2: SUMMARY of STUDIES on SARBANES-OXLEY COMPLIANCE COSTS
Companies Time Frame and
Studies Selected Focused Costs Results
American Financial Section 404 * 0.06% of Revenue when
Electronics Executives Compliance Revenue > 5 Billion
Association International Costs * 0.16% of Revenue when
(AeA) 2005 study and 5 Billion > Revenue >
AeA's Section 1 Billion
404 working * 0.27% of Revenue when
group's 1 Billion > Revenue >
estimation 500 Million
* 0.53% of Revenue when
500 Million > Revenue
> 100 Million
* 2.55% of Revenue when
Revenue < 100 Million
Financial 217 public Year 1 of * Internal Labor Costs:
Executives companies Section 404 $1,337,935
International with average Compliance * External Consulting
(FEI) March revenue of Costs and Technology Costs:
2005 Survey $5 billion $1,716,987
* Auditor Attestation
Fees: $1,301,050
* Total Section 404
Compliance Costs:
$4,355,972
Carney 2005 44 companies Year 2004 * Median Net Income:
filed to go Compliance $421,000
private that Cost of * Average costs of
mentioned the securities compliance to
costs of laws including securities laws:
compliance SOX $291,000
* Average reported SOX
costs: $174,000
Exhibit 3: ONE-DAY ABNORMAL RETURNS by QUINTILE
Exhibit 3 includes results of the event study analysis around the
day that the U.S. House and Senate agreed on the final Sarbanes-Oxley
bill (July 24, 2002). The standard market model is used to construct the
abnormal returns. Abnormal returns are calculated as: A[R.sub.it] =
[R.sub.it] - [[alpha].sub.[iota]] - [beta]([R.sub.mt]), where [R.sub.it]
is the return to firm i on day t, [[alpha].sub.[iota]] is an intercept
term, [beta] is the market beta for the ith firm estimated using the 225
trading days prior to 90 trading days returns before July 24, 2002, and
[R.sub.m] is the market return on day t. The CRSP value-weighted market
index is used as a proxy for the market returns.
Quintile Assets Day (0) Market Capitalization Day (0)
1 (Smallest) -2.97*** -2.54***
(14.13) (12.46)
2 -3.17*** -3.66***
(16.82) (24.08)
3 -1.86*** -2.53***
(10.86) (14.57)
4 -1.20*** -.94***
(6.66) (3.32)
5 (Largest) .22*** .04***
(12.08) (10.68)
All Firms -1.79*** -1.93***
(16.02) (19.57)
*** indicates significance 1% level
** indicates significance 5% level
* indicates significance 10% level
Patell Z-statistic in parentheses
Exhibit 4: ABNORMAL RETURNS BY DECILE (Asset Deciles)
Exhibit 4 includes results of the event study analysis around the
day that the U.S. House and Senate agreed on the final Sarbanes-Oxley
bill (July 24, 2002). The standard market model is used to construct the
abnormal returns. Abnormal returns are calculated as: A[R.sub.it] =
[R.sub.it] - [[alpha].sub.[iota]] - [beta]([R.sub.mt]), where [R.sub.it]
is the return to firm i on day t, [[alpha].sub.[iota]] is an intercept
term, [beta] is the market beta for the ith firm estimated using the 225
trading days prior to 90 trading days returns before July 24, 2002, and
[R.sub.m] is the market return on day t. The CRSP value-weighted market
index is used as a proxy for the market returns. Cumulative abnormal
returns (CAR) are the sum of the one-day abnormal return estimates.
AR CAR CAR Number
Decile Day (0) Days (-1, 0) Days (-1, 0, 1)
1 (Smallest) -3.27*** -4.33*** -3.43*** 428
(10.14) (9.84) (6.32)
2 -2.26*** -4.04*** -4.27*** 433
(9.84) (10.89) (8.94)
3 -3.38*** -4.76*** -5.11*** 420
(12.16) (13.66) (11.74)
4 -2.98*** -4.29*** -4.82*** 437
(11.64) (14.41) (12.15)
5 -1.91*** -3.04*** -3.31*** 432
(8.09) (11.06) (8.83)
6 -1.81*** -2.75*** -2.41*** 423
(7.26) (10.23) (5.94)
7 -1.63*** -2.51*** -2.63*** 433
(7.71) (11.49) (7.67)
8 -.77** -2.00*** -2.07*** 429
(1.62) (9.88) (6.08)
9 -.21*** -1.48*** -1.35 429
(2.77) (6.54) (.713)
10 (Largest) 64*** -.83 -.28*** 439
(14.27) (.048) (7.199)
All Firms -1.79*** -3.00*** -2.96*** 4,303
(16.20) (30.98) (19.30)
*** indicates significance 1% level
** indicates significance 5% level
* indicates significance 10% level
Patell Z-statistic in parentheses
Diagram 1: ONE-DAY ABNORMAL RETURNS GRAPH (Asset Deciles)
Diagram 1 is a graph of one-day abnormal returns from the
asset-based sample. The standard market model is used to construct the
abnormal returns. Abnormal returns are calculated as: A[R.sub.it] =
[R.sub.it] - [[alpha].sub.[iota]] - b(Rmt), where [R.sub.it] it the
return to firm i on day t, [[alpha].sub.[iota]] is an intercept term,
[beta] is the market beta for the ith firm estimated using the 225
trading days prior to 90 trading days returns before July 24, 2002, and
[R.sub.m] is the market return on day t. The CRSP value-weighted market
index is used as a proxy for the market returns
[GRAPHIC OMITTED]
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