The stock market reaction to layoff announcements in germany

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THE STOCK MARKET REACTION TO LAYOFF
ANNOUNCEMENTS rN GERMANY
by
Edward R. Kohl
submitted to the
Faculty of the College of Arts and Sciences
o f American University
in Partial Fulfillment o f
the Requirements for the Degree o f
M aster of Arts
in
Economics

Chair:
Graham. Associate Professor of Economics

, Julia I. Lane. Professor of Economics

Howard M. Wachtel. Dean. College of Arts and Sciences

3-i

Date

AfJ.
1999
American University
Washington, D.C. 20016
TMm ijts.jG c .t_ h u n tV L L S IT Y LIBRA?;?

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THE STOCK MARKET REACTION TO LAYOFF
ANNOUNCEMENTS IN GERMANY

BY
Edward R. Kohl
ABSTRACT

Previous studies on shareholder reaction to layoff announcements have concentrated
on American stock markets. This paper extends research to shareholder reactions on the
Frankfurt Stock Exchange during the years 1990 to 1996. Using event study methodology
and daily return data from the Karlsruher Kapitalmarktdatenbank, the shares o f 30 firms are
tested for abnormal returns on and around the day of a layoff announcement. Daily
abnormal returns were found to be significant and negative for the announcement day itself
and the days just prior to it. Cumulative abnormal returns were found to be significant and
negative for the ten days preceding the announcement and significant and positive for the
ten days following the announcement. These results suggest that while layoffs are generally
perceived as bad news by investors in Germany, they are also seen as a sign that a company
is heading in the right direction.

ii

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TABLE OF CONTENTS

ABSTRACT............................................................................................................................ ii
LIST OF TA B LES................................................................................................................... iv
LIST OF FIGURES.................................................................................................................... v

1. INTRODUCTION................................................................................................

1

2. THEORETICAL CONSIDERATIONS AND
PREVIOUS LITERATURE.................................................................................... 2
3. SAMPLE D A T A ................................................................................................... 6
4. METHODOLOGY................................................................................................ 9
5. EMPIRICAL RESULTS .................................................................................... 19
6. CON CLU SIO N ..................................................................................................... 24

BIBLIOGRAPHY ............................................................................................................... 25

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LIST OF TABLES

T a b le t. Firm C atalo g u e..........................................................................................................8
Table 2. Distributional Properties o f Daily R e tu rn s........................................................ 15
Table 3. Daily Abnormal Returns and Test Statistics........................................................ 20
Table 4. Cumulative Abnormal Returns and Test Statistics

........................................... 20

iv

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LIST OF FIGURES

Figure 1. Estimation and Event P e rio d s ........................................................................... 11

Figure 2. Development o f Mean Cumulative Returns ................................................... 22

v

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1
INTRODUCTION
In the first six years following reunification, Germany experienced a period of
booming stock markets accompanied by rising unemployment. The Deutsche Aktienindex
(DAX) more than doubled in value during this period while German companies, faced with
high costs and foreign competition, were forced to lay off workers in record numbers.
Although the stock market boom was attributed to external factors, such as low interest rates,
a strong dollar, an influx o f foreign capital, and a bullish Wall Street, labor unions and
politicians began to question the link between booming share prices and rising
unemployment. They did not fail to notice that a firm’s share price often rose following a
layoff announcement.
In a country where labor-management consensus traditionally ensures adequate
employment, this development led to accusations that firms were not doing their fair share
in helping to reduce unemployment. Several politicians, including former Labor Minister
Norbert Blum, even suggested that higher share prices had come at the cost o f jobs in
Germany.1 This paper puts such popular claims to the test by examining the share price
response to layoff announcements made by German firms during the period 1990 to 1996.
By testing market reactions on the Frankfurt Stock Exchange, this paper also complements
previous studies which have concentrated on American stock markets.
{Die Welt, 15 February 1995.
1

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THEORETICAL CONSIDERATIONS AND
PREVIOUS LITERATURE
The financial consequences o f layoff announcements are ultimately decided by
investors and their perceptions regarding the reasons for the layoff. A layoff perceived as
good news will be rewarded with higher share prices while one perceived as bad news will
be disciplined with lower share prices. In the former case, investors often see the layoff as
an attempt by the company to increase efficiency and profitability by reducing labor costs.
This is especially true for firms in decline where layoffs are seen as evidence that the
organization is taking steps toward reversing the fortunes of the firm (Cameron 1988). In
a study which examined the valuation effects o f such cost-cutting efforts, Lin (1987)
showed that rationalization, including layoffs, produced positive economic benefits for a
firm as measured by share price movements. Likewise, a layoff can be perceived by
investors as an attempt to “cut the fat” when a company has become overstaffed or
inefficient. Tsay (1993) found evidence that deep cuts in inefficient capital spending are
associated with positive stock market effects.

In the eyes o f investors, efforts aimed at

cutting costs and increasing efficiency will often lead to higher expected future earnings and,
consequently, higher prices for the firm’s share.
A layoff perceived as bad news on the other hand is often seen as a signal that a firm

2

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3

is actually in worse shape than was previously thought. Under these circumstances, the
anno u n c e m en t reveals to the market an unfavorable situation which management has already

acted upon by laying o ff workers. A layoff undertaken at this stage is perceived more as an
act o f desperation than as a rational strategy to increase efficiency, and is thus met with
lower share prices. Worrel, Davidson, and Sarma (1991) found evidence that firms in
financial

distress

experienced

negative stock

market returns following layoff

announcements. In a further study examining displaced workers in the United States, Caves
and Krepps (1993) found that for U.S. corporations announcing downsizing in the period
1987 to 1991, average daily excess returns on stocks were negative following layoff
announcements.
Alternatively, a layoff announcement may produce no observable reaction on the
stock market. This may occur if both positive and negative reactions are present and their
effects cancel each other out. It may also arise i f a layoff announcement brings no new
information to investors. This is likely for a firm which is known to have problems and for
which a layoff comes as no great surprise to investors. In an interesting study on market
perceptions o f layoffs in the United States, Chatrath, Ramchander and Song (1995) found
that perceptions o f layoffs can even change over time. They showed that while the market
reaction to layoff announcements was generally negative in the early to mid eighties, it
became increasingly positive in the late eighties and early nineties. This finding is not
surprising given the trend toward lean management which emerged during that period.

When examining market reactions to layoff announcements in Germany, it is
desirable to consider the legal and institutional hurdles to layoffs which are present in

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4
Germany and which affect how and when a firm carries out layoffs. The most prominent
o f these is the Betriebsverfassungsgesetz (Works Councils Act), a law which, among other
things, guarantees workers the right to co-determination in the workplace and which
stipulates specific procedures for dismissing workers. A primary component o f this law is
the right o f workers to set up their own Betriebsrat (employees’ council) in firms with five
or more employees. The council is a permanent liaison between workers and management
and is involved in all major decisions regarding the firm, including those having to do with
layoffs. It is common for the management to seek the advice and approval of the Betriebsrat
before undertaking a layoff. Although the Betriebsrat, ultimately, cannot prevent a layoff
from taking place, it can influence whom the layoff affects and how the layoff is carried out.
Its members participate, for example, in the drafting o f a “social closing plan,” a document
required by the Betriebsverfassungsgesetz of any firm undertaking a major restructuring
involving significant job cuts.
Once the layoffs proceed, the Betriebsrat also ensures that they are carried out
“socially” and in accordance with regulations of the Betriebsverfassungsgesetz. Specifically,
this could mean that a worker’s familial status is considered before a layoff decision is made
or that a dismissed worker is awarded an appropriate severance payment.2 Although not
required, the Betriebsrat’s approval is always sought in cases o f layoffs since failure to do
so entitles affected workers to a hearing at the Arbeitsgericht (labor court) where the
prospects are good that he will be reinstated. Although these regulations are intended to
protect the rights o f workers, they often have the unwanted side-effect o f making urgently
2 See Siebert (1997) for a summary of job protection legislation for five West European
countries.

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5
needed layoffs more difficult and costlier to carry out.
Given that layoffs are more costly in Germany, it is reasonable to assume that a firm
will generally only consider a layoff after its position has become fairly critical or after
previous attempts to improve its position have failed. Likewise, it is only under these
extreme circumstances that management will be in a position to convince the Betriebsrat
that a layoff is necessary and unavoidable. Since investors are aware of these facts and
know' that layoffs are only carried out under extreme circumstances, one could speculate that
investor reaction to layoff announcements would be negative.

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3
SAMPLE DATA
Layoff announcements were collected by searching the business news section of the
WISO I ( Wirtschafts- und Sozialwissenschaften) CD-ROM index. Key words, such as
layoff, job cut, and dismissal were used to search newspapers for articles containing layoff
announcements for the pericd 1990 to 1996.

The search initially yielded 73 layoff

announcements to which the following criteria were then applied: (1) firms were omitted
whose lays-offs were precipitated by a take-over, merger, or imminent bankruptcy, (2) only
firms which are continuously traded on the Frankfurt Stock Exchange were retained in the
sample,3 (3) firms were omitted whose shares had missing values on days surrounding the

layoff announcement, (4) firms that were recently privatized, such as Lufthansa and
Deutsche Telekom, were omitted from the sample, (5) if the layoff announcement was
accompanied by another major announcement, the firm was omitted from the sample. If the
layoff announcement appeared in several newspapers on different dates, the earliest date was
chosen. Although not a criterion for inclusion in the sample, all announcements appeared
in the newspapers Handelsblatt, Frankurter Allgemeine Zeitung, and Siiddeutsche Zeitung.
The final sample consists o f 30 firms which represent 5.7 % o f the approximately
3 Continuously traded shares are bought and sold during the entire trading day. The number of
firms which meet this criteria is approximately 220 but varies from year to year. See Gdppel and
Schutz (1995). In contrast, many shares in Germany are traded “E in h eitsku rsmeaning their
prices are determined once a day, usually at noon, based on bid-ask spreads.
6

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7
525 firms traded on the Frankfurt Stock Exchange.4 Table 1 presents a catalogue o f the
sample firms, their industry branches, the announcement dates o f the layoffs, and the size
of the layoffs, measured as a proportion o f the firm’s total workforce. The industries
represented in the sample reflect Germany’s overall industrial make-up with a relatively
large showing o f machinery, chemical, and motor-vehicle related companies. The month
of November saw the largest number o f layoffs with six, followed by January and July with
four, and December and February with three. The largest layoff was made by Berliner Kraft
und Licht, while the smallest ones were made by Mannesmann and Schering. The average
layoff size was 5.0 % o f the work force.
Daily share

price and

return data were provided

by the Karlsruher

Kapitalmarktdatenbank (KKMDB), a data bank administered by the University of Karlsruhe
which makes capital market data available to researchers for academic purposes. This daily
return data for individual firms has been cleaned, meaning that returns have been adjusted
for splits, cash dividends and issuance of new shares.

4There are approximately 800 companies traded on the eight stock exchanges in Germany.
These are Berlin, Bremen, Diisseldorf, Frankfurt, Hamburg, Hannover, Munchen, Stuttgart. The
largest firms, e.g., those in the DAX index, are traded in Frankfurt and on all other stock
exchanges.

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8
Table 1. Firm Catalogue
Catalogue o f sample firms, industry branches, layoff dates, and layoff sizes. The layoff date is defined
as the date on which news o f the layoff first appeared in a newspaper. Layoff size is the percentage of
employees affected by the layoff.
Industry branch

Layoff date

Machinery, Electrical Equipment

11/17/1995

Layoff size
(%)
5.0

2. Allianz

Insurance Carriers

06/02/1995

2.0

3. BASF

Chemicals, Paints, Coatings

11/19/1993

5.3

4. BMW

Motor Vehicle Manufacturing

02/10/1992

4.0

5. Bankgesellschaft Berlin

Banking, Credit Intermediation

02/08/1996

10.0

Pharmaceuticals, Chemicals

12/28/1995

3.0

7. Bayerische Hyp.& Wech.-Bank

Banking, Credit Intermediation

07/31/1995

8. Bayerische Vereinsbank

Banking, Credit Intermediation

07/28/1995

4.0
*

9. Berliner Kraft- & Licht

Utilities, Power Generation

12/13/1994

18.0

Beverage Manufacturing

07/20/1995

14.0

Banking, Credit Intermediation

05/17/1993

12. Continental

Tires, Motor Vehicle Parts

10/26/1995

3.0
*

13. Daimler Benz

Transportation Equipment

11/18/1993

11.7

Chemicals, High-Grade Metals

03/10/1992

3.0

15. Deutsche Babcock

Industrial Machinery

03/16/1993

4.0

16. FAG Kugelfischer

Machinery, Conveyors

01/17/1992

3.0

Food Processing, Refrigeration

05/07/1996

3.0

18. Henkel

Chemicals, Detergents

12/03/1992

4.7

19. Hoechst

Chemicals, Pharmaceuticals

07/03/1995

4.9

Electrical Equipment, Printing

10/18/1995

8.5

Utility Vehicles, Printing

04/06/1993

4.5

Machinery, Telecommunication

11/07/1996

1.0

23. Phoenix

Tires, Motor Vehicle Parts

01/21/1992

5.0

24. Preussag

Basic Materials, Machinery

08/20/1996

12

Utilities, Mining

01/29/1993

1.4

26. Schering

Pharmaceuticals, Medicine

02/17/1993

1.0

27. Thyssen

Machinery, Steel

01/20/1993

28. Volkswagen

Motor Vehicle Manufacturing

06/18/1993

5.0
*

29. Varta

Electrical Equipment, Batteries

11/22/1994

1.9

Insurance Carriers

11/09/1994

1.1

Name o f firm
1. Agiv

6. Bayer

10. Brau und Brunnen
11. Commerzbank

14. Degussa

17. GEA-Gruppe

20. Linotype-Hell
2 1 .MAN
22. Mannesmann

25.RWE

30. Volksfiiersorge Holding
*Exact size o f layoff not announced.

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4
METHODOLOGY
Using the terminology o f Fama (1991), an event study examines the adjustment of

security prices to publically available information such as stock splits or layoff
announcements.5 These studies were initially used to test the information efficiency o f
markets, that is, whether or not markets react to new information and how quickly this
reaction occurs. More recently, however, financial economists have turned their attention
to measuring the effects o f a particular economic event on the stock market value o f a firm.6
This movement away from the traditional use o f event studies was due primarily to the
increasingly widespread acceptance o f the information efficiency of security markets— an
abundance o f empirical evidence from event studies have shown that, on average, stock
prices do react to new information and generally within a period of one day relative to the
event (Fama 1991). Fama even refers to event studies as a growth industry in the financial
economics literature. He attributes this to the widespread availability o f financial market
data, and the general applicability o f event study methodology to a variety o f situations.7
5 In his original work on market efficiency (Fama, 1970, 383), Fama uses the term semi-strong
test to describe market efficiency tests of this kind. In his more recent work (Fama, 1991,1577),
he proposes a change in terminology from semi-strong test to event study in recognition of its
wide-spread use in the financial economics literature.
6 For a brief history of event studies see Campbell, Lo & MacKinlay, 1997, 149-50 .
7 The bibliography contains references to 19 event studies. See, for example, Fama, Fisher,
Jensen & Roll(1969), Patell(1976), Dodd & Wamer(1983), Johnson, Magee, Nagarajan &
Newman(1985), Furtado & Rozeff(1987), Warner, Watts & Wruck(1988).
9

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10

This paper follows standard event study procedures as described by Brown and Warner
(1985) and Campbell, Lo & MacKinlay (1997).
The first step in an event study is the defining o f the event o f interest and

establishing the period over which the stock market reaction will be examined. For this
study, the event is defined as the appearance o f the layoff announcement in a newspaper.
The day on which the announcement appears is called the event day and is designated
day 0 (see Figure 1). Days prior to the announcement are given negative values and days
following the announcement are given positive values.

A date three days before an

announcement is thus day -3, and a date ten days after an announcement is day 10.
In addition to examining the market reaction on the event day itself, there is good
reason to examine the days surrounding the event. Assuming, for example, that the actual
layoff announcement occurs one day prior to the article’s appearance, an initial reaction to
the layoff can be expected on day -1, and further reactions on days 0 and 1 as news o f the
layoff spreads. Pre-event day reactions, especially those occurring before day -1, can also
be interpreted as evidence o f information leakage, that is, evidence that investors have
gotten word o f the layoff prior to its public announcement and have begun to act upon it.
Surrounding days are also examined in order to detect trends which may remain hidden in
single day analysis. Testing for such trends will be taken up later when cumulative returns
are examined. The period surrounding the event day is designated the event period. For this
study, the event period is defined as days -10 to 10 (see Figure 1).
In order to provide a basis for comparison, share performance is also measured for
a number o f months prior to the event period. The results are then used to calculate the

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11

Event Day

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

I------------------------------------------------------------ 1
165-Day Estimation Penod

21-Day Event Period

Figure 1. Estimation and Event Periods

normal or expected share performance for the event period, that is, the performance that
would be expected if no event were to take place. This period is designated the estimation
period and consists o f the 165 trading days from day -185 to day -20 (see Figure 1). Share
performance in all periods is measured as the simple net daily return on a share,

n

_

PiJ

1

' PDi j -1 ” 1 ■

0>

where R u is the return for share / on day t, p u is the share price on day t, and

is the share

price on day t-1.
Expected returns for the event period are generated from returns in the estimation

period and the OLS Market Model.8 This statistical model relates the return o f any given
security to the return on a market portfolio. The market model is given by

R ij

-

a i

+

P i R m ,t

+

e i ,t

’

where Ru is the return for security i on day t, R ^, is the return on a stock market index,
and Pt are OLS estimators of the intercept and slope o f the market model regression, and elt
is the zero mean disturbance term. Market returns for this study are net simple returns on
8For a comparison of the various return generating models, see Brown and Wamer(1980, 6-7),
and Campbell, Lo, and MacKinlay(l997,153-157).

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12
the D AFOX-BC index (Deutscher Aktienindex fur Forschungszwecke - Blue Chips), a valueweighted stock index o f continuously-traded, blue-chip shares on the Frankfurt Stock

Exchange. This index was chosen because it contains all firms in the sample while being
limited to only those firms which are continuously traded—a criterion which was also used
in the selection o f sample firms.
After applying the market model to the estimation period returns, the OLS slope and
intercept estimators derived for each firm from equation (2) are inserted into equation (3)
to generate expected or normal returns for each firm.9 Normal returns are given by

(3)
where a i and /?. are the OLS estimators for firm /, Rw is the return on the market index on
day t, and NRU is the expected or normal return on day t.
Finally, normal returns are subtracted from actual returns to yield the prediction error
or abnormal return for each day in the event period:

(4)
where Rl t is the actual return for firm / on day t, NRit is the normal return, and AR^ is the
prediction error or abnormal return.
Under the null hypothesis, abnormal returns will be zero for days in the event period,
implying that no stock market reaction has taken place. The null hypothesis is rejected when
significant positive or negative abnormal returns are detected during this period, implying
a stock market reaction to a layoff announcement. In order to test the significance of

9A11 estimators were found to be significant and positive.

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13
abnormal returns during the event period, the abnormal returns o f all firms for a single event
day are first aggregated to yield the mean daily abnormal return (Brown and Warner 1985),
1

N

(5)

where A R t is the mean abnormal return for day t, and N is the number o f firms in the
sample. The test statistic, Tpn is then defined as the ratio o f the mean daily abnormal return
to its estimated standard deviation (Brown and Warner 1985),

ARt
SQAR,)

(6)

where

S (^ ) =J

I

(AR, - Ar )2 \ 164

(7)

1
(8)
and 165 is the length of the estimation period, days -185 to -20. Borrowing from the
terminology o f Campbell and Wasley (1993), this test statistic will be called the portfolio
test statistic since it tests the significance o f abnormal returns for a portfolio o f stocks.
Under the null hypothesis, it is distributed Student t with 164 degrees o f freedom, that is,

approximately unit normal (Brown and Warner 1985).
In addition to its simplicity, the portfolio test statistic is favored in event studies
because it accounts for statistical complications which may arise when using daily returns.10

10 See Brown and Wamer(1985) for a treatment o f the statistical issues surrounding daily returns.

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14
Since the estimated variance in equation (6) is calculated using the time series o f aggregated
abnormal returns, for example, the test statistic explicitly accounts for cross-sectional
dependence in security-specific abnormal returns. Failure to account for this dependence
could lead to Type I errors, since such dependence would result in an underestimation o f the
variance o f mean abnormal returns (Brown and Warner 1985). Cross-sectional dependence
in event studies typically occurs in the presence o f clustering, a term used to describe the
occurrence, or clustering, of many events around a single calender day. Although the
consequences o f clustering are most critical in studies e x a m in in g the stock market reaction
o f many shares to a single event, such as a Federal Reserve Board announcement, the test
statistic is adopted for this study since the sample exhibits four cases of overlapping event
periods (see Table 1).
The portfolio test statistic also inherently accounts for the non-normality o f daily
returns.

It is well established in financial economics literature that daily returns are

generally non-normal (Brown and W amerl985). As the first row o f Table 2 indicates, this
also holds true for daily returns in this study.11 Correct specification, however, does not
require the normality o f daily returns. The Central Limit Theorem guarantees that if crosssectional (portfolio) abnormal returns are independent and identically distributed, the
distribution o f the sample mean abnormal return will converge to normal as the number o f

firms increases (Brown and Warner 1985). As the second row o f Table 2 shows, this
convergence to normal does occur for portfolio mean abnormal returns. The resulting
portfolio test statistic also exhibits convergence to normal as the third row demonstrates.

11 German returns have also been found to be non-normal, see Akgiray (1989).

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15
Table 2. Distributional Properties o f Daily Returns
Distributional properties of daily returns, portfolio mean abnormal returns, and portfolio test statistics.
Measures are based on the 165-day estimation period. Daily return statistics are based on thirty 165day samples. Portfolio mean abnormal returns and the test statistic are based on 165 portfolios.
Although daily returns are non-normal, the cross-section o f mean abnormal returns and the portfolio
test statistic converge to normal.
Mean

Standard Deviation

Skewness

Kurtosis

t
Goodness
o f Fit

Daily Returns

-2.62e-04

0.0144

-0.75

41.61

1800.27

Portfolio Mean
Abnormal Returns

-4.05e-07

0.0022

0.03

324

4.09“

Portfolio Test
Statistic

-1.90e-04

1.0000

0.03

3.16

2.6 l b

1 Using sample estimates for sigma and mu, 6 degrees o f freedom
b Using sample estimates for sigma and mu, 7 degrees o f freedom

Although the portfolio test statistic is well specified, it is desirable to conduct
additional tests using a non-parametric test statistic. Such statistics are often used in
conjunction with their parametric counterparts to check the robustness of event study results
(Campbell, Lo and MacKinlay 1997). Although a number of different non-parametric test
statistics are available, this study will adopt the relatively new rank statistic proposed by
Corrado (1989).12
The rank test statistic is appealing for several reasons. First, in contrast to the sign
test, this test statistic remains well specified in the presence o f a skewed distribution of
abnormal returns; moreover, it is less susceptible to misspecification caused by increases in
the variance o f abnormal returns around the time o f the event day (Campbell, Lo and
MacKinlay 1997). In a study comparing the portfolio and rank statistics (along with the

12 The terminology for this test statistic is borrowed from Campbell and Wasley (1993).

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16
so-called standardized test statistic), Campbell and Wasely (1993) found that, for NASDAQ
stock returns, the rank statistic allows more reliable inferences than do its parametric
counterparts. It is constructed by first transforming the time-series o f firm-specific abnormal
returns into their respective ranks,

K it = ra n k( ARU),

t= -1 8 5 ,...,-2 0 ,-1 0 ,...,+ 1 0 ,

(9)

where K it denotes the rank o f the abnormal return AR„ for security i o f the time series o f 186
abnormal returns in the estimation and event periods.13 The rank test statistic, Tn for any
given day t is then the ratio of the mean deviation of all securities’ ranks on a given day to
the estimated standard deviation o f the portfolio mean abnormal rank,

( 10)

where

S (K ) =

( 11)

N is the number o f securities, and 93.5 is the average rank calculated as one-half plus half
the number of observations. In contrast to the portfolio test statistic, the standard deviation
o f the mean abnormal rank is calculated using both the estimation and the event periods.
Under the null hypothesis, the rank statistic converges to unit normal as the number of
securities in the portfolio increases (Corrado 1989).
While the portfolio and rank test statistics are adequate for testing abnormal returns

13 T ies are treated using the method o f mid-ranks.

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17
on specific days, they may fail to detect trends which emerge over a series o f days. In order
to detect such trends, event studies employ statistics which aggregate returns over time.
These aggregated returns are called cumulative abnormal returns or CARs. The construction
o f test statistics for cumulative returns is similar to that o f daily returns in that the mean
returns are divided by their estimated standard deviation to yield a test statistic. Using
notation previously introduced, the test statistic for portfolio cumulative abnormal returns
is given by

Tpcar

CAR
S(CAR)

( 12)
’

where
(13)

(14)

and L xand L 2 are the beginning and end of the chosen event period. The value of
in equation (14) is equivalent to that in equation (7). Since the aggregation o f abnormal
returns into portfolios accounts for cross correlation o f abnormal returns, it is not necessary
to assume zero covariances among individual sample CARs (Cambell, Lo and MacKinlay
1997). The test statistic is assumed unit normal under the null hypothesis.
The cumulative test statistic for ranked returns is constructed in a similar way and
is given by

CAR
Trcar

S (C A R )

(15)
’

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