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Running event studies using Stata: the estudy
Fausto Pacicco
LIUC - Universit`a Carlo Cattaneo
Castellanza (VA), Italy
Luigi Vena
LIUC - Universit`a Carlo Cattaneo
Castellanza (VA), Italy
Andrea Venegoni
LIUC - Universit`a Carlo Cattaneo
Castellanza (VA), Italy
Abstract. This paper proposes the Stata command estudy and illustrates how it
can be used to perform an event study customizing the statistical framework, from
the estimates of abnormal returns to the tests for their statistical significance. Our
program significantly improves the existing modules both in terms of completeness
and users’ comprehension.
Keywords: estudy, event study, financial econometrics
1 Introduction
If and how a given event affects financial markets is a relevant question that researchers
and practitioners aim to answer. This is why the event study framework has nowadays
become a statistical technique used in many areas, from economics to accounting, from
finance to law. According to Kothari and Warner (2008) between 1974 and 2000 almost
600 studies conducted in various fields employed such a technique. If we consider that
the mentioned analysis takes into account only four main academic journals, it is easy to
understand that the numbers describing the popularity of such a technique exponentially
grow when we extend the focus to other academic journals, as well as private and public
This paper proposes and comments on the estudy Stata program. Such program
performs an event study permitting the user to: i) work with multiple varlists,com-
puting the Abnormal Returns (and the Average Abnormal Returns), henceforth ARs
(and AARs) as well as Cumulative Abnormal Returns and Cumulative Average Abnor-
mal Returns (henceforth, respectively CARs and CAARs)1; ii) specify up to six event
windows; iii) customize the length of the estimation window; iv) select the model for
the calculus of (ab)normal returns; v) specify the diagnostic test, among the parametric
and non-parametric ones that we propose and that are the most commonly used in the
literature; vi) customize the output table; vii) store the results into an excel file as well
as in a Stata dataset file.
1. Throughout the entire paper, we refer to ARs only for exposition’s sake.
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2Running event studies using Stata
It improves the existing modules that allow to perform an event study on Stata
under several perspectives:
computes simultaneously ARs (CARs) of more than one groups of variables (se-
curities’ returns), without repeating the command;
offers the possibility to work with different levels of aggregation, running the
event study on single firms (groups of them) computing ARs and CARs (AARs
and CAARs) and testing their statistical significance;
provides a customizable output, according to the needs of the user;
simplifies the approach for the user, resulting in an easier and faster setup.
2 The Event Study Framework
Should an event be unexpected and value relevant for some firms, it is bound to cause
an abnormal return as measured by the actual ex-post return net to the normal (or
expected) one over the same period (see for example MacKinlay 1997). The event study
technique allows to measure such abnormal return, hence allowing to assess whether a
given fact has proved able to influence firms securities’ market value. We refer generally
to firms’ securities as the event study applies most frequently on common stocks, even if
they are conducted on others securities like bonds (Bessembinder et al. 2009) or credit
default swaps (Andres et al. 2016).
The Equation 1 defines the AR of a generic firm iin the period t:
ARi,t =Ri,t E(Ri,t |Xt)(1)
where Ri,t is the actual ex-post return and E(Ri,t |Xt) is the expected return conditioned
to the information Xof period t, unrelated to the event.
2.1 Measuring abnormal returns
As pointed out by MacKinlay (1997), the conduction of the event study customarily
follows an established flow divided in these steps:
1. Definition of the event window;
2. Computation of the normal returns;
a. Definition of the estimation window;
b. Choice of the estimation model;
3. Estimation of the abnormal returns;
4. Statistical testing for the significance of the abnormal returns;
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The procedure begins with the definition of the period(s) over which the event is
supposed to influence the market return of firms’ securities, i.e. the event window(s).
Usually, each event window spans over one or more days including the event date it-
self. It is common to include the days before and/or after the event, allowing for the
possibility of news leakages preceding the event itself or delayed reactions of the markets.
In order to define the abnormal return, it is necessary to proceed to the second step
of the analysis and compute the normal or expected performance. This task requires
the definition of an estimation window, i.e. a sample period prior to the event window,
usually leaving a cushion of at least one month in order to exclude market returns
influenced by the event, avoiding the estimation window to include anticipation effects
(and/or news leakages).
The estimation of normal returns is carried out using different models. The two that
are most commonly used are the historical mean model (HMM) and the single index
model (SIM).
E(Ri,t|Xt)=αi+βiRm,t (3)
With respect to the former (Eq. 2), the security’s historical mean return over the
estimation window represents the expected normal performance unconditioned to the
Conversely, according to the single index model (see Eq. 3), the normal return depends
on the parameters αiand βi(estimated over the estimation windows), and the market
return Rm,t. A special case of this model is the market adjusted model (MAM), where
a constraint on the parameters αiand βiwants them to be set equal to 0 and 1,
In an attempt to improve the variance explained by the single index model (hence
facilitating ARs detection), sometimes the expected return is estimated using more
than one factor, i.e. modelling a multi factor model (MFM) such as the 3 factors model
proposed by Fama and French (1993).
Once normal returns are computed, it is possible to obtain abnormal returns (ARs).
When the aim is to compute the event impact for each single security on a single day
event, it is possible to obtain ARs by applying Equation 1. Sometimes, the user can also
be interested in investigating the effect of the event on a multi-day period and hence
becomes necessary to operate a time series aggregation of the ARs, obtaining the CARs
as described by Equation 4.
ARi,t (4)
with t1<t
2and t1,t
2(event window).
If, instead, the object of interest is the impact on a pool of firms, a cross-section
aggregation becomes necessary and Average Abnormal Returns calculation can be per-
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4Running event studies using Stata
formed using Equation 5.
ARi,t (5)
where ARi,t represents the abnormal return estimated on the i-th security and N the
securities’ population. In the words of Kothari and Warner (2008), the cross-sectional
aggregation of abnormal returns makes sense if one aims either at studying if the event
alters, on average, the security holders’ wealth, or at testing economic models and
alternative hypotheses suggesting the sign of the mean impact.
Lastly, when the focus is on the average effect over multiple days it is necessary to
perform both of the aggregations just described and compute the Cumulative Average
Abnormal Returns (CAARs), by summing over time the AARs, as shown in Equation
The literature suggests an alternative method to compute both AARs and CAARs,
named the portfolio approach. Levering on an equally weighted portfolio that groups
all securities under scrutiny (before computing the abnormal components), one can
compute the portfolio ARs (a substitute for the AARs) and CARs (instead of the
CAARs), considering the portfolio as a single security. By default, estudy program
performs both techniques.
2.2 Statistical properties of abnormal returns
Once abnormal returns are computed in any form suits the analysis, it is necessary
to study their stastical significance. To assume economic relevance, ARs2must be
statistically significant, i.e. their difference from zero must be verified employing an
ad-hoc test.
To this end, the literature offers two types of tests, parametric and non-parametric:
while the former assumes a certain distribution of returns, the latter is not anchored to
any a-priori assumption.
With respect to the former family, under the assumption of Normally distributed
securities’ returns, ARs follow a Normal distribution centered on 0, with variance σ2
Accordingly, also AARs, CARs, and CAARs are Normally distributed with mean 0 and
var ianc e σ2
3. We dub this test “Normal”.
Alternatively, Patell (1976) proposes a parametric test that, basing on scaled abnormal
returns, brings a twofold benefit. On the one hand, the test takes into account the di-
verse standard deviation between event-period and estimation period residuals. On the
other hand, it prevents securities with large variance to heavily influence the outcome;
2. The same holds for AARs, CARs and CAARs
3. For a complete description of these variances see MacKinlay (1997) and Binder (1998) among
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Boehmer et al. (1991) (BMP test) improve Patell’s test, by taking into account the pos-
sible cross-sectional increase in the variance of the returns that may occur within the
event window.
These three tests (Normal, Patell and BMP), however, suffer from the cross-sectional
correlation of abnormal returns that heavily affects their outcome in case of event
day clustering, that verifies when a single event simultaneously affects all securities
included in the analysis. To overcome this problem, Kolari and Pynn¨onen (2010) mod-
ifies both Patell and BMP tests, introducing a correction for the cross-correlation and
hence proposing the adjusted Patell (AdjPatell) and Kolari and Pynn¨onen (2010) (KP)
Being linked to the Normality assumption of the securities’ returns distributions, the
aforementioned tests may underperform when returns are not Normal. Thus, without
relying on any distribution, the test proposed by Wilcoxon (1945) check for the statis-
tical significance of AARs considering both the signs and the magnitude of ARs, while
the Kolari and Pynnonen (2011) generalized rank test (GRANK) outperforms both the
previous rank tests and the parametric ones without suffering either from the serial
correlation of ARs or from the event-induced volatility.
All the listed tests are included in the estudy package.
The estudy command performs the event study, computing the ARs and running the
proper diagnostic, as described in the previous section. The syntax for estudy is
estudy varlist1(varlist 2) ... (varlistN) , datevar(varname) evdate(date)
dateformat(string) lb1(#) ub1(#)lb1(#) ub1(#) ... lb6(#)
ub6(#) modtype(string) indexlist(varlist ) eswlbound(#) eswubound(#)
diagnosticstat(string) suppress(string) decimal(#) showpvalues nostar
outpuptfile(string) mydataset(string)
The (maximum) N varlists must be the securities logarithmic return of the financial
instruments subject to the event study. Each varlist, with the sole exception of the first
one, must be specified in brackets.
3.1 Options
The options for estudy can be divided in two parts, mandatory and additional. Only
the former, below indicated with an asterisk, are strictly required to make the program
*datevar(varname) specifies the date variable in the dataset. The program cannot
perform the event studies if the time series of securities return is not linked to a
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6Running event studies using Stata
date variable. When the variable here indicated is not date-formatted, the program
*evdate(string) specifies the date of the event. No matter the format of datevar,
evdate may be expressed as “mmddyyyy ”, “ddmmyyyy ”, and “yyyymmdd”.
*dateformat(string) specifies the date format of the event date (evdate). There are
three cases: MDY ”, “DMY ”, “YMD” to indicate that the evdate option has been
specified, respectively, as“mmddyyyy”, “ddmmyyyy ”, and “yyyymmdd ”.
*lb1(#) ub1(#) [ ... lb6(#) ub6(#)] specify up to six event windows around
the event date (only the first event window is mandatory). For each event window,
both the lower and upper bounds must be specified, and both must have an integer
modtype(string)specifies which model must be used to compute the (ab)normal returns.
The available options are: (i)-“SIM”, single index model (dafault option). In this
case, only one variable must be specified in the indexlist option; (ii)-“MAM”,
market adjusted model. As before, the indexlist option must indicate only one
var iabl e; (iii)-“MFM”, multi-factor model. indexlist must indicate at least
two variables (factors); (iv )-HMM”, historical mean model. In this case, the
command ignores the indexlist option.
indexlist(varlist)specifies the varlist useful to compute (ab)normal component of
securities returns and is conditional to the modtype option. When either the single
index model (“SIM”) or the market adjusted model (“MAM”) has been specified,
this option must indicate only one variable. With the multi-factor model (“MFM”)
more than one variable must be specified. When the historical mean model (“HMM”)
has been set, the program ignores this option.
eswlbound(#)specifies the lower bound of the estimation window. By default, the
program uses the first trading day in the database.
eswubound(#)specifies the upper bound of the estimation window. By default, it
corresponds to the 30th trading day prior to the event, thus being sure to avoid an
overlap between the estimation and the event windows.
diagnosticstat(string)specifies which test must be used to analyse whether ARs
statistically differ from zero. The available options are: (i)-“Normal” (default
option), assuming that securities returns, and hence ARs, are Normally distribute
and heteroscedastic across the estimation and the event windows. Despite these
assumptions are often violated, this test is commonly used to evaluate the statis-
tical significance of ARs and CARs on single securities; (ii )-“Patell”performs
the test proposed by Patell (1976); (iii)-“ADJPatell” performs the test pro-
posed by Patell (1976) with the Kolari and Pynn¨onen (2010) adjustment. (iv )-
BMP” performs the test proposed by Boehmer et al. (1991) that improves the one
by Patell, taking into account the event-induced volatility; (v)-“KP”performs
the BMP test corrected for the cross-sectional correlation of abnormal returns (see
Kolari and Pynn¨onen 2010, for further details). (vi)-“Wilcoxon”performsthe
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nonparametric signed rank test proposed by Wilcoxon (1945); (vii)-“GRANK
performs the generalized rank test (GRANK) proposed by Kolari and Pynnonen
suppress(string) specifies the format of the output table. The option suppress may be
either “group”or“ind”. With the former, the output table shows only the ARs on
each input variable, hiding those on the group as whole and on the portfolio. On the
opposite, with the latter, only group ARs and the results for the portfolio approach
are shown, with individual ARs excluded from the output table. If not specified,
the output table prints the single ARs for each security of each varlist, the portfolio
ARs and te group AR of each varlist. A horizontal line separates the varlists.
decimal(#)specifies the number of decimal that must be used in the output table.
Seven is the maximum value. By default the number of decimals is set equal to two.
showpvalues specifies that the output table must show the p-value of each abnormal
return. When this option is specified, p-values are shown in brackets below the
corresponding AR.
nostar specifies that the output file must not contain the stars indicating the significance
level. If not specified, ***, ** , and * denote, by default, that ARs are statistically
significant at the 1%, 5% and 10% level, respectively.
outpuptfile(string)specifies the name of the .xlsx file in which both the ARs (always
without significance stars) and the p-values are stored in two separate sheets. The
format imposed with suppress is maintained. The program automatically replaces
the file, should it already exist.
mydataset(string)specifies the name of the Stata .dta file in which ARs (always without
significance stars) are stored. The format imposed with suppress is maintained.
The program automatically replaces the file, should it already exist. The workfile,
stored in the directory in use, contains a first variable with the securities labels and
the ARs on each event window in just as many variables.
We illustrate how estudy works, using the dataset data estudy provided by us. This
dataset contains the time series of market returns for ten companies’ shares, as well as
the Fama and French (1993) three factors and the risk-free rate. Through our example,
we show the command syntax, clarifying how each option can be used to customize the
program thus meeting the users’ needs.
As previously pointed out, the options for estudy can be divided in two groups,
required and additional. While the former is necessary, the latter can be used to cus-
tomize the analysis but do not impair the functioning of the program. We first show the
basic model, encompassing only required options leaving to the subsequent examples
the demonstration and use of the additional ones.
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8Running event studies using Stata
Thus, we start with a simple set-up, performing an event study on two (separate)
varlists, with only one event window of seven days (from -3 to +3) around 09 July
2015, i.e. the event date. In addition to the evdate and lb1/lb2 options (useful to
specify, respectively, the event date and window) two other options are mandatory: 1)
dateformat, the format of the event date (in this case “MDY” as the event date has
the format “mmddyyyy ”); 2) datevar, the date variable present in the dataset.
Since we are not specifying any model type, (ab)normal returns are computed according
to a Single Index Model (which is set to be the default). As such, the market (or index)
return must be indicated compiling the option indexlist.
. use data_estudy.dta
. estudy boa ford boeing (apple netflix amazon facebook google) , datevar(date)
> evdate(07092015) dateformat(MDY) indexlist(mkt) lb1(-3) ub1(3)
By default the upper bound of the estimation window has been set to (-30)
Event date: 09jul2015, with 1 event windows specified, under the Normality assum
> ption
Bank of America Corporation -1.15%
Ford Motor Company -1.85%
The Boeing Company 3.48%
Ptf CARs n 1 (3 securities) 0.16%
CAAR group 1 (3 securities) 0.16%
Apple Inc -2.12%
Netflix Inc 3.00%
Amazon com Inc 4.17%
Facebook Inc 0.00%
Alphabet Inc 5.33%*
Ptf CARs n 2 (5 securities) 2.08%
CAAR group 2 (5 securities) 2.08%
*** p-value < .01, ** p-value <.05, * p-value <.1
When the estimation window is not specified, as in this case, by default the program
considers it to be from the first available to the 30th trading day prior to the event
(-30). A warning message reminds the user of this. Moreover, the header of the output
briefly recaps the set-up of the event study performed, reminding the event date, the
number of event windows specified, and the diagnostic test implemented.
The first column reports the labels of the variables on which the event study has been
performed. By default, the program adds two rows per varlist showing the results for
the portfolio approach as well as the group ARs, both useful to evaluate the average
impact of the event. The remaining column reports the ARs (CARs and CAARs over
the [-3, 3] window, in this case). Statistically significant ARs are identified by asterisks
as explained by the legend at the bottom of the table. Horizontal lines separate the
table in panels, each showing the specified varlists.
In the next example, we customize our analysis by: (i) changing the statistical test
implemented, with the option diagnosticstat; (ii) setting a precise estimation window,
using the options eswlbound and eswubound to specify the lower and the upper bound,
respectively; (iii) and adding two event windows (options lb2,ub2,lb3,andub3).
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(Continued on next page)
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10 Running event studies using Stata
. use data_estudy.dta
. estudy boa ford boeing (apple netflix amazon facebook google) , datevar(date)
> evdate(07092015) dateformat(MDY) indexlist(mkt) lb1(-3) ub1(3) lb2(-3) ub2(-1)
> lb3(0) ub3(3) diagn(BMP) eswlb(-250) eswub(-20)
Event date: 09jul2015, with 3 event windows specified, using the Boehmer, Musume
> ci, Poulsen test
SECURITY CA(A)R[-3,3] CA(A)R[-3,-1] CA(A)R[0,3]
Bank of America Corporation -1.29% -2.99%* 1.70%
Ford Motor Company -1.42% -1.43% 0.01%
The Boeing Company 3.71% 2.57% 1.14%
Ptf CARs n 1 (3 securities) 0.33% -0.62% 0.95%
CAAR group 1 (3 securities) 0.33% -0.62% 0.95%*
Apple Inc -3.00% -1.72% -1.27%
Netflix Inc 3.77% 0.70% 3.07%
Amazon com Inc 4.02% -0.54% 4.56%
Facebook Inc 0.54% -0.39% 0.94%
Alphabet Inc 5.86%** 0.42% 5.44%***
Ptf CARs n 2 (5 securities) 2.24% -0.31% 2.55%
CAAR group 2 (5 securities) 2.24% -0.31% 2.55%
*** p-value < .01, ** p-value <.05, * p-value <.1
As we have set the estimation window, there is no warning message. The output
table now has two more columns showing the new event windows. The table header
recalls that the Boehmer et al. (1991) test has been implemented to test the significance
of ARs over the three event windows specified.
Should one be interested in the mean effect of an event, ARs on the single variables
can be suppressed. The option suppress(ind ) meets this need.
. use data_estudy.dta
. estudy boa ford boeing(ibm facebook apple) (netflix cocacola amazon) (facebook
> boa ford boeing google) , datevar(date) evdate(07092015) dateformat(MDY) modt
> ype(HMM) lb1(-3) ub1(3) lb2(-3) ub2(-1) lb3(0) ub3(3) diagn(KP) eswlb(-250) es
> wub(-20) supp(ind)
Event date: 09jul2015, with 3 event windows specified, using the Boehmer, Musume
> ci, Poulsen test, with the Kolari and Pynnonen adjustment
SECURITY CA(A)R[-3,3] CA(A)R[-3,-1] CA(A)R[0,3]
Ptf CARs n 1 (3 securities) 1.71% -2.34% 4.05%**
CAAR group 1 (3 securities) 1.71% -2.34% 4.05%***
Ptf CARs n 2 (3 securities) 0.94% -2.25% 3.19%
CAAR group 2 (3 securities) 0.94% -2.25%** 3.19%***
Ptf CARs n 3 (3 securities) 4.96% -0.78% 5.74%**
CAAR group 3 (3 securities) 4.96%*** -0.78% 5.74%***
Ptf CARs n 4 (5 securities) 2.85% -2.08% 4.93%***
CAAR group 4 (5 securities) 2.85% -2.08% 4.93%**
*** p-value < .01, ** p-value <.05, * p-value <.1
As required, the table reports only the portfolio and group ARs. Furthermore, in
this case, ARs are computed according to the Historical Mean Model (HMM) specified
through the option modtype. Since normal returns are supposed to be equal to the
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historical averages, the option indexlist (specifying the market returns) is no longer
required. The output table now is divided in four panels, reporting the variables specified
in each of the four varlists.
In contrast should one be interested only in the ARs on each variable, the option
suppress(group) may be specified.
. use data_estudy.dta
. estudy boa ford boeing(ibm facebook apple) (netflix cocacola amazon) (facebook
> boa ford boeing google) , datevar(date) evdate(07092015) dateformat(MDY) modt
> ype(MFM) indexlist(mkt smb hml) lb1(-3) ub1(3) lb2(-3) ub2(-1) lb3(0) ub3(3) d
> iagn(KP) eswlb(-250) eswub(-20) supp(group) showpvalues nostar
Event date: 09jul2015, with 3 event windows specified, using the Boehmer, Musume
> ci, Poulsen test, with the Kolari and Pynnonen adjustment
SECURITY CAAR[-3,3] CAAR[-3,-1] CAAR[0,3]
Bank of America Corporation 0.25% -2.03% 2.28%
(0.9181) (0.1942) (0.2076)
Ford Motor Company -1.07% -1.21% 0.14%
(0.7036) (0.5100) (0.9464)
The Boeing Company 3.30% 2.32% 0.98%
(0.2198) (0.1878) (0.6293)
IBM Corp 1.48% 0.48% 1.00%
(0.5680) (0.7778) (0.6093)
Facebook Inc -0.77% -1.13% 0.36%
(0.8076) (0.5830) (0.8781)
Apple Inc -3.93% -2.31% -1.63%
(0.1743) (0.2235) (0.4575)
Netflix Inc 3.55% 0.57% 2.98%
(0.6047) (0.8989) (0.5654)
The Coca-Cola Company 3.72% 1.64% 2.08%
(0.1030) (0.2717) (0.2283)
Amazon com Inc 3.05% -1.13% 4.18%
(0.5393) (0.7284) (0.2658)
Facebook Inc -0.77% -1.13% 0.36%
(0.8076) (0.5830) (0.8781)
Bank of America Corporation 0.25% -2.03% 2.28%
(0.9181) (0.1942) (0.2076)
Ford Motor Company -1.07% -1.21% 0.14%
(0.7036) (0.5100) (0.9464)
The Boeing Company 3.30% 2.32% 0.98%
(0.2198) (0.1878) (0.6293)
Alphabet Inc 5.30% 0.09% 5.22%
(0.0397) (0.9593) (0.0074)
p-values in parentheses
Contrary to the previous example, the table now reports only ARs on single secu-
rities, hiding those on the portfolio and of the group as a whole. Moreover, the option
showpvalues prints in brackets the p-value of each significance test below the ARs
which is referred to. Although some ARs are statistically different from zero, asterisks
do not appear in the table, due to option nostar. ARs are computed according to
the Fama and French (1993) 3 factors model, through the options modtype(MFM )and
indexlist(mkt smb hml ).
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12 Running event studies using Stata
4.1 Export
Table 1 and 2 show what the program exports when the option outputfile is specified,
using the same set-up of the last example4. This option creates, or replace should it
already exist, an .xlsx file containing two sheets, respectively reporting ARs and p-
values. In both cases, the program stores in the first column the labels of securities
on which the event study is performed (i.e. those included in each varlist), whereas
the specified event windows are reported in the first row. In Table 1 (Table 2), each
intersection is filled with the corresponding ARs (p-values).
Table 1: Output results: ARs
[-3,3] [-3,-1] [0,3]
Bank of America Corporation 0.0025... -0.0203... 0.0228...
Ford Mo t o r C ompany -0.0107... -0.0121... 0.0014...
The Boeing Company 0.033... 0.0232... 0.0098...
Ptf CARs n 1 (3 securities) 0.0083... -0.0031... 0.0113...
CAAR group 1 (3 securities) 0.0083... -0.0031... 0.0113...
IBM Corp 0.0148... 0.0048... 0.01...
Facebook Inc -0.0077... -0.0113... 0.0036...
Apple Inc -0.0393... -0.0231... -0.0163...
Ptf CARs n 2 (3 securities) -0.0107... -0.0099... -0.0009...
CAAR group 2 (3 securities) -0.0107... -0.0099... -0.0009...
Netflix Inc 0.0355... 0.0057... 0.0298...
The Coca-Cola Company 0.0372... 0.0164... 0.0208...
Amazon com Inc 0.0305... -0.0113... 0.0418...
Ptf CARs n 3 (3 securities) 0.0344... 0.0036... 0.0308...
CAAR group 3 (3 securities) 0.0344... 0.0036... 0.0308...
Facebook Inc -0.0077... -0.0113... 0.0036...
Bank of America Corporation 0.0025... -0.0203... 0.0228...
Ford Mo t o r C ompany -0.0107... -0.0121... 0.0014...
The Boeing Company 0.033... 0.0232... 0.0098...
Alphabet Inc 0.053... 0.0009... 0.0522...
Ptf CARs n 4 (5 securities) 0.014... -0.0039... 0.018...
CAAR group 4 (5 securities) 0.014... -0.0039... 0.018...
4. We omit the option suppress in order to obtain the most complete tables.
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Table 2: Output results: p-values
[-3,3] [-3,-1] [0,3]
Bank of America Corporation 0.9181... 0.1942... 0.2076...
Ford Mo t o r C ompany 0.7036... 0.51... 0.9464...
The Boeing Company 0.2198... 0.1878... 0.6293...
Ptf CARs n 1 (3 securities) 0.5787... 0.7523... 0.3135...
CAAR group 1 (3 securities) 0.4945... 0.7806... 0.076...
IBM Corp 0.568... 0.7778... 0.6093...
Facebook Inc 0.8076... 0.583... 0.8781...
Apple Inc 0.1743... 0.2235... 0.4575...
Ptf CARs n 2 (3 securities) 0.5448... 0.3949... 0.9488...
CAAR group 2 (3 securities) 0.5738... 0.2965... 0.9488...
Netflix Inc 0.6047... 0.8989... 0.5654...
The Coca-Cola Company 0.103... 0.2717... 0.2283...
Amazon com Inc 0.5393... 0.7284... 0.2658...
Ptf CARs n 3 (3 securities) 0.2603... 0.857... 0.1825...
CAAR group 3 (3 securities) 0.0131... 0.5092... 0...
Facebook Inc 0.8076... 0.583... 0.8781...
Bank of America Corporation 0.9181... 0.1942... 0.2076...
Ford Mo t o r C ompany 0.7036... 0.51... 0.9464...
The Boeing Company 0.2198... 0.1878... 0.6293...
Alphabet Inc 0.0397... 0.9593... 0.0074...
Ptf CARs n 4 (5 securities) 0.258... 0.628... 0.0553...
CAAR group 4 (5 securities) 0.2478... 0.6121... 0.0599...
For exposition ease we have truncated both ARs and p-values to the fourth decimal.
Yet, the program always exports numbers with 16 decimals.
5 References
Andres, C., A. Betzer, and M. Doumet. 2016. Measuring abnormal credit default swap
spreads .
Bessembinder, H., K. M. Kahle, W. F. Maxwell, and D. Xu. 2009. Measuring abnormal
bond performance. Review of Financial Studies 22(10): 4219–4258.
Binder, J. 1998. The event study methodology since 1969. Review of quantitative
Finance and Accounting 11(2): 111–137.
Boehmer, E., J. Musumeci, and A. B. Poulsen. 1991. Event-study methodology under
conditions of event-induced variance. Journal of financial economics 30(2): 253–272.
Under review by the STATA Journal
14 Running event studies using Stata
Fama, E. F., and K. R. French. 1993. Common risk factors in the returns on stocks and
bonds. Journal of financial economics 33(1): 3–56.
Kolari, J. W., and S. Pynn¨onen. 2010. Event study testing with cross-sectional correla-
tion of abnormal returns. Review of Financial Studies 23(11): 3996–4025.
Kolari, J. W., and S. Pynnonen. 2011. Nonparametric rank tests for event studies.
Journal of Empirical Finance 18(5): 953–971.
Kothari, S., and J. B. Warner. 2008. Econometrics of Event Studies. Handbook of
Empirical Corporate Finance SET 2: 1.
MacKinlay, A. C. 1997. Event studies in economics and finance. Journal of economic
literature 35(1): 13–39.
Patell, J. M. 1976. Corporate forecasts of earnings per share and stock price behavior:
Empirical test. Journal of accounting research 246–276.
Wilcoxon, F. 1945. Individual comparisons by ranking methods. Biometrics bulletin
1(6): 80–83.

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Full-text available
In event study analyses of abnormal returns on a single day, Corrado's (1989) nonparametric rank test and its modification in Corrado and Zivney (1992) have good empirical power properties, but problems arise in their application to cumulative abnormal returns (CARs). This paper proposes a generalized rank (GRANK) testing procedure that can be used for testing both single day and cumulative abnormal returns. Asymptotic distributions of the associated test statistics are derived and empirical properties of the test statistics are studied with simulations of CRSP returns. The results show that the proposed GRANK procedure outperforms previous rank tests of CARs and is robust to abnormal return serial correlation and event-induced volatility. Moreover, the GRANK procedure exhibits superior empirical power relative to parametric tests by Patell (1976) and Boehmer, Musumeci, and Poulsen (1991).
Full-text available
This paper discusses the event study methodology, beginning with FFJR (1969), including hypothesis testing, the use of different benchmarks for the normal rate of return, the power of the methodology in different applications and the modeling of abnormal returns as coefficients in a (multivariate) regression framework. It also focuses on frequently encountered statistical problems in event studies and their solutions. Copyright 1998 by Kluwer Academic Publishers
This paper examines the size and power of test statistics designed to detect abnormal changes in credit risk as measured by credit default swap (CDS) spreads. In a spirit similar to that of Brown and Warner (1980, 1985) and Bessembinder et al. (2009), we follow a simulation approach to examine the statistical properties of normal and abnormal CDS spreads and assess the performance of normal return models and test statistics. Using daily CDS data, we find that parametric test statistics are generally inferior to non-parametric tests, with the rank test performing best. Some of the classical normal return models, such as the market model, are found to be poorly specified. A CDS factor model based on factors identified in the empirical literature is generally well specified and more powerful in detecting abnormal performance. If factor information is not available, a simple mean-adjusted approach should be used. Finally, we examine performance in the presence of event-induced variance increases and bootstrapped p-values. Our inferences hold for US and European CDS data and are not affected by reference entity credit quality.
The comparison of two treatments generally falls into one of the following two categories: (a) we may have a number of replications for each of the two treatments, which are unpaired, or (b) we may have a number of paired comparisons leading to a series of differences, some of which may be positive and some negative. The appropriate methods for testing the significance of the differences of the means in these two cases are described in most of the textbooks on statistical methods.
The number of published event studies exceeds 500, and the literature continues to grow. We provide an overview of event study methods. Short-horizon methods are quite reliable. While long-horizon methods have improved, serious limitations remain. A challenge is to continue to refine long-horizon methods. We present new evidence that properties of event study methods can vary by calendar time period and can depend on event sample firm characteristics such as volatility. This reinforces the importance of examining event study statistical properties for non-randomly selected samples.
This article examines the issue of cross-sectional correlation in event studies. When there is event-date clustering, we find that even relatively low cross-correlation among abnormal returns is serious in terms of over-rejecting the null hypothesis of zero average abnormal returns. We propose a new test statistic that modifies the t-statistic of Boehmer, Musumeci, and Poulsen (1991) to take into account cross-correlation and show that it performs well in competition with others, including the portfolio approach, which is less powerful than other alternatives under study. Also, our statistic is readily useable to test multiple-day cumulative abnormal returns. The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail:, Oxford University Press.
This paper identifies five common risk factors in the returns on stocks and bonds. There are three stock-market factors: an overall market factor and factors related to firm size and book-to-market equity. There are two bond-market factors, related to maturity and default risks. Stock returns have shared variation due to the stock-market factors, and they are linked to bond returns through shared variation in the bond-market factors. Except for low-grade corporates, the bond-market factors capture the common variation in bond returns. Most important, the five factors seem to explain average returns on stocks and bonds.
We analyze the empirical power and specification of test statistics designed to detect abnormal bond returns in corporate event studies, using monthly and daily data. We find that test statistics based on frequently used methods of calculating abnormal monthly bond returns are biased. Most methods implemented in monthly data also lack power to detect abnormal returns. We also consider unique issues arising when using the newly available daily bond data, and formulate and test methods to calculate daily abnormal bond returns. Using daily bond data significantly increases the power of the tests, relative to the monthly data. Weighting individual trades by size while eliminating noninstitutional trades from the TRACE data also increases the power of the tests to detect abnormal performance, relative to using all trades or the last price of the day. Further, value-weighted portfolio-matching approaches are better specified and more powerful than equal-weighted approaches. Finally, we examine abnormal bond returns to acquirers around mergers and acquisitions to demonstrate how the abnormal return model and use of daily versus monthly data can affect inferences. The Author 2008. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail:, Oxford University Press.
Many authors have identified the hazards of ignoring event-induced variance in event studies. To determine the practical extent of the problem, we simulate an event with stochastic effects. We find that when an event causes even minor increases in variance, the most commonly-used methods reject the null hypothesis of zero average abnormal return too frequently when it is true, although they are reasonably powerful when it is false. We demonstrate that a simple adjustment to the cross-sectional techniques produces appropriate rejection rates when the null is true and equally powerful tests when it is false.