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Event Studies Motivation

Outline

1 Linear Factor Models
Motivation
Time-series approach
Cross-sectional approach
Comparing approaches
Odds and ends

2 Event Studies
Motivation
Basic methodology
Bells and whistles

Michael W. Brandt Methods Lectures: Financial Econometrics


What is an event study?

An event study measures the immediate and short-horizon
delayed impact of a speciﬁc event on the value of a security.

Event studies traditionally answer the question
Does this event matter? (e.g., index additions)
but are increasingly used to also answer the question
Is the relevant information impounded into prices immediately
or with delay? (e.g., post earnings announcement drift)

Event studies are popular not only in accounting and ﬁnance, but
also in economics and law to examine the role of policy and
regulation or determine damages in legal liability cases.



Short- versus long-horizon event studies
Short-horizon event studies examine a short time window, ranging
from hours to weeks, surrounding the event in question.

Since even weekly expected returns are small in magnitude, this
allows us to focus on the information being released and (largely)
abstract from modeling discount rates and changes therein.

There is relatively little controversy about the methodology and
statistical properties of short-horizon event studies.

However event study methodology is increasingly being applied to
longer-horizon questions. (e.g., do IPOs under-perform?)

Long-horizon event studies are problematic because the results
are sensitive to the modeling assumption for expected returns.

The following discussion focuses on short-horizon event studies.


Event Studies Basic methodology

Outline

Motivation
Odds and ends

2 Event Studies
Motivation
Basic methodology
Bells and whistles



Setup

Basic event study methodology is essentially unchanged since
Ball and Brown (1968) and Fama et al. (1969).

Anatomy of an event study
1. Event Deﬁnition and security selection.
2. Speciﬁcation and estimation of the reference model
characterizing "normal" returns (e.g., market model).
3. Computation and aggregation of "abnormal" returns.
4. Hypothesis testing and interpretation.

#1 and the interpretation of the results in #4 are the real economic
meat of an event study – the rest is fairly mechanical.



Reference models

Common choices of models to characterize "normal" returns
Constant expected returns
ri,t+1 = µi + i,t+1
Market model
ri,t+1 = αi + βi rm,t+1 + i,t+1

Linear factor models

ri,t+1 = αi + βi ft+1 + i,t+1

(Notice the intercepts.)

Short-horizon event study results tend to be relatively insensitive
to the choice of reference models, so keeping it simple is ﬁne.



Time-line and estimation

A typical event study time-line is

Source: MacKinlay (1997)

The parameters of the reference model are usually estimated over
the estimation window and held ﬁxed over the event window.



Abnormal returns
Using the market model as reference model, deﬁne
ˆ ˆ
AR i,τ = ri,τ − αi − βi rm,τ τ = T1 + 1, ..., T 2.
ˆ

Assuming iid returns
2
ˆ 1 (rm,τ − µm )
ˆ
Var AR i,τ = σ 2i + 1+ .
T1 − T0 σm
ˆ

due to estimation error

Estimation error also introduces persistence and cross-correlation
in the measured abnormal returns, even when true returns are iid,
which is an issue particularly for short estimation windows.

Assume for what follows that estimation error can be ignored.



Aggregating abnormal returns

Since the abnormal return on a single stock is extremely noisy,
returns are typically aggregated in two dimensions.
1. Average abnormal returns across all ﬁrms undergoing the
same event lined up in event time

¯ 1 N ˆ
AR τ = AR i,τ .
N i=1
2. Cumulate abnormal returns over the event window
ˆ T2 ˆ
CAR i (T1 , T2 ) = τ =T1 +1 AR i,τ

or
¯ T2 ¯
CAR(T1 , T2 ) = τ =T1 +1 AR τ .



Hypothesis testing
Basic hypothesis testing requires expressions for the variance of
¯ ˆ ¯
AR τ , CAR i (T1 , T2 ), and CAR(T1 , T2 ).

If stock level residuals i,τ are iid through time

ˆ
Var CAR i (T1 , T2 ) = (T2 − T1 )σ 2i .

The other two expressions are more problematic because they
depend on the cross-sectional correlation of event returns.

If, in addition, event windows are non-overlapping across stocks

¯ 1 N 2
Var AR τ = 2 i=1 σ i
N
¯ T2 ¯
Var CAR(T1 , T2 ) = τ =T1 +1 Var AR τ .



Example
Earnings announcements

Source: MacKinlay (1997)


Event Studies Bells and whistles

Outline

Motivation
Odds and ends

2 Event Studies
Motivation
Basic methodology
Bells and whistles



Dependence

If event windows overlap across stocks, the abnormal returns are
correlated contemporaneously or at lags.

One solution is Brown and Warner’s (1980) "crude adjustment"
Form a portfolio of ﬁrms experiencing an event in a given
month or quarter (still lined up in event time, of course).
Compute the average abnormal return of this portfolio.
Normalize this abnormal return by the standard deviation of
the portfolio’s abnormal returns over the estimation period.



Heteroskedasticity

Two forms of heteroskedasticity to deal with in event studies
1. Cross-sectional differences in σ i .
¯
• Standardize ARi,τ by σ i before aggregating to AR τ .
• Jaffe (1974).

2. Event driven changes in σ i ,t
.
• Cross-sectional estimate of Var [ARi,τ ] over the event window.
• Boehmer et al. (1991).



Regression based approach
An event study can alternatively be run as multivariate regression
L
r1,t+1 = α1 + β1 rm,t+1 + γ1,τ D1,t+1,τ + u1,t+1
τ =0
L
r2,t+1 = α2 + β2 rm,t+1 + γ2,τ D2,t+1,τ + u2,t+1
τ =0
...
L
rn,t+1 = αn + βn rm,t+1 + γn,τ Dn,t+1,τ + un,t+1
τ =0

where Di,t,τ = 1 if ﬁrm i had an event at date t − τ (= 0 otherwise).

In this case, γi,τ takes the place of the abnormal return ARi,τ .


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