pages from fin econometrics brandt_2

Event Studies Motivation

Outline

1 Linear Factor ModelsMotivationTime-series approachCross-sectional approachComparing approachesOdds and ends

2 Event StudiesMotivationBasic methodologyBells and whistles

Michael W. Brandt Methods Lectures: Financial Econometrics


What is an event study?

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

Event studies traditionally answer the questionDoes this event matter? (e.g., index additions)

but are increasingly used to also answer the questionIs the relevant information impounded into prices immediatelyor with delay? (e.g., post earnings announcement drift)

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



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

Since even weekly expected returns are small in magnitude, thisallows 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 andstatistical properties of short-horizon event studies.

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

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

The following discussion focuses on short-horizon event studies.


Event Studies Basic methodology

Outline





Setup

Basic event study methodology is essentially unchanged sinceBall 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 economicmeat 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 + εi,t+1

Market model

ri,t+1 = αi + βi rm,t+1 + εi,t+1

Linear factor models

ri,t+1 = αi + β′i ft+1 + εi,t+1

(Notice the intercepts.)

Short-horizon event study results tend to be relatively insensitiveto 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 overthe estimation window and held fixed over the event window.



Abnormal returns

Using the market model as reference model, define

AR i,τ = ri,τ − αi − βi rm,τ τ = T1 + 1, ...,T 2.

Assuming iid returns

Var[AR i,τ

]= σ2

εi+

1T1 − T0

[1 +

((rm,τ − µm)

σm

)2]

︸︷︷︸due to estimation error

.

Estimation error also introduces persistence and cross-correlationin 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 thesame event lined up in event time

ARτ =1N∑N

i=1 AR i,τ .

2. Cumulate abnormal returns over the event window

ˆCAR i(T1,T2) =∑T2

τ=T1+1 AR i,τ

or¯CAR(T1,T2) =

∑T2τ=T1+1 ARτ .



Hypothesis testing

Basic hypothesis testing requires expressions for the variance ofARτ , ˆCAR i(T1,T2), and ¯CAR(T1,T2).

If stock level residuals εi,τ are iid through time

Var[

ˆCAR i(T1,T2)]

= (T2 − T1)σ2εi.

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

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

Var[ARτ

]=

1N2

∑Ni=1 σ

2εi

Var[

¯CAR(T1,T2)]

=∑T2

τ=T1+1 Var[ARτ

].



Example

Earnings announcements

Source: MacKinlay (1997)


Event Studies Bells and whistles

Outline





Dependence

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

One solution is Brown and Warner’s (1980) "crude adjustment"

Form a portfolio of firms experiencing an event in a givenmonth 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 ofthe portfolio’s abnormal returns over the estimation period.



Heteroskedasticity

Two forms of heteroskedasticity to deal with in event studies

1. Cross-sectional differences in σεi .• Standardize ARi,τ by σεi before aggregating to ARτ .• Jaffe (1974).

2. Event driven changes in σεi ,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

r1,t+1 = α1 + β1rm,t+1 +L∑

τ=0

γ1,τ D1,t+1,τ + u1,t+1

r2,t+1 = α2 + β2rm,t+1 +L∑

τ=0

γ2,τ D2,t+1,τ + u2,t+1

...

rn,t+1 = αn + βnrm,t+1 +L∑

τ=0

γn,τ Dn,t+1,τ + un,t+1

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 .


pages from fin econometrics brandt_2

Documents