Empirical Financial Economics 3. Semistrong tests: Event Studies Stephen Brown NYU Stern School of Business UNSW PhD Seminar, June 19-21 2006.

Empirical Financial Economics

3. Semistrong tests: Event Studies

Stephen Brown NYU Stern School of Business

UNSW PhD Seminar, June 19-21 2006

Outline

Efficient Markets Hypothesis framework

Standard Event Study approachBrown/WarnerSystems Estimation issuesAsymmetric Information contextFFJR Redux

Efficient Markets Hypothesis

ln [ln | ] [ln | ]t t it t tp E p E p

[ln (ln | )] 0t t t tE p E p z

tz

which implies the testable hypothesis ...

where is part of the agent’s information set

In returns:

it

[ [ | )] 0t t t tE r E r z ln lnt t tr p p where

Examples

Random walk model

Assumes information set is constant

Event studies

For event dummy (event)

Time variant risk premia models

zt includes X

Important role of conditioning information

Serial covariance = [ ( )] 0t t tE r E r r

Average residual = [ ( )] 0t t tE r E r

0 1 1( ) ( ) ( ) ( )t t t K K tE r X X X

1t

Efficient Markets Hypothesis

Tests of Efficient Markets HypothesisWhat is information?Does the market efficiently process

information?Estimation of parameters

What determines the cross section of expected returns?

Does the market efficiently price risk?

[ [ | )] 0t t t tE r E r z

Standard Event Study approach

0 5 10 15 20 25 30t

rt1

rt2

rt3

rt4

u01u11u21 …

u02u12u22 …

u03u13u23 …

u04u14u24 … u05u15u25 …

EVENT

EVENT

EVENT

EVENT

EVENT

Orthogonality condition

[ [ | )] 0t t t tE r E r z

, , ,[ ( | , )]i i i it i t i t t M t tu r E r r z

1tz

Event studies measure the orthogonality condition

using the average value of the residual

where is good news and is bad news

1tz

If the residuals are uncorrelated, then the average residual will be asymptotically Normal with expected value equal to the orthogonality

condition, provided that the event zt has no market wide impact

Fama Fisher Jensen and Roll

Cumulative residuals around stock split

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-30 -20 -10 0 10 20 30

Month relative to split - m

Cum

ulat

ive

aver

age

resi

dual

- U

m

Brown and Warner

Model for observations:

Also considered quantile regressions, multifactor models

, 0

, 0

0, 1

,

jt j j Mt jt

j j

j j j

j j

j j

v

r r

Raw returns

r Mean adjusted returns

Market adjusted returns

OLS Market Model

(multiple models)

Block resampled bootstrap procedure

0 5 10 15 20 25 30t

rt1

rt2

rt3

rt4

Choose securities at random

Block resampled bootstrap procedure

0 5 10 15 20 25 30t

rt1

rt2

rt3

rt4

EVENT(chosen at random)

EVENT(chosen at random)

EVENT(chosen at random)

EVENT(chosen at random)

EVENT(chosen at random)

Choose ‘event dates’ at random

Block resampled bootstrap procedure

0 5 10 15 20 25 30t

rt1

rt2

rt3

rt4

EVENT(chosen at random)

EVENT(chosen at random)

EVENT(chosen at random)

EVENT(chosen at random)

EVENT(chosen at random)

Test period

Test periodEstimation period

Test period

Test period

Estimation period

Test periodEstimation period

Check if sufficient data exists around ‘event date’

Basic result

Actual level of Abnormal Performance at day “0”

Method 0 0.005 0.01 0.015

Mean adjusted return

6.4% 25.2% 75.6% 99.6%

Market Adjusted return

4.8 26.0 79.6 99.6

Market Model 4.4 27.2 80.4 99.6

Loss of power when event date uncertain

Days inEvent period

Level of abnormal performance

Method 0 0.01 0.02

Mean adjusted return

111

4.0%6.4

13.6%75.6

37.6%99.6

Market Adjusted return

111

4.04.8

13.279.6

32.099.6

Market Model 111

2.84.4

13.280.4

37.299.6

Misspecification when events coincide

Level of abnormal performance

Method 0 0.01 0.02

Mean adjusted return

Clustering

Nonclustering

13.6%4.0

21.2%13.6

29.6%37.6

Market Adjusted return

Clustering

Nonclustering

4.04.0

14.413.2

46.032.0

Market Model Clustering

Nonclustering

3.22.8

15.613.2

46.037.2

Schipper and Thompson Analysis

jt j j Mt jt j jtr r

The best linear unbiassed estimator of is

where is the difference in average return between announcement and non

announcement periods, and is the regression coefficient of the event dummy

on the market

j2

2 2 2 1ˆ M j M jM j M j

MM M

s s s s

j s s s

However, event study procedure assumes = 0

Systems estimation interpretation

11 1 11 111

1

1 1 11

1 1 1 1

1

0

1

1

0

1

M

t Mt t t

m M m m m

m

mt Mt mt m mt

r r

r r

r r

r r

R X

, with error covariance matrix or

Gain from systems estimation

11 1

1

1 1 1ˆ [ ' ] '

t m t

t

m t mm t

I I

I

I I

X X X R

GLS estimator is

No gain in efficiency if Events differ in calendar time ( diagonal) All events occur at same time ( )

Gain in efficiency if constant across securities

Is this reasonable?

mX I X

Sons of Gwalia example

AaClaim AssayReport ( oz/ton)

Operations

,|

, '

[ ] [ | ] ( ) 0

s

s

h dig for golds s e

l don t dig

E E s p s

Market observes decision s, but not assay report

,value to corporation

Market equilibrium requires

Event study implication

( | ) ( | )

( | ) , ( | )1

[ | ] ( ) (1 ) 01

[ ]

,

s

h ls

h l

jt j j Mt ht ht lt lt jt

ht lt

E s E s

a aE h E l

A Aa a

E s p s A AA A

r r d I d I

d d

This implies that which gives the

return model

How do we get ?

Justification for corporate finance event study application

Gwalia will dig if assay report is high enough

A standard Probit modelTaylor series expansion justification

for cross section regression of excess returns on firm characteristics

'

'

t jt

t jt

s h if z

s l if z

FFJR Redux

Cumulative residuals around stock split

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-30 -20 -10 0 10 20 30

Month relative to split - m

Cum

ulat

ive

aver

age

resi

dual

- U

m

Original FFJR results

Cumulative residuals around stock split

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-30 -20 -10 0 10 20 30

Month relative to split - m

Cum

ulat

ive

aver

age

resi

dual

- U

m