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