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 approach
Brown/Warner
Systems Estimation issues
Asymmetric Information context
FFJR Redux
Efficient Markets Hypothesis
ln pt  E[ln pt  | it ]  E[ln pt  | t ]
which implies the testable hypothesis ...
E[ln pt   E (ln pt  | t )] zt  0
where
zist part of the agent’s information set
 it
In returns:
E[rt   E[rt  | t )] zt  0 wher rt   ln pt   ln pt
e
Examples
Random walk model
Serial covariance = E[rt   E(rt  )] rt  0

 Assumes information set
is constant
Event studies
Average residual = E[rt   E (rt  )] t  0
 For event dummy
 t  1 (event)
Time variant risk premia models
E (rt  )  0 ( X t )  11 ( X t ) 

  K K ( X t )
zt includes X
Important role of conditioning information
Efficient Markets Hypothesis
E[rt   E[rt  | t )] zt  0
Tests of Efficient Markets Hypothesis
What 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?
Standard Event Study approach
EVEN
T
rt1
u01 u11u21 …
EVEN
T
rt2
u02 u12u22 …
EVEN
T
rt3
u03 u13u23 …
0
EVEN
T
EVEN
T
u04 u14u24 …
u05 u15u25 …
5
10
15
20
25
30
rt4
t
Orthogonality condition
Event studies measure the orthogonality condition
E[rt   E[rt  | t )] zt  0
using the average value of the residual
u t  [ri ,ti   E (ri ,ti  |  ti , rM ,ti  )] zt
where
zt  1is good news andzt  1
is bad news
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
Cumulat ive residuals around st ock split
Cumulat ive average residual - Um
0 .4
0 .35
0 .3
0 .25
0 .2
0 .15
0 .1
0 .0 5
0
-30
-20
-10
0
10
20
Mont h relat ive t o split - m
30
Brown and Warner
 Model for observations:
rjt   j   j rMt  jt
Raw returns
 j ,  j  0

 j  rj ,  j  0 Mean adjusted returns

 j  0,  j  1 Market adjusted returns
 , 
OLS Market Model
 j j
 v (multiple models)
 Also considered quantile regressions, multifactor
models
Block resampled bootstrap
procedure
rt1
rt2
rt3
rt4
0
5
10
15
20
25
Choose securities at random
30
t
Block resampled bootstrap
procedure
EVENT(chosen at
random)
EVENT(chosen at
random)
rt2
EVENT(chosen at
random)
rt3
EVENT(chosen at
random)
EVENT(chosen at
random)
0
5
rt1
10
15
20
25
Choose ‘event dates’ at random
30
t
rt4
Block resampled bootstrap
procedure
EVENT(chosen at
random)
Estimation
period
EVENT(chosen at
random)
Test period
Test period
rt2
EVENT(chosen at
random)
Estimation
rt3
Test period
EVENT(chosen
at
period
random)
EVENT(chosen at
random)
Estimation
period
Test period
0
5
rt1
10
15
Test period
20
25
30
t
Check if sufficient data exists around ‘event date’
rt4
Basic result
Actual level of Abnormal Performance at
day “0”
Method
0
0.005
0.01
0.015
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
Mean adjusted return
Loss of power when event date
uncertain
Method
Days in
Event
period
Level of abnormal performance
0
0.01
0.02
Mean adjusted return
11
1
4.0%
6.4
13.6%
75.6
37.6%
99.6
Market Adjusted
return
11
1
4.0
4.8
13.2
79.6
32.0
99.6
Market Model
11
1
2.8
4.4
13.2
80.4
37.2
99.6
Misspecification when events
coincide
Level of abnormal
performance
Method
0
0.01
0.02
Mean adjusted
return
Clustering
Nonclusteri
ng
13.6%
4.0
21.2%
13.6
29.6%
37.6
Market Adjusted
return
Clustering
Nonclusteri
ng
4.0
4.0
14.4
13.2
46.0
32.0
Market Model
Clustering
Nonclusteri
3.2
2.8
15.6
13.2
46.0
37.2
Schipper and Thompson Analysis
rjt   j   j rMt   jt j   jt
The best linear unbiassed estimator of
j
ˆ j 
2
sM s j  sM  s jM
2 2
2
sM
s  sM


is
 j  M  j
1 M 
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
However, event study procedure assumes
 = 0
Systems estimation interpretation
 r11  1 rM 1 11
  
  
 r1t  1 rMt 1t
  
 
 rm1  
  
0
  
r  
 mt  
  1   11 
   
0
 1   
   1   1t 
   
  
1 rM 1  m1   m   m1 
   
  m   
1 rMt  mt    m   mt 
o R  X  , with error covariance matrix 
r
Gain from systems estimation
  11I t


 I
 m1 t
 1m I t 

    It
 mm I t 
GLS estimator is
ˆ  [ X ' 1 X ]1 X ' 1R
No gain in efficiency if
 ( diagonal)
Events differ in calendar time
 All events occur at same time
)
X ( I m  X

Gain in efficiency if constant across
securities

Is this reasonable?
Sons of Gwalia example
Claim

AssayReport
( oz/ton)
Operations
a
A
h, dig for gold
s
,value to corporation | s   s  e
l , don ' t dig

Market observes decision s, but not assay report
Market equilibrium requiresE[ ] 
 E[ | s] p(s)  0
s

Event study implication
E ( | s )   s E ( | s)
a
a
E ( | h)  , E ( | l )  
A
1 A
a
a
s E[ | s] p(s)   h A A   l 1  A (1  A)  0
This implies that  h   l   which gives the return model
rjt   j   j rMt   [d ht I ht  dlt I lt ]  jt
How do we getd ht , dlt ?
Justification for corporate finance
event study application
Gwalia will dig if assay report is high
enough s  h if t   ' z jt
sl
if t   ' z jt
A standard Probit model
Taylor series expansion justification for
cross section regression of excess
returns on firm characteristics
FFJR Redux
Cumulat ive residuals around st ock split
Cumulat ive average residual - Um
0 .4
0 .35
0 .3
0 .25
0 .2
0 .15
0 .1
0 .0 5
0
-30
-20
-10
0
10
20
Mont h relat ive t o split - m
30
Original FFJR results
Cumulat ive residuals around st ock split
Cumulat ive average residual - Um
0 .4
0 .35
0 .3
0 .25
0 .2
0 .15
0 .1
0 .0 5
0
-30
-20
-10
0
10
20
Mont h relat ive t o split - m
30