Empirical Financial Economics
The Efficient Markets
Hypothesis
Review of Empirical Financial
Economics
Stephen Brown NYU Stern School of
Business
UNSW PhD Seminar, June 19-21 2006
Major developments over last 35
years
Portfolio theory
Major developments over last 35
years
Portfolio theory
Asset pricing theory
Major developments over last 35
years
Portfolio theory
Asset pricing theory
Efficient Markets Hypothesis
Major developments over last 35
years
Portfolio theory
Asset pricing theory
Efficient Markets Hypothesis
Corporate finance
Major developments over last 35
years
Portfolio theory
Asset pricing theory
Efficient Markets Hypothesis
Corporate finance
Derivative Securities, Fixed Income
Analysis
Major developments over last 35
years
Portfolio theory
Asset pricing theory
Efficient Markets Hypothesis
Corporate finance
Derivative Securities, Fixed Income
Analysis
 Market Microstructure
Major developments over last 35
years
Portfolio theory
Asset pricing theory
Efficient Markets Hypothesis
Corporate finance
Derivative Securities, Fixed Income
Analysis
Market Microstructure
Behavioral Finance
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?
Efficient Markets Hypothesis
E[rt   E[rt  | t )] t  0
 Weak form tests of Efficient Markets Hypothesis
1 sell
 Example: trading rule tests
 Semi-strong form tests of EMH
1
 Example: Event studies

 t  0
1


 t  0
1

bad news
no news
good news
 Strong form tests of EMH
 Example: Insider trading studies (careful about
conditioning!)
hold
buy
Trading Rules: Cowles 1933
Cowles, A., 1933 Can stock market
forecasters forecast? Econometrica 1 309325
William Peter Hamilton’s Track Record
1 41 sell

1902-1929
E[r  E[r |  )]  3.5%
  0
74 hold

Classify editorials as Sell, Hold or Buy
1

t 
t 
t
Return on DJI
t
t
140 buy
Asset pricing models: GMM
paradigm
E[rt   E[rt  | t )] zt  0
Match moment conditions with sample
moments
Test model by examining extent to which
data matches moments
Estimate parameters
Example: Time varying risk premia
Time varying risk premia
 t   0  X t 1
imply a predictable component of excess
returns
rt  rf    0  X t 1   f t B   t
where the asset pricing model imposes
 B
constraint
Estimating asset pricing models:
GMM
 Define residuals t
 rt  (rf   0  X t 1  ft B)
 Residuals should not be predictable using
instruments zt-1 that include the predetermined
variables1Xt-1
 t zt 1  E{[rt  E (rt |  , X t 1 ) ]zt 1}  0

T t
 Choose parameters to minimize residual
1
predictability
 z 0

T
t
t t 1
Estimating asset pricing models:
Maximum likelihood
t
 Define residuals
 rt  (rf   0  X t 1  ft B)
1
2

 Choose parameters to minimize
 t
T t
 Establishes a connection to Fama and MacBeth
 Resolves the “measurement error problem”
 Relationship to GMM: when instruments zt include
the predetermined variables Xt
1
FOC :
 t zt 1  0

T t
Fama and MacBeth procedure
rit  rft  ( t  f t ) i  estimate i
0
5
10
15
20
25
30
t
Fama and MacBeth procedure
rit  rft  ( t  ft ) i
 estimate  t  ft
0
5
10
15
20
25
30
t
Fama and MacBeth procedure
rit  rft  ( t  f t ) i  estimate i
rit  rft  ( t  ft ) i
 estimate  t  ft
0
5
10
15
20
25
30
t
The Likelihood Function
 t  ft
i
The market model regression
 t  ft
ˆi
i
The Fama MacBeth cross section
regression
 t  ft
ˆt  fˆt
ˆi
i
Updating market model
 t  ft
ˆt  fˆt
ˆi
i
Full Information Maximum
Likelihood
 t  ft
ˆt  fˆt
ˆi
i
Estimating asset pricing models: A
simpler way
Time varying risks and time varying
premia:
rkt   0t   t  Kt  ft  Kt  kt ;
k K
This
aˆ Ktsimpler
model
rkt collapses
 Kt  kt ; to 
 rkt
k K
rjt   w jK  Kt  jt
which generalizes:
 Investment
(GSC)
K
management style analysis
Conclusion
Efficient Market Hypothesis is alive and well
EMH central to recent developments in empirical
Finance
EMH highlights importance of appropriate
conditioning
 in
empirical financial research