Empirical Financial Economics
The Efficient Markets
Hypothesis
Stephen J. Brown
NYU Stern School of Business
2009 Merton H. Miller Doctoral Seminar
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
t
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

t
e
Efficient Markets Hypothesis


E  rt   E  rt  | t  zt  0
t
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?
Tests of Efficient Markets Hypothesis


E  rt   E  rt  | t   t  0
t
 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
Random Walk Hypothesis


E  rt   E  rt  | t  zt  0
t
Random Walk Hypothesis


E  rt   E  rt  |  t   zt  0
t
zt  rt
t  
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Random Walk Hypothesis


E  rt   E  rt    rt  0
Serial covariance tests:


E  rt   E  rt    E  rt   0
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests


E  rt   E  rt    rt  E  rt   0
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Variance Ratio tests
 1
Var( rt  )
k
 1  2 (1  )  ( k )2(  1)]  1
 Var( rt )

k 1
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Variance Ratio tests
Momentum literature


E  rj ,t   E  rj ,t   rj ,t  0
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Variance Ratio tests
Momentum literature


E  rj ,t   E  rj ,t    rj ,t  rt   0
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Variance Ratio tests
Momentum literature


E  rj ,t   E  rj ,t    rj ,t  rt   0
Zero investment portfolio
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Variance Ratio tests
Momentum literature
Assumes stationarity
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Variance Ratio tests
Momentum literature
Assumes stationarity
t  
Random Walk Hypothesis


E  rt   E  rt   rt  0
Serial covariance tests
Variance Ratio tests
Momentum literature
Assumes stationarity
Neither necessary nor sufficient for
EMH
Trading rule tests of EMH


E  rt   E  rt  | t   t  0
t
1

 t  0
1

sell
hold
buy
Trading rule tests of EMH


E  rt   E  rt  | t   t  0
t
Timmerman (2007) survey
1

 t  0
1

Naïve models using past sample means hard to
beat
Recent financial data is most relevant
Short lived episodes of limited predictability
sell
hold
buy
Trading rule tests of EMH


E  rt   E  rt  | t   t  0
t
Timmerman (2007) survey
1

 t  0
1

sell
hold
buy
Naïve models using past sample means hard to beat
Recent financial data is most relevant
Short lived episodes of limited predictability
Predictability is not profitability
Necessity: Do not consider all possible patterns of
returns
Sufficiency: Cannot profit if all markets rise and fall
together
Trading rule tests of EMH


E  rt   E  rt  | t   t  0
t
Timmerman (2007) survey
1

 t  0
1

sell
hold
buy
Naïve models using past sample means hard to beat
Recent financial data is most relevant
Short lived episodes of limited predictability
Predictability is not profitability
Necessity: Do not consider all possible patterns of
returns
Sufficiency: Cannot profit if all markets rise and fall
together
An important seminal reference …
Trading Rules: Cowles 1933
 Cowles, A., 1933 Can stock market forecasters
forecast? Econometrica 1 309-325
 William Peter Hamilton’s Track Record 1902-1929
 Classify editorials as Sell, Hold or Buy
Eˆ [rt   E  rt  |  t ] t  3.5%
Return on DJI
 Novel bootstrap in strategy space
 1

 t  0
 1

41 sell
74 hold
140 buy
Trading rule predicting sign of excess return
January 1970 - December 2005
Trading rule value
S&P500 value
Factor-augmented AR logit based on prior 120 month rolling window
Cowles Bootstrap
Jan 1970-Dec 2005
Annualized excess fund return
Sharpe ratio of fund
Sharpe ratio of S&P500
Peseran & Timmermann (1992) p-value
Cowles bootstrap p-value
2.203%
0.063
0.049
4.83%
6.32%
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
i  I all
using the average value of the residual across
events
u i  [ri ,ti   E ( ri ,ti  |  ti , rM ,ti  )] zti
wherezt  1
is good news zand
t  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 average residual - Um
Cumulat ive residuals around st ock split
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-30
-20
-10
0
10
20
Mont h relat ive t o split - m
30
FFJR Redux
Cumulat ive average residual - Um
Cumulat ive residuals around st ock split
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-30
-20
-10
0
10
20
Mont h relat ive t o split - m
30
Original FFJR results
Cumulat ive average residual - Um
Cumulat ive residuals around st ock split
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-30
-20
-10
0
10
20
Mont h relat ive t o split - m
30

Asset pricing models: GMM
paradigm

E  rt   E  rt  | t  zt  0
t
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
 Relationship to GMM: when instruments zt include
the predetermined variables Xt-1
1
FOC :
 t zt 1  0

T t
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