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Empirical Financial Economics
The Efficient Markets Hypothesis
Stephen J. BrownNYU Stern School of Business
2009 Merton H. Miller Doctoral Seminar
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Major developments over last 35 years
Portfolio theory
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Major developments over last 35 years
Portfolio theoryAsset pricing theory
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Major developments over last 35 years
Portfolio theoryAsset pricing theoryEfficient Markets Hypothesis
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Major developments over last 35 years
Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate finance
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Major developments over last 35 years
Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate financeDerivative Securities, Fixed
Income Analysis
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Major developments over last 35 years
Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate financeDerivative Securities, Fixed
Income Analysis Market Microstructure
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Major developments over last 35 years
Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate financeDerivative Securities, Fixed
Income AnalysisMarket MicrostructureBehavioral Finance
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Efficient Markets Hypothesis
ln [ln | ] [ln | ]t t it t tp E p E p
[ln (ln | )] 0t
t 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 t tE r E r z ln lnt t tr p p whe
re
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Efficient Markets Hypothesis
Tests of Efficient Markets HypothesisWhat is information?Does the market efficiently process
information?
Estimation of parametersWhat determines the cross section of
expected returns?Does the market efficiently price risk?
| 0t
t t t tE r E r z
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Tests of Efficient Markets Hypothesis
Weak form tests of Efficient Markets Hypothesis Example: trading rule tests
Semi-strong form tests of EMH Example: Event studies
Strong form tests of EMH Example: Insider trading studies (careful about
conditioning!)
| 0t
t t t tE r E r
10
1t
sellholdbuy
10
1t
bad newsno newsgood news
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Random Walk Hypothesis
| 0t
t t t tE r E r z
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Random Walk Hypothesis
| 0t
t t t t
t t
t
E r E r z
z r
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Random Walk Hypothesis
Serial covariance tests 0t t tE r E r r
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Random Walk Hypothesis
Serial covariance tests:
0
0
t t t
t t t
E r E r r
E r E r E r
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Random Walk Hypothesis
Serial covariance tests
0
0
t t t
t t t t
E r E r r
E r E r r E r
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Random Walk Hypothesis
1
1
0
Var( ) 1 2 (1 ) ( )2( 1)] 1Var( )
t t t
t
kt
E r E r r
r k kr
Serial covariance testsVariance Ratio tests
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Random Walk Hypothesis
, , ,
0
0
t t t
j t j t j t
E r E r r
E r E r r
Serial covariance testsVariance Ratio testsMomentum literature
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Random Walk Hypothesis
, , ,
0
0
t t t
j t j t j t t
E r E r r
E r E r r r
Serial covariance testsVariance Ratio testsMomentum literature
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Random Walk Hypothesis
, , ,
0
0
t t t
j t j t j t t
E r E r r
E r E r r r
Serial covariance testsVariance Ratio testsMomentum literature
Zero investment portfolio
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Random Walk Hypothesis
0t t tE r E r r Serial covariance testsVariance Ratio testsMomentum literatureAssumes stationarity
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Random Walk Hypothesis
0t t tE r E r r Serial covariance testsVariance Ratio testsMomentum literatureAssumes stationarity
t
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Random Walk Hypothesis
0t t tE r E r r Serial covariance testsVariance Ratio testsMomentum literatureAssumes stationarityNeither necessary nor
sufficient for EMH
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Trading rule tests of EMH
| 0t
t t t tE r E r
10
1t
sellholdbuy
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Trading rule tests of EMH
Timmerman (2007) surveyNaïve models using past sample means
hard to beatRecent financial data is most relevantShort lived episodes of limited
predictability
| 0t
t t t tE r E r
10
1t
sellholdbuy
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Trading rule tests of EMH
Timmerman (2007) surveyNaïve models using past sample means hard
to beatRecent financial data is most relevantShort lived episodes of limited predictability
Predictability is not profitabilityNecessity: Do not consider all possible
patterns of returnsSufficiency: Cannot profit if all markets rise
and fall together
| 0t
t t t tE r E r
10
1t
sellholdbuy
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Trading rule tests of EMH
Timmerman (2007) surveyNaïve models using past sample means hard
to beatRecent financial data is most relevantShort lived episodes of limited predictability
Predictability is not profitabilityNecessity: Do not consider all possible
patterns of returnsSufficiency: Cannot profit if all markets rise
and fall togetherHow can we examine significance of
trading profits?
| 0t
t t t tE r E r
10
1t
sellholdbuy
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An important seminal reference …
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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
Novel bootstrap in strategy space
1 41
ˆ[ | ] 3.5% 0 741 140
t t t t t
sellE r E r hold
buy
Return on DJI
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Trading rule predicting sign of excess returnJanuary 1970 - December 2005
Factor-augmented AR logit based on prior 120 month rolling window
Trading rule valueS&P500 value
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Cowles BootstrapJan 1970-Dec 2005
Annualized excess fund return 2.203%Sharpe ratio of fund 0.063Sharpe ratio of S&P500 0.049
Peseran & Timmermann (1992) p-value 4.83%Cowles bootstrap p-value 6.32%
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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
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Orthogonality condition
[ [ | )] 0t t t tE r E r z
, , ,[ ( | , )]i i i i ii 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 across all events
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
i I
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Fama Fisher Jensen and RollCumulative 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
Cumu
lative
ave
rage
resid
ual -
Um
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FFJR ReduxCumulative 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
Cumu
lative
ave
rage
resid
ual -
Um
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Original FFJR resultsCumulative 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
Cumu
lative
ave
rage
resid
ual -
Um
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Asset pricing models: GMM paradigm
Match moment conditions with sample moments
Test model by examining extent to which data matches moments
Estimate parameters
| 0t
t t t tE r E r z
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Example: Time varying risk premia
Time varying risk premia
imply a predictable component of excess returns
where the asset pricing model imposes constraint
0 1
0 1
t t
t f t t t
X
r r X f B
B
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Estimating asset pricing models: GMM
Define residuals
Residuals should not be predictable using instruments zt-1 that include the predetermined variables Xt-1
Choose parameters to minimize residual predictability
1 1 11 {[ ( | , ) ] } 0t t t t t t
t
z E r E r X zT
0 1( )t t f t tr r X f B
11 0t t
t
zT
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Estimating asset pricing models: Maximum likelihood
Define residuals
Choose parameters to minimize
Relationship to GMM: when instruments zt include the predetermined variables Xt-1
21t
tT
0 1( )t t f t tr r X f B
11: 0t t
t
FOC zT
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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
in practical applications