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 theoryAsset pricing theory

Major developments over last 35 years

Portfolio theoryAsset pricing theoryEfficient Markets Hypothesis

Major developments over last 35 years

Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate finance

Major developments over last 35 years

Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate financeDerivative Securities, Fixed

Income Analysis

Major developments over last 35 years

Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate financeDerivative Securities, Fixed

Income Analysis Market Microstructure

Major developments over last 35 years

Portfolio theoryAsset pricing theoryEfficient Markets HypothesisCorporate financeDerivative Securities, Fixed

Income AnalysisMarket MicrostructureBehavioral Finance

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

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 tE r E r 1

0

1t

sell

hold

buy

1

0

1t

bad news

no news

good news

Trading Rules: Cowles 1933

Cowles, A., 1933 Can stock market forecasters forecast? Econometrica 1 309-325

William Peter Hamilton’s Track Record 1902-1929Classify editorials as Sell, Hold or Buy

Novel bootstrap in strategy space

1 41

[ [ | )] 3.5% 0 74

1 140t t t t t

sell

E r E r hold

buy

Return on DJI

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 tE r E r z

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

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 1

1{[ ( | , ) ] } 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

1

10t t

t

zT

Estimating asset pricing models: Maximum likelihood

Define residuals

Choose parameters to minimize

Establishes a connection to Fama and MacBeth Resolves the “measurement error problem”

Relationship to GMM: when instruments zt include the predetermined variables Xt

21t

tT

0 1( )t t f t tr r X f B

1

1: 0t t

t

FOC zT

Fama and MacBeth procedure

( )it ft t t i ir r f estimate

0 5 10 15 20 25 30 t

Fama and MacBeth procedure

0 5 10 15 20 25 30 t

( )it ft t t i

t t

r r f

estimate f

Fama and MacBeth procedure

( )it ft t t i ir r f estimate

0 5 10 15 20 25 30 t

( )it ft t t i

t t

r r f

estimate f

The Likelihood Function

i

t tf

The market model regression

i

t tf

i

The Fama MacBeth cross section regression

i

t tf

i

ˆt tf

Updating market model

i

t tf

i

ˆt tf

Full Information Maximum Likelihood

i

t tf

i

ˆt tf

Estimating asset pricing models: A simpler way

Time varying risks and time varying premia:

This collapses to a simpler model

which generalizes:

Investment management style analysis (GSC)

Performance benchmark issues“Pure play” definitions

0 ;kt t t Kt t Kt ktr f k K

ˆ;kt Kt kt Kt ktr r k K

jt jK Kt jtK

r w

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