empirical financial economics

Empirical Financial Economics

The Efficient Markets Hypothesis

Stephen J. BrownNYU 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 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 t tE p E p z

tz

which implies the testable hypothesis ...

where is part of the agent’s information set

In returns:

it

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t t t tE r E r z ln lnt t tr p p whe

re

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

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

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bad newsno newsgood news

Random Walk Hypothesis

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Random Walk Hypothesis

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Random Walk Hypothesis

Serial covariance tests 0t t tE r E r r

Random Walk Hypothesis

Serial covariance tests:

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Random Walk Hypothesis

Serial covariance tests

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Serial covariance testsVariance Ratio tests

Random Walk Hypothesis

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Serial covariance testsVariance Ratio testsMomentum literature

Random Walk Hypothesis

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Serial covariance testsVariance Ratio testsMomentum literature

Random Walk Hypothesis

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Zero investment portfolio

Random Walk Hypothesis

0t t tE r E r r Serial covariance testsVariance Ratio testsMomentum literatureAssumes stationarity

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 stationarityNeither necessary nor

sufficient for EMH

Trading rule tests of EMH

| 0t

t t t tE r E r

10

1t

sellholdbuy

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

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

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

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

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

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

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%

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

Orthogonality condition

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, , ,[ ( | , )]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

Fama Fisher Jensen and RollCumulative residuals around stock split

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FFJR ReduxCumulative residuals around stock split

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Original FFJR resultsCumulative residuals around stock split

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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

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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

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

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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

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