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 which implies the testable hypothesis ... where is part of the agent’s information set In returns: where

Efficient Markets Hypothesis 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 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!)

Random Walk Hypothesis

Random Walk Hypothesis

Random Walk Hypothesis Serial covariance tests

Random Walk Hypothesis Serial covariance tests:

Random Walk Hypothesis Serial covariance tests

Random Walk Hypothesis Serial covariance tests Variance Ratio tests

Random Walk Hypothesis Serial covariance tests Variance Ratio tests Momentum literature

Random Walk Hypothesis Serial covariance tests Variance Ratio tests Momentum literature

Random Walk Hypothesis Serial covariance tests Variance Ratio tests Momentum literature Zero investment portfolio

Random Walk Hypothesis Serial covariance tests Variance Ratio tests Momentum literature Assumes stationarity

Random Walk Hypothesis Serial covariance tests Variance Ratio tests Momentum literature Assumes stationarity

Random Walk Hypothesis Serial covariance tests Variance Ratio tests Momentum literature Assumes stationarity Neither necessary nor sufficient for EMH

Trading rule tests of EMH

Trading rule tests of EMH Timmerman (2007) survey Naïve models using past sample means hard to beat Recent financial data is most relevant Short lived episodes of limited predictability

Trading rule tests of EMH Timmerman (2007) survey 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 Timmerman (2007) survey 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 How can we examine significance of trading profits?

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 Return on DJI

Factor-augmented AR logit based on prior 120 month rolling window 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 2.203% Sharpe ratio of fund 0.063 Sharpe ratio of S&P500 0.049 Peseran & Timmermann (1992) p-value 4.83% Cowles bootstrap p-value 6.32%

Standard Event Study approach rt1 u01 u11 u21 … EVENT rt2 u02 u12 u22 … EVENT rt3 u03 u13 u23 … EVENT EVENT rt4 u04 u14 u24 … u05 u15 u25 … 5 10 15 20 25 30 t

Orthogonality condition Event studies measure the orthogonality condition using the average value of the residual across all events where is good news and 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

FFJR Redux

Original FFJR results

Asset pricing models: GMM paradigm Match moment conditions with sample moments Test model by examining extent to which data matches moments Estimate parameters

Example: Time varying risk premia imply a predictable component of excess returns where the asset pricing model imposes constraint

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

Estimating asset pricing models: Maximum likelihood Define residuals Choose parameters to minimize Relationship to GMM: when instruments zt include the predetermined variables Xt-1

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