Economics 201FS Professors Tim Bollerslev Spring 2006 and George Tauchen Market Efficiency and Financial Econometrics: A Brief Historical Perspective J.Y. Campbell, A.W. Lo and A.C. MacKinlay, 1997, The Econometrics of Financial Markets . Princeton, NJ: Princeton University Press. Chapters 1, 2 and 12. Bollerslev, T., (2001), "Financial Econometrics: Past Developments and Future Challenges," Journal of Econometrics , Vol.100, p.41-51. Engle, R.F. (2001), "Financial Econometrics - A New Discipline with New Methods," Journal of Econometrics , Vol.100, p.53-56. Tauchen, G. (2001), "Notes on Financial Econometrics," Journal of Econometrics , Vol.100, p.57-64.
· Financial Market Efficiency Fama (1970) · Do Prices Fully Reflect All Available Information ? or · Is it Possible to Formulate Trading Strategies which Generate Abnormal Profits/Returns ? · Information Set, I t · Weak / Semi-Strong / Strong * · Fair Return, r t · Asset Pricing Model * = r t,f + � t · � t,m · r t CAPM * � I t-1 ) = 0 ( � 0) · E( r t - r t · Market Efficiency - Joint Hypothesis
· Fair Return Cochrane (2001) E( m t ·r t � I t-1 ) = 1 ( � 1) · · Pricing Kernel / Stochastic Discount Factor / State Price Density r f,t = E( m t � I t-1 ) -1 · E( r t � I t-1 ) = r f,t - r f,t · Cov( r t , m t � I t-1 ) · · Complete Markets, No-Arbitrage · m t > 0 a.s. and Unique · CCAPM, Time-Separable u'(c t-1 ) = � · E(r t · u'(c t ) � I t-1 ) FOC · m t = � · u'(c t )/u'(c t-1 ) · IMRS m t = � · (c t /c t-1 ) - � · CRRA
· Risk Neutral Distribution E( m t ·r t � I t-1 ) = 1 · E*( r t � I t-1 ) = r f,t · · Option Pricing
· Random Walk / Martingale Model Bachelier (1900) * = µ · Fair Return, r t ( Cov(r t , m t � I t-1 ) Constant ) * � I t-1 ) = 0 · E( r t - r t · r t Serially Uncorrelated but NOT Necessarily i.i.d. N( · , · ) r t � logP t - logP t-1 � p t - p t-1 · p t = µ + p t-1 + � t E( � t � I t-1 ) = 0 · · Gross / Continuously Compounded (log) Returns 1 + R t � P t /P t-1 = exp( r t ) = lim n �� [1 + (r t /n)] n ·
· Multiperiod Returns · 1 + R t (k) = (1 + R t ) · ... · (1+ R t-k+1 ) = P t /P t-k r t (k) � logP t - logP t-k = r t + r t-1 + ... + r t-k+1 · · Limited Liability 1 + R t � 0 · r t � ] - � , � [ · · Portfolio Returns · R t,P = w 1 R t,1 + ... + w N R t,N r t,P � w 1 r t,1 + ... + w N r t,N · · Dividens · 1 + R t = (P t + D t ) / P t-1 r t � log(1 + R t ) = log(P t + D t ) - logP t-1 · � k + � p t + (1- � )d t - p t-1 � � 1/[1 + exp(d - p)] k � -log � - (1- � )log( � -1 - 1)
Then ( � 1980 ) Now Return No Short-Run (Daily, Weekly): Not Much Predictability Bid-Ask, Non-Synchronous Trading, etc. Long-Run (Multi-Year): Probably Statistical Biases Dividend Yields, P/E Ratios, etc. High-Frequency (Intraday): ? Return i.i.d. / R.W. Time Varying Volatility Distributions Fat Tails ARCH / GARCH / Stochastic Volatility Models Efficiency Yes / Cross-Sectional CAPM Size, Book-to-Market, Momentum, ... Systematic Risks APT and Multi-Factor Models Intertemporal CCAPM Equity Premium Puzzle Alternative Preferences Behavioral Finance
Financial Econometrics - Then ( � 1980) � Now · · Time Varying Volatility Models - ARCH Engle (Econometrica, Vol.50, No.4, 1982) · GARCH / EGARCH / ARCH-M / FIGARCH / ... · Stochastic Volatility Models · MLE / QMLE / Adaptive Estimation / ... · Multivariate Representations · Temporal and Cross-Sectional Aggregation · Continuous Time Approximations · Filtering and Forecasting · Flexible Estimation Procedures - GMM Hansen (Econometrica, Vol.50, No.4, 1982) · Optimal Instruments · Long-Run Covariance Matrix Estimation · Simulated Methods of Moments · Indirect Inference and EMM
· Current Research Themes · Time Varying Volatility Models · Long-Run Dependencies Long-Memory Models / Structural Shifts · Large Dimensional Systems Tractability · High-Frequency Data Intraday Patterns / Discreteness / Uneven Spacing · Realized Volatilities Measuring / Modeling / Forecasting · Jumps Parametric Models / Nonparametric Measurements · Flexible Estimation Procedures · Continuous Time Models Multivariate SV Models / Lévy-Driven Models · Objective and Risk Neutral Distributions Joint Estimation / Market Risk Premia
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