Market Efficiency and Financial Econometrics: A Brief Historical - - PDF document

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 ?

• r

· Is it Possible to Formulate Trading Strategies which Generate Abnormal Profits/Returns ? · Information Set, It · Weak / Semi-Strong / Strong · Fair Return, rt

*

· Asset Pricing Model · rt

* = rt,f + t·t,m

CAPM · E( rt - rt

* It-1 ) = 0 ( 0)

· Market Efficiency - Joint Hypothesis

· Fair Return Cochrane (2001) · E( mt·rt It-1 ) = 1 ( 1) · Pricing Kernel / Stochastic Discount Factor / State Price Density · rf,t = E( mt It-1 )-1 · E( rt It-1 ) = rf,t - rf,t · Cov( rt , mt It-1) · Complete Markets, No-Arbitrage · mt > 0 a.s. and Unique · CCAPM, Time-Separable · u'(ct-1 ) = · E(rt · u'(ct )It-1) FOC · mt = · u'(ct )/u'(ct-1) IMRS · mt = · (ct /ct-1)- CRRA

· Risk Neutral Distribution · E( mt·rt It-1 ) = 1 · E*( rt It-1 ) = rf,t · Option Pricing

· Random Walk / Martingale Model Bachelier (1900) · Fair Return, rt

* = µ

( Cov(rt , mt It-1) Constant ) · E( rt - rt

*It-1) = 0

· rt Serially Uncorrelated but NOT Necessarily i.i.d. N( · , · ) · rt logPt - logPt-1 pt - pt-1 · pt = µ + pt-1 + t E(t It-1) = 0 · Gross / Continuously Compounded (log) Returns · 1 + Rt Pt /Pt-1 = exp( rt ) = limn[1 + (rt /n)]n

· Multiperiod Returns · 1 + Rt(k) = (1 + Rt ) · ... · (1+ Rt-k+1 ) = Pt /Pt-k · rt(k) logPt - logPt-k = rt + rt-1 + ... + rt-k+1 · Limited Liability · 1 + Rt 0 · rt ] - , [ · Portfolio Returns · Rt,P = w1Rt,1 + ... + wN Rt,N · rt,P w1rt,1 + ... + wN rt,N · Dividens · 1 + Rt = (Pt + Dt ) / Pt-1 · rt log(1 + Rt ) = log(Pt + Dt) - logPt-1 k + pt + (1-)dt - pt-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