THE MEANING OF MARKET EFFICIENCY

Fama defined an efficient market as one in which prices always “fully reflect” available information. This paper formalizes this definition and provides various characterizations relating to equilibrium models, profitable trading strategies, and equivalent martingale measures. These various characterizations facilitate new insights and theorems relating to efficient markets. In particular, we overcome a well-known limitation in tests for market efficiency, i.e., the need to assume a particular equilibrium asset pricing model, called the joint-hypothesis or bad-model problem. Indeed, we show that an efficient market is completely characterized by the absence of both arbitrage opportunities and dominated securities, an insight that provides tests for efficiency that are devoid of the bad-model problem. Other theorems useful for both the testing of market efficiency and the pricing of derivatives are also provided.

[1]  M. Yor,et al.  Equivalent and absolutely continuous measure changes for jump-diffusion processes , 2005, math/0508450.

[2]  J. Jacod Calcul stochastique et problèmes de martingales , 1979 .

[3]  Jia-An Yan A numeraire-free and original probability based framework for financial markets , 2003, math/0305017.

[4]  E. Fama EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[5]  M. C. Jensen Some Anomalous Evidence Regarding Market Efficiency , 1978 .

[6]  Philip Protter,et al.  STRUCTURAL VERSUS REDUCED FORM MODELS: A NEW INFORMATION BASED PERSPECTIVE , 2004 .

[7]  S. Shreve,et al.  Methods of Mathematical Finance , 2010 .

[8]  D. Duffie Dynamic Asset Pricing Theory , 1992 .

[9]  R. Dana Existence, uniqueness and determinacy of Arrow–Debreu equilibria in finance models , 1993 .

[10]  E. Fama Market Efficiency, Long-Term Returns, and Behavioral Finance , 1997 .

[11]  Robert J. Elliott,et al.  On Models of Default Risk , 2000 .

[12]  E. Fama,et al.  Efficient Capital Markets : II , 2007 .

[13]  F. Delbaen,et al.  Arbitrage possibilities in Bessel processes and their relations to local martingales , 1995 .

[14]  Robert C. Dalang,et al.  Equivalent martingale measures and no-arbitrage in stochastic securities market models , 1990 .

[15]  P. Meyer,et al.  La mesure de H. Föllmer en théorie des surmartingales , 1972 .

[16]  Rose Anne Dana Existence and Uniqueness of Equilibria When Preferences Are Additively Separable , 1993 .

[17]  Rose-Anne Dana,et al.  On the Existence of an Arrow-Radner Equilibrium in the Case of Complete Markets. A Remark , 1992, Math. Oper. Res..

[18]  F. Delbaen,et al.  A general version of the fundamental theorem of asset pricing , 1994 .

[19]  Constantinos Kardaras,et al.  The numéraire portfolio in semimartingale financial models , 2007, Finance Stochastics.

[20]  J. Jacod,et al.  Grossissement initial, hypothese (H′) et theoreme de Girsanov , 1985 .

[21]  M. Jeanblanc,et al.  Default Times, Non-Arbitrage Conditions and Change of Probability Measures , 2008, 0812.4064.

[22]  Anat R. Admati The informational role of prices: A review essay , 1991 .

[23]  Ruth J. Williams,et al.  Introduction to Stochastic Integration , 1994 .

[24]  C. Sin Complications with stochastic volatility models , 1998, Advances in Applied Probability.

[25]  J. Ruf,et al.  HEDGING UNDER ARBITRAGE , 2010, 1003.4797.

[26]  Editors , 1986, Brain Research Bulletin.

[27]  A. Lo,et al.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1996, Macroeconomic Dynamics.

[28]  Probabilités neutres au risque et asymétrie d'information , 1999 .

[29]  P. Protter,et al.  1 Asset Price Bubbles in Complete Markets , 2006 .

[30]  David Hobson,et al.  Comparison results for stochastic volatility models via coupling , 2010, Finance Stochastics.

[31]  Marc Yor,et al.  Changes of filtrations and of probability measures , 1978 .

[32]  Sara Biagini,et al.  Utility maximization in incomplete markets for unbounded processes , 2005, Finance Stochastics.

[33]  F. Delbaen,et al.  The fundamental theorem of asset pricing for unbounded stochastic processes , 1998 .

[34]  Delia Coculescu,et al.  Default times, no-arbitrage conditions and changes of probability measures , 2012, Finance Stochastics.

[35]  P. Protter Stochastic integration and differential equations , 1990 .

[36]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[37]  P. Protter,et al.  ASSET PRICE BUBBLES IN INCOMPLETE MARKETS * , 2008 .

[38]  Hans Föllmer,et al.  The exit measure of a supermartingale , 1972 .

[39]  Roy Radner,et al.  Rational expectations in microeconomic models: An overview , 1982 .

[40]  John P. Lehoczky,et al.  Existence and Uniqueness of Multi-Agent Equilibrium in a Stochastic, Dynamic Consumption/Investment Model , 1990, Math. Oper. Res..

[41]  A. Cherny,et al.  ON THE MARTINGALE PROPERTY OF TIME-HOMOGENEOUS DIFFUSIONS , 2009 .

[42]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[43]  I. Karatzas,et al.  Relative arbitrage in volatility-stabilized markets , 2005 .

[44]  E. Fernholz Stochastic Portfolio Theory , 2002 .

[45]  Kiyosi Itô,et al.  Extension of Stochastic Integrals , 1987 .

[46]  Darrell Duffie,et al.  Stochastic Equilibria: Existence, Spanning Number, and the 'No Expected Financial Gain from Trade' Hypothesis , 1986 .

[47]  W. Schachermayer,et al.  THE BANACH SPACE OF WORKABLE CONTINGENT CLAIMS IN ARBITRAGE THEORY. L’ESPACE DE BANACH DES ACTIFS , 1998 .

[48]  Hui Wang,et al.  Utility maximization in incomplete markets with random endowment , 2001, Finance Stochastics.

[49]  I. Karatzas,et al.  Optimal Consumption from Investment and Random Endowment in Incomplete Semimartingale Markets , 2001, 0706.0051.

[50]  Sanford J. Grossman The Informational Role of Prices , 1990 .

[51]  K. Parthasarathy,et al.  Probability measures on metric spaces , 1967 .

[52]  A Paul,et al.  SAMUELSON, . Proof that properly anticipated prices fluctuate randomly, Industrial Management Review, . , 1965 .

[53]  N. Ikeda,et al.  A comparison theorem for solutions of stochastic differential equations and its applications , 1977 .

[54]  A. Mijatović,et al.  On the martingale property of certain local martingales , 2009, 0905.3701.

[55]  T. Bielecki,et al.  Credit Risk: Modeling, Valuation And Hedging , 2004 .

[56]  W. Andrew,et al.  LO, and A. , 1988 .

[57]  Christophe Stricker,et al.  Quasimartingales, martingales locales, semimartingales et filtration naturelle , 1977 .

[58]  Gordan Zitkovic,et al.  Financial equilibria in the semimartingale setting: Complete markets and markets with withdrawal constraints , 2007, Finance Stochastics.

[59]  W. Schachermayer,et al.  The asymptotic elasticity of utility functions and optimal investment in incomplete markets , 1999 .