Minimal Dynamic Equilibria

We define dynamic models as multiperiod models with no static representations and demonstrate that current prevalent asset pricing empirical implementations are inconsistent with dynamic equilibria. Specifically, empirical implementations are misspecified with respect to three essential asset pricing questions (TEQ): dependency on higher moments, complexity of risk premia, and mean-variance efficiency of the “market portfolio” (ability to proxy pricing kernels/SDFs). While we already know that “Merton” models, and their derivatives, differ from static models in all TEQ, we show that this is the case even the “minimal” dynamic equilibria.

[1]  Dave Feldman,et al.  Linear Beta Pricing with Inefficient Benchmarks , 2013 .

[2]  W. Sharpe CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[3]  Avi Bick,et al.  The Mathematics of the Portfolio Frontier: A Geometry-Based Approach , 2002 .

[4]  Michael U. Dothan,et al.  Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy , 1986 .

[5]  F. Black Capital Market Equilibrium with Restricted Borrowing , 1972 .

[6]  Larry G. Epstein SHARING AMBIGUITY , 2007 .

[7]  E. Fama,et al.  A Five-Factor Asset Pricing Model , 2014 .

[8]  R. Litzenberger,et al.  SKEWNESS PREFERENCE AND THE VALUATION OF RISK ASSETS , 1976 .

[9]  Tomas Björk,et al.  Optimal investment under partial information , 2010, Math. Methods Oper. Res..

[10]  J. Detemple Asset Pricing in a Production Economy with Incomplete Information , 1986 .

[11]  R. Lucas ASSET PRICES IN AN EXCHANGE ECONOMY , 1978 .

[12]  R. Jagannathan,et al.  The Conditional CAPM and the Cross-Section of Expected Returns , 1996 .

[13]  W. Sharpe A Simplified Model for Portfolio Analysis , 1963 .

[14]  Oldrich A. Vasicek An equilibrium characterization of the term structure , 1977 .

[15]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[16]  Campbell R. Harvey,et al.  Conditional Skewness in Asset Pricing Tests , 1999 .

[17]  J. Mossin Optimal multiperiod portfolio policies , 1968 .

[18]  R. C. Merton,et al.  An Analytic Derivation of the Efficient Portfolio Frontier , 1972, Journal of Financial and Quantitative Analysis.

[19]  J. Mossin EQUILIBRIUM IN A CAPITAL ASSET MARKET , 1966 .

[20]  Dave Feldman Logarithmic Preferences, Myopic Decisions, and Incomplete Information , 1992, Journal of Financial and Quantitative Analysis.

[21]  Robert F. Dittmar Nonlinear Pricing Kernels, Kurtosis Preference, and the Cross-Section of Equity Returns , 2001 .

[22]  Stephen A. Ross,et al.  On the Cross-sectional Relation between Expected Returns and Betas , 1994 .

[23]  A. David,et al.  Fluctuating Confidence in Stock Markets: Implications for Returns and Volatility , 1997, Journal of Financial and Quantitative Analysis.

[24]  N. H. Hakansson. OPTIMAL INVESTMENT AND CONSUMPTION STRATEGIES UNDER RISK FOR A CLASS OF UTILITY FUNCTIONS11This paper was presented at the winter meeting of the Econometric Society, San Francisco, California, December, 1966. , 1970 .

[25]  Larry G. Epstein,et al.  Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework , 1989 .

[26]  S. Ross,et al.  AN INTERTEMPORAL GENERAL EQUILIBRIUM MODEL OF ASSET PRICES , 1985 .

[27]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[28]  R. Stambaugh,et al.  Portfolio Inefficiency and the Cross-Section of Expected Returns , 1994 .

[29]  Fousseni Chabi-Yo,et al.  Pricing Kernels with Stochastic Skewness and Volatility Risk , 2008, Manag. Sci..

[30]  Éric Renault,et al.  Aggregation of preferences for skewed asset returns , 2014, J. Econ. Theory.

[31]  David Feldman,et al.  Incomplete information equilibria: Separation theorems and other myths , 2007, Ann. Oper. Res..

[32]  T. Sargent,et al.  Robust Control and Model Uncertainty , 2001 .

[33]  J. Harrison,et al.  Martingales and stochastic integrals in the theory of continuous trading , 1981 .

[34]  P. Samuelson LIFETIME PORTFOLIO SELECTION BY DYNAMIC STOCHASTIC PROGRAMMING , 1969 .

[35]  Dietmar P. J. Leisen A Perturbation Approach to Continuous-Time Portfolio Selection , 2016 .

[36]  Evan L. Porteus,et al.  Temporal Resolution of Uncertainty and Dynamic Choice Theory , 1978 .

[37]  David Feldman,et al.  Simple Construction of the Efficient Frontier , 2001 .

[38]  X. Zhou,et al.  MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE‐DEPENDENT RISK AVERSION , 2014 .

[39]  Suleyman Basak,et al.  Dynamic Mean-Variance Asset Allocation , 2009 .

[40]  G. Vilkov,et al.  Non-Myopic Betas , 2017, Journal of Financial Economics.

[41]  J. Lewellen The Cross Section of Expected Stock Returns , 2014 .

[42]  J. Lintner THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[43]  Andrey D. Ukhov Expanding the Frontier One Asset at a Time , 2005 .

[44]  R. C. Merton,et al.  Optimum Consumption and Portfolio Rules in a Continuous-Time Model* , 1975 .

[45]  Jun Liu Portfolio Selection in Stochastic Environments , 2007 .

[46]  Dietmar P. J. Leisen Heterogeneity in Risk Preferences Leads to Stochastic Volatility , 2018, International Journal of Theoretical and Applied Finance.