Within the standard mean-variance framework, this paper provides a procedure to aggregate the heterogeneous beliefs in not only risk preferences and expected payoffs but also variances/covariances into a market consensus belief. Consequently, an asset equilibrium price under heterogeneous beliefs is derived. We show that the market aggregate behavior is in principle a weighted average of heterogeneous individual behaviors. The CAPM-like equilibrium price and return relationships under heterogeneous beliefs are obtained. The impact of diversity of heterogeneous beliefs on the market aggregate risk preference, asset volatility, equilibrium price and optimal demands of investors is examined. As a special case, our result provides a simple explanation for the empirical relation between cross-sectional volatility and expected returns.

From the field's leading authority, the most authoritative and comprehensive advanced-level textbook on asset pricing In Financial Decisions and Markets, John Campbell, one of the field’s most respected authorities, provides a broad graduate-level overview of asset pricing. He introduces students to leading theories of portfolio choice, their implications for asset prices, and empirical patterns of risk and return in financial markets. Campbell emphasizes the interplay of theory and evidence, as theorists respond to empirical puzzles by developing models with new testable implications. The book shows how models make predictions not only about asset prices but also about investors’ financial positions, and how they often draw on insights from behavioral economics. After a careful introduction to single-period models, Campbell develops multiperiod models with time-varying discount rates, reviews the leading approaches to consumption-based asset pricing, and integrates the study of equities and fixed-income securities. He discusses models with heterogeneous agents who use financial markets to share their risks, but also may speculate against one another on the basis of different beliefs or private information. Campbell takes a broad view of the field, linking asset pricing to related areas, including financial econometrics, household finance, and macroeconomics. The textbook works in discrete time throughout, and does not require stochastic calculus. Problems are provided at the end of each chapter to challenge students to develop their understanding of the main issues in financial economics. The most comprehensive and balanced textbook on asset pricing available, Financial Decisions and Markets is an essential resource for all graduate students and practitioners in finance and related fields. Integrated treatment of asset pricing theory and empirical evidence Emphasis on investors’ decisions Broad view linking the field to financial econometrics, household finance, and macroeconomics Topics treated in discrete time, with no requirement for stochastic calculus Forthcoming solutions manual for problems available to professors

We consider a pure exchange economy where the drift of aggregate consumption is unobservable. Agents with heterogeneous beliefs and preferences act competitively on a financial and good markets. We discuss how equilibrium market prices of risk differ across agents, and in particular we discuss the properties of the market price of risk under the physical (objective) probability measure. We provide a number of specification of risk aversions and beliefs where the market price of risk is much higher than in the equivalent full information economy (homogeneous and heterogeneous preferences) and thus could provide an(other) answer to the equity premium puzzle. We also provide a representation of the equilibrium volatility and numerically assess the role of heterogeneity. We show that high level of stock volatility can be obtained with low level of aggregate consumption volatility when beliefs are heterogeneous. Finally we discuss how heterogeneity may explain the apparent predictability in stock return, and show that in-sample predictability can not be exploited by the agents, as it is in fact a result of their learning process.

The models of portfolio selection and asset price dynamics in this volume seek to explain the market dynamics of asset prices. Presenting a range of analytical, empirical, and numerical techniques as well as several different modeling approaches, the authors depict the state of debate on the market selection hypothesis. By explicitly assuming the heterogeneity of investors, they present models that are descriptive and normative as well, making the volume useful for both finance theorists and financial practitioners. - Explains the market dynamics of asset prices, offering insights about asset management approaches - Assumes a heterogeneity of investors that yields descriptive and normative models of portfolio selections and asset pricing dynamics

Real world investors differ in their tastes and attitudes and they do not have, in general, perfect information about the future prospects of the economy. Most theoretical models, however, assume to the contrary that investors are homogeneous and perfectly informed about the market. In this book, an attempt is made to overcome these shortcomings. In three different case studies, the effect of heterogeneous time preferences, heterogeneous beliefs and imperfect information about the economy's growth on the term structure of interest rates are studied. The initial chapter gives an introduction to the theory of financial markets in continuous time under imperfect information and establishes the existence of an equilibrium with complete markets.