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Heterogeneous Beliefs, Asset Prices, and Volatility in a Pure Exchange Economy

Heterogeneous Beliefs, Asset Prices, and Volatility in a Pure Exchange Economy
Author: Tao Li
Publisher:
Total Pages: 37
Release: 2006
Genre:
ISBN:

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This paper extends the Lucas (1978) model to a setting in which investors have heterogeneous beliefs about the structure of a dividend process. By assuming that all investors have logarithmic preferences and different subjective discount rates, we can obtain a closed-form representation of the stock price. This closed-form solution enables us to analyze the dynamics of the stock price and its volatility. The model can simutaneously generate several well-known empirical facts - excessive volatility, leverage effects, and positive relationships between price and trading volume and between volatility and volume. All of these effects are driven by the different beliefs of investors.


Incomplete Information, Heterogeneous Beliefs and the Statistical Properties of Asset Prices

Incomplete Information, Heterogeneous Beliefs and the Statistical Properties of Asset Prices
Author: Tony Berrada
Publisher:
Total Pages: 50
Release: 2003
Genre:
ISBN:

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I consider a pure exchange economy where the growth rate of aggregate consumption is mean reverting and unobservable. Agents have heterogenous beliefs which they continuously update. I study the properties of asset prices as they can be measured by an outside observer (objective probability). First, it is shown that under the objective probability, the market price of risk (Sharpe ratio) is larger than the complete information equivalent, if the agents with higher level of expectations about the growth rate also have higher level of conditional variances. I provide an analytical formula for the volatility of the stock price which identifies the respective contributions of information incompleteness and heterogeneity in beliefs. It is shown that the volatility can be higher or lower than the complete information case, depending on the parametrization. I found that a parametric specification which yields a high level of volatility necessarily implies a negative covariance of the stock return with the interest rate. Finally I discuss why asset returns appear predictable in the objective probability measure when agents rationally update their beliefs by taking into account the observable variations of the dividend.


Incomplete Information, Heterogeneity, and Asset Pricing

Incomplete Information, Heterogeneity, and Asset Pricing
Author: Tony Berrada
Publisher:
Total Pages:
Release: 2010
Genre:
ISBN:

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We consider a pure exchange economy where the drift of aggregate consumption is unobservable. Agents with heterogeneous beliefs and preferences act competitively on financial and goods 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 propose a number of specifications of risk aversions and beliefs where the market price of risk is much higher, and the riskless rate of return lower, than in the equivalent full information economy (homogeneous and heterogeneous preferences) and thus can provide an(other) answer to the equity premium and risk-free rate puzzles. We also derive a representation of the equilibrium volatility and numerically assess the role of heterogeneity in beliefs. We show that a high level of stock volatility can be obtained with a low level of aggregate consumption volatility when beliefs are heterogeneous. Finally, we discuss how incomplete information may explain the apparent predictability in stock returns and show that in-sample predictability cannot be exploited by the agents, as it is in fact a result of their learning processes.


Asset Pricing With Heterogenous Beliefs in a Two Trees Setting

Asset Pricing With Heterogenous Beliefs in a Two Trees Setting
Author: Simon Lysbjerg Hansen
Publisher:
Total Pages: 43
Release: 2007
Genre:
ISBN:

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This paper studies the stock price formation in a pure-exchange economy populated by investors who disagree on the expected dividend growth rates. The homogenous beliefs equilibrium model of Cochrane, Longstaff, and Santa-Clara (2005) is extended to allow for belief heterogeneity, and the equilibrium is characterized. Stock prices and the volatility structure is expressed as conditional expectations, which can be solved numerically with Monte-Carlo simulations. The equilibrium is solved for in three stylized examples. First, confidence in the numerical scheme is obtained by replicating the results of Cochrane et al. (2005). Then, parameter uncertainty (but homogenous beliefs) is introduced and is found to decrease (increase) expected rates of return of the asset that constitutes less (more) of the market portfolio. Return volatilities increase and return correlation decreases as a consequence of parameter uncertainty. Finally, belief heterogeneity is found to complicate the economy even further, the effect being most profound for the return volatility and correlation structures.


Heterogeneity and Volatility Puzzles in International Finance

Heterogeneity and Volatility Puzzles in International Finance
Author: Tao Li
Publisher:
Total Pages: 40
Release: 2011
Genre:
ISBN:

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We develop an equilibrium model in a two-country, two-good, pure exchange economy in which investors with logarithmic utility functions have heterogeneous beliefs about exogenously given output or endowment processes. We obtain closed-form representations of real exchange rate and of stock prices. We show that heterogeneous beliefs, together with heterogeneous preferences make the volatility of real exchange rates and of stocks exhibit some properties that have been well documented in the empirical literature. These properties include the high volatility of both real exchange rates and stocks compared with that of economic fundamentals, the high correlation of stocks during periods of volatile markets. The model can also generate the clustering of the volatility of foreign exchange rate and stocks if the differences of beliefs are clustering.


Long-Run Heterogeneity in an Exchange Economy with Fixed-Mix Traders

Long-Run Heterogeneity in an Exchange Economy with Fixed-Mix Traders
Author: Giulio Bottazzi
Publisher:
Total Pages: 44
Release: 2016
Genre:
ISBN:

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We consider an exchange economy with heterogeneous agents and multiple assets and investigate the coupled dynamics of assets' prices and agents' wealth. We assume that agents have heterogeneous beliefs and invest on each asset a fraction of wealth proportional to its expected dividends. Our main finding is that long-run coexistence of heterogeneous agents is a generic outcome of the market dynamics. We provide sufficient conditions for the latter, as well as sufficient conditions for the relative wealth of any given agent converging to zero or to one. Since we use a direct approach that combines the inter-temporal dynamics of wealth and prices via agents' portfolio rules, we can characterize when long-run heterogeneity occurs for both complete and incomplete asset markets.


Adaptive Beliefs and the Volatility of Asset Prices

Adaptive Beliefs and the Volatility of Asset Prices
Author:
Publisher:
Total Pages:
Release: 2000
Genre:
ISBN:

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I present a simple model of an evolutionary financial market with heterogeneous agents, based on the concept of adaptive belief systems introduced by Brock and Hommes (1997a). Agents choose between different forecast rules based on past performance, resulting in an evolutionary dynamics across predictor choice coupled to the equilibrium dynamics. The model generates endogenous price fluctuations with similar statistical properties as those observed in real return data, such as fat tails and volatility clustering. These similarities are demonstrated for data from the British, German, and Austrian stock market. (author's abstract).


Aggregation of Heterogeneous Beliefs and Asset Pricing Theory

Aggregation of Heterogeneous Beliefs and Asset Pricing Theory
Author: Carl Chiarella
Publisher:
Total Pages: 23
Release: 2008
Genre:
ISBN:

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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.


Global Analysis of Dynamic Models in Economics and Finance

Global Analysis of Dynamic Models in Economics and Finance
Author: Gian Italo Bischi
Publisher: Springer Science & Business Media
Total Pages: 449
Release: 2012-08-07
Genre: Business & Economics
ISBN: 3642295037

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The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bifurcations in complementarity games, international subsidy games and issues in economic geography. A number of stochastic dynamic models are also analysed. The book is a collection of essays in honour of the 60th birthday of Laura Gardini.​


Recent Advances in Financial Engineering

Recent Advances in Financial Engineering
Author: Masaaki Kijima
Publisher: World Scientific
Total Pages: 284
Release: 2010
Genre: Business & Economics
ISBN: 9814304077

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This book consists of 11 papers based on research presented at the KIER-TMU International Workshop on Financial Engineering, held in Tokyo in 2009. The Workshop, organised by Kyoto University's Institute of Economic Research (KIER) and Tokyo Metropolitan University (TMU), is the successor to the Daiwa International Workshop on Financial Engineering held from 2004 to 2008 by Professor Kijima (the Chair of this Workshop) and his colleagues. Academic researchers and industry practitioners alike have presented the latest research on financial engineering at this international venue. These papers address state-of-the-art techniques in financial engineering, and have undergone a rigorous selection process to make this book a high-quality one. This volume will be of interest to academics, practitioners, and graduate students in the field of quantitative finance and financial engineering