Asset price volatility and trading volume with rational beliefs

Summary. This paper develops a model of speculative trading in a large economy with a continuum of investors. In our model the investors are assumed to have diverse beliefs which are rational in the sense of being compatible with observed data. We demonstrate the existence of price amplification effects and show that the equilibrium prices can be higher or lower than the rational expectation equilibrium price. It is also shown that trading volume is positively related to the directions of price changes. Moreover, we study how asset price volatility and trading volume are influenced by belief structures, short selling constraints and the amount of fund available for investment.Received: 23 January 2003, Revised: 30 April 2003, JEL Classification Numbers: D84, G12.We are grateful to Professors Mordecai Kurz, Kenneth Arrow, Kenneth Judd, Carsten Nielsen, Maurizio Motolese, Mark Garmaise, Jean-Michel Grandmont, Peter Hammond, Karl Shell, Jan Werner and participants of the Society for the Advancement of Economic Theory (SAET) Conference and Stanford Institute of Theoretical Economics (SITE) Conference for many helpful suggestions. Correspondence to: H.-M. Wu     

On rational belief equilibria

Summary We study equilibria in which agent's belief are rational in the sense of Kurz [1994]. The market is formulated by specifying a stochastic demand function and a continuum of producers, each with a quadratic cost function who must select their output before knowing prices. Holding Rational Beliefs about future prices, producers maximize expected profits. In a Rational Belief Equilibrium (RBE) agents select diverse forecast functions but each one is rational in the sense that it is based on a theory which cannot be rejected by the data. It is shown that there exists a continuum of RBE's and they could entail very different patterns of time series for the economy and consequently different aggregate levels of longterm volatility. Since the model contains exogenously specified random variables, the difference in the level of long-term volatility of prices among the different RBE's arises endogenously as an amplification of the volatility of exogenous variables. The paper derives exact bounds on the possible levels of such amplification.This research was supported by NSF Grant IRI-8814954 to Stanford University. The author is thankful to Steven N. Durlauf and Carsten K. Nielsen for useful comments on an earlier draft.     

Endogenous uncertainty and market volatility

We advance the theory that the distribution of beliefs in the market is the most important propagation mechanism of economic volatility. Our model is based on the theory of Rational Beliefs (RB) and Rational Belief Equilibrium (RBE) developed by Kurz (1994, 1997). We argue that the diverse market puzzles which are examined, such as the equity premium puzzle, are all driven by the structure of market expectations. In support of our view, we present an RBE model with which we study financial markets. The model is able to simulate the correct order of magnitude of: (i) the long term mean and standard deviation of the price\dividend ratio; (ii) the long term mean and standard deviation of the risky rate of return on equities; (iii) the long term mean and standard deviation of the riskless rate; (iv) the long term mean equity premium. In addition, the model predicts (v) the GARCH property of risky asset returns; (vi) the observed pattern of the predictability of long returns on assets, and (vii) the Forward Discount Bias in foreign exchange markets. The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs such that some agents are optimistic and some pessimistic about future capital gains. The model has a unique parameterization under which the model makes all the above predictions simultaneously. The parameterization requires the optimists to be in the majority but the rationality of belief conditions of the RBE require the pessimists to have a higher intensity level. In simple terms, the large equity premium and the low equilibrium riskless rate are the result of the fact that at any moment of time there are agents who hold extreme pessimistic beliefs and they have a relatively stronger impact on the market. The paper also studies the effect of correlation of beliefs among investors. It shows that the main effect of such correlation is on the dynamic patterns of asset prices and returns and is hence important for studying such phenomena as stochastic volatility. Received: May 16, 2000; revised version: November 15, 2000     

Construction of a state space for interrelated securities with an application to temporary equilibrium theory

Summary We construct an endogenous state space in an exchange economy with possibly infinite horizon. Every period agents trade securities whose payoffs depend on future dividends and asset prices. We reject the perfect foresight assumption on the ground that agents have not only limited knowledge of other individuals' endowments and preferences, but also limited capacity to compute equilibria. We choose instead absence of arbitrage as the principle which allows agents to determine if a system of future prices is possible. We give an alogrithm to compute the set of nonarbitrage prices every period, with both finite and infinite horizon. We then apply this endogenous structure of uncertainty to an infinite horizon temporary equilibrium model.I would like to thank Professor Donald Brown for his constant help and guidance. I have also greatly benefited from helpful discussions with Professors Jacques Drèze, Bernard Dumas, Mordecai Kurz, Carsten Nielsen, Jan Werner, and Ho-Mou Wu.     

Investor sentiment,information and asset pricing model

We present an asset pricing model with investor sentiment and information, which shows that the investor sentiment has a systematic and significant impact on the asset price. The equilibrium price's rational term drives the asset price to the rational, and the sentiment term leads to the asset price deviating from it. In our model, the proportion of sentiment investors and the information quality could amplify the sentiment shock on the asset price. Finally, the information is fully incorporated into prices when sentiment investors learn from prices. The model could offer a partial explanation of some financial anomalies: price bubbles, high volatility, asset prices' momentum effect and reversal effect.     

Rational Expectations is not Generally Valid for Econometric Models: Evidence from Stock Market Data

In applying the rational expectations hypothesis to generate expectations in an econometric model it is assumed that (1) the model itself is capable of generating reasonable forecasts of all required expectations variables included in the model, and that (2) the economic agents whose behavior is being modeled act as if they form their psychological expectations as conditional mathematical expectations generated by the model. Both assumptions can be invalid, as demonstrated by the historical data on Hong Kong stock prices and by the successful application of the adaptive expectations hypothesis to explain panel data of prices of individual stocks and aggregate time series data on stock price indices of the United States and of Hong Kong.     

Option smiling when investors’ estimates of asset volatility disagree

This study sheds light on why heterogeneous beliefs in volatility manifest the smile effect of options and how the degree of belief disagreement influences option-implied volatility. It is found that when investors’ level of heterogeneous beliefs increases, agents who over estimate volatility raise their subjective probability about those outer dividend states and hence increase more consumption to those states. As a result, an increase of consumption causes a decrease of their marginal rate of transformation in outer states. The raising subjective probability increases the prices of outer states, while the lower marginal rate of transformation decreases the prices of that. However, the influence of the former dominates the latter, causing a fatter tail of the state-price density. As a consequence, the values increase for those call options with high strike prices and put options with low strike prices, leading to a U-shaped implied volatility and hence causes a smell effect.     

OPTIMAL MONETARY POLICY AND ASSET PRICE MISALIGNMENTS

This paper analyses the relationship between monetary policy and asset prices in the context of optimal policy rules. The transmission mechanism is represented by a linearized rational expectations model augmented for the effect of asset prices on aggregate demand. Stabilization objectives are represented by a discounted quadratic loss function penalizing inflation and output gap volatility. Asset prices are allowed to deviate from their intrinsic value due to momentum trading. We find that in the presence of wealth effects and inefficient markets, asset price misalignments from their fundamentals should be included in the optimal interest rate reaction function.     

流动性约束与货币政策的资产价格效应

本文在新凯恩斯主义分析框架下,基于一个动态随机模型探讨了代理人消费流动性约束下的货币政策的资产价格效应,得到下列结论：资产价格波动通过财富效应影响代理人的消费。以利率为操作目标的最优货币政策应对股价、房价等资产价格波动做出反应,而其反应强度依赖于受流动性约束的代理人所占的比重。由于资产价格波动导致了流动性约束的时变性,最优利率规则对股价、房价等资产价格波动的最优权重也具有时变性。本文的实证分析表明,我国央行对房价和股价波动的利率调整具有时变性,以及此次金融危机爆发期间显现的这种时变性特征,与本文理论分析结果相吻合。     

Financial leverage and market volatility with diverse beliefs

We study a general equilibrium model of asset trading with financial leverage, where the investors can engage in speculative trading with diverse beliefs about the asset??s fundamental value. We show that an increase in the leverage ratio causes the stock price to rise in the current period through a ??leverage effect??, and will result in more borrowing and more stock purchase that pumps the stock price higher in the subsequent period, known as the ??pyramiding effect??. There can also be a ??depyramiding effect?? when the price falls because lenders issue margin calls and force stock sales, contributing to further stock price plummeting. Price changes from depyramiding effect, however, may not take effect when margin calls are not triggered. We demonstrate that, under certain conditions, decreasing leverage ratios leads to lower stock price volatility, measured by the variation of prices caused by an exogenous shock, when the shock is unanticipated. The influences of dispersion of beliefs and available investment funds on the relation between financial leverage and market volatility are also examined. When the shock is anticipated, we demonstrate that reducing leverage ratios may not lower stock price volatility, which poses an important challenge to future studies on this issue.     

Should monetary policy respond to asset price misalignments?

This paper analyses the relationship between monetary policy and asset prices using a structural rational expectations open economy model that allows for the effect of asset prices and exchange rates on aggregate demand. We assume that asset prices and exchange rates follow a partial adjustment mechanism whereas they are positively affected by past changes, thus allowing for ‘momentum trading’, while at the same time we allow for reversion towards fundamentals. We then conduct stochastic simulations using two alternative monetary policy rules, inflation-forecast targeting and the standard Taylor rule. The results indicate that, under both rules, interest rate setting that takes into account asset price misalignments leads to lower overall macroeconomic volatility, as measured by the postulated loss function of the central bank.     

Internal rationality, imperfect market knowledge and asset prices

We present a decision theoretic framework in which agents are learning about market behavior and that provides microfoundations for models of adaptive learning. Agents are ‘internally rational’, i.e., maximize discounted expected utility under uncertainty given dynamically consistent subjective beliefs about the future, but agents may not be ‘externally rational’, i.e., may not know the true stochastic process for payoff relevant variables beyond their control. This includes future market outcomes and fundamentals. We apply this approach to a simple asset pricing model and show that the equilibrium stock price is then determined by investors? expectations of the price and dividend in the next period, rather than by expectations of the discounted sum of dividends. As a result, learning about price behavior affects market outcomes, while learning about the discounted sum of dividends is irrelevant for equilibrium prices. Stock prices equal the discounted sum of dividends only after making very strong assumptions about agents? market knowledge.     

Ergodic properties of conditional forecast functions of stable systems

Summary This paper analyzes the behavior of conditional forecast functions in stable systems. We study convergence of optimal forecast functions, of forecast functions obtained by conditioning on previous values, and conditional and joint densities.The research was done as part of the author's master thesis under Mordecai Kurz. The author thanks Mordecai Kurz, Carsten Nielsen, and Ho-Mou Wu for a careful reading of the paper and the Statistics Department of Stanford University for financial support. This research was supported in part by Fondazione ENI Enrico Mattei of Milan, Italy.     

Speculative trading with rational beliefs and endogenous uncertainty

Summary. This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are “rational” in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions Received: March 15, 2001; revised version: April 26, 2002 RID="*" ID="*" We are deeply grateful to Mordecai Kurz for his constant encouragement and inspiring guidance over the years. We wish to express our gratitude to an anonymous referee for the very valuable comments provided. We also thank Kenneth Arrow, Peter Hammond, Roko Aliprantis and Nicholas Yannelis for their helpful suggestions and Academia Sinica and the National Science Council of the R.O.C. for their indispensable support. Correspondence to: H.-M. Wu     

On the impact of leverage constraints on asset prices and trading volume

Abstract. Researchers have used stylized facts on asset prices and trading volume in stock markets (in particular, the mean reversion of asset returns and the correlations between trading volume, price changes and price levels) to support theories where agents are not rational expected utility maximizers. This paper shows that this empirical evidence is in fact consistent with a standard infinite horizon – perfect information – expected utility economy where some agents face leverage constraints similar to those found in todays financial markets. In addition, and in sharp contrast to the theories above, we explain some qualitative differences that are observed in the price-volume relation on stock and on futures markets. We consider a continuous-time economy where agents maximize the integral of their discounted utility from consumption under both budget and leverage constraints. Building on the work by Vila and Zariphopoulou (1997), we find a closed form solution, up to a negative constant, for the equilibrium prices and demands in the region of the state space where the constraint is non-binding. We show that, at the equilibrium, stock holdings volatility as well as its ratio to stock price volatility are increasing functions of the stock price and interpret this finding in terms of the price-volume relation. We would like to thank the editor and two anonimous referees for valuable substantive comments. Our gratitude also to Franklin Allen, Kerry Back, Domenico Cuoco, Xavier Freixas, Sanford Grossman, Michel Habib, Lutz Hendricks, Richard Kihlstrom, Fernando Restoy, Mary Thomson, Jean-Luc Vila, participants to seminars at Birkbeck College, Carnegie-Mellon, Columbia, ESSEC, HEC, IAE, INSEAD, London Business School, London School of Economics, McGill, Michigan, National University of Singapore, Pompeu Fabra, North Carolina, Washington-St-Louis, Wharton, the Jornadas de Economía Financiera BBV, and the Meetings of the Society for Economic Dynamics and Control and the American Finance Association. Special thanks are due to Süleyman Basak for his enthusiastic support and many helpful suggestions. The usual disclaimer applies. We gratefully acknowledge the support of the BBV and Caja de Madrid Foundations and CREF (both authors) and of the Spanish Ministry of Education under DGICYT grant no. PB93-0388 (first author).     

Endogenous uncertainty in a general equilibrium model with price contingent contracts

Summary This paper views uncertainty and economic fluctuations as being primarily endogenous and internally propagated phenomena. The most important Endogenous Uncertainty examined in this paper is price uncertainty which arises when agents do not have structural knowledge and are complelled to make decisions on the basis of their beliefs. We assume that agents adopt Rational Beliefs as in Kurz [1994a]. The trading of endogenous uncertainty is accomplished by using Price Contingent Contracts (PCC) rather than the Arrow-Debreu state contingent contracts. The paper provides a full construction of the price state space which requires the expansion of the exogenous state space to include the state of beliefs. This construction is central to the analysis of equilibrium with endogenous uncertainty and the paper provides an existence theorem for a Rational Belief Equilibrium with PCC. It shows how the PCC completes the markets for trading endogenous uncertainty and lead to an allocation which is Pareto optimal. This paper also demonstrates that endogenous uncertainty is generically present in this new equilibrium.This research was supported in part by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the National Science Council of Taiwan. The authors thank Carsten K. Nielsen for valuable suggestions.     

Fiscal policy and asset price volatility

This paper investigates the relationship between volatility of different asset prices and the volatility of various indicators of fiscal policy (primary balance, spending and revenue). We find evidence that asset price volatility affects the volatility of fiscal policy stance in a positive and significant way. The effect comes primarily through residential property and equity price volatility on government revenue and spending. Increased volatility in commercial property prices is associated with increased variability of government revenue. Output growth volatility is the dominant determinant of revenue and primary balance variability, whereas bad budgetary conditions and the size of the public sector are the most significant determinants of spending variability. Trade openness leads to greater variability of government spending, revenue and primary balance to GDP ratios.     

How equilibrium prices reveal information in a time series model with disparately informed, competitive traders

Accommodating asymmetric information in a dynamic asset pricing model is technically challenging due to the problems associated with higher-order expectations. That is, rational investors are forced into a situation where they must forecast the forecasts of other agents. In a dynamic setting, this problem telescopes into the infinite future and the dimension of the relevant state space approaches infinity. By using the frequency domain approach of Whiteman [Linear Rational Expectations Models: A User's Guide, University of Minnesota Press, Minneapolis, 1983] and Kasa [Forecasting the forecasts of others in the frequency domain, Rev. Econ. Dynam. 3 (2000) 726-756], this paper demonstrates how information structures previously believed to preserve asymmetric information in equilibrium, converge to a symmetric information, rational expectations equilibrium. The revealing aspect of the price process lies in the invertibility of the observed state space, which makes it possible for agents to infer the economically fundamental shocks and thus eliminating the need to forecast the forecasts of others.     

Overconfidence and Market Efficiency with Heterogeneous Agents

We study financial markets in which both rational and overconfident agents coexist and make endogenous information acquisition decisions. We demonstrate the following irrelevance result when a positive fraction of rational agents (endogenously) decides to become informed in equilibrium, prices are set as if all investors were rational, and as a consequence the overconfidence bias does not affect informational efficiency, price volatility, rational traders’ expected profits or their welfare. Intuitively, as overconfidence goes up, so does price informativeness, which makes rational agents cut their information acquisition activities, effectively undoing the standard effect of more aggressive trading by the overconfident. The main intuition of the paper, if not the irrelevance result, is shown to be robust to different model specifications.We would like to thank Alberto Bisin, Xavier Freixas, Ken French, Moshe Kim, Jose Marín, and Terrance Odean for comments on an early draft, as well as an anonymous referee and seminar participants at HEC Geneva, the 2004 EFA meetings, the 2004 European Econometric Society meetings and the 2005 SAET conference. Diego García and Branko Urošević gratefully acknowledge financial support by SECCF (Belgrade).     

资产价格与货币政策

随着资本市场的发展和金融资产存量的增加 ,资产价格的波动对货币政策提出了诸多挑战。本文讨论了资产价格与货币政策目标的关系 ;资产价格在货币政策传导过程中对消费、投资和金融体系的影响 ;以及货币政策操作中有关资产价格的争论 ;最后提出了这一研究领域中存在的问题