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     

Endogenous uncertainty and the non-neutrality of money

Summary. We study some implications of the Theory of Rational Beliefs to monetary policy. We show that monetary policy in a Rational Beliefs environment can have an important effect on the characteristics of economic fluctuations. In Rational Beliefs Equilibria money is generically non-neutral unlike Rational Expectations Equilibria in which money is neutral and monetary policy is ineffective. Under Rational Beliefs Equilibria nominal prices and real output change not only in response to changes in the exogenous growth rate of money but also in response to changes in the state of beliefs. In Rational Beliefs Equilibria monetary shocks have real effects even when they are observed but are not fully anticipated. Furthermore, the non-neutrality of money results in a short run Phillips curve. When money “flutters, real output sputters” [8]. We show that Endogenous Uncertainty and the distribution of market beliefs are the major explanatory variables of such fluctuations. Under Rational Expectations monetary policy is ineffective because agents neutralize it by predicting correctly the effect of the policy. Under Rational Beliefs it is shown instead that inflation and recessions can be substantially aggravated by the distribution of market beliefs. Received: January 14, 2002; revised version: April 5, 2002 RID="*" ID="*" I would like to thank Mordecai Kurz for his constant help and support. Most of the ideas developed hereby have been inspired by innumerable and fruitful discussions with him. I have also greatly benefited from helpful comments by Stanley Black, Luigi Campiglio, Carsten Nielsen and Ho-Mou Wu. I also received valuable remarks from participants at the V meeting of “The Society for the Advancement of Economic Theory” held in Ischia, Italy, on July 2-8, 2001, where an initial draft of the present work was presented.     

Equity risk premium and time horizon: What do the U.S. secular data say?

We consider a representative investor whose wealth is made up of the equity market portfolio and the riskless asset, and who maximizes the expected utility of his/her future wealth for a given horizon. The solution of this program shows that the equilibrium value of the equity risk premium – the latter being measured by the difference between the expected equity portfolio return and the risk-free interest rate – is given by the product of the price of risk by the expected variance of stock returns. When returns are predictable, these two magnitudes are both time-varying and horizon-dependent. In accordance with this theoretical framework, our paper presents an econometric model of the equity risk premia for two traditional horizons: the one-period-ahead horizon (i.e. the ‘short-term’ premium) and the infinite-time horizon (i.e. the ‘long-term’ premium). Using annual US secular data from 1871 to 2008, and representing the expected returns by mixing the three traditional adaptive, extrapolative and regressive processes, large disparities in the dynamics of the two premia are evidenced. Concerning the determination of the equilibrium values of the two premia, the expected variances depend on the past values of the centered squared returns while the prices of risk (unobservable variables) are estimated according to the Kalman filter methodology, which enables us to capture the influence of hidden variables and of non-directly measurable psychological effects. A spread of interest rates adds to this determination. Possibly due to risky arbitrage and transaction costs, the results show that observed premia gradually converge towards their equilibrium values, this process being described by an error correction model. Overall, our model provides a rather satisfactory representation of ‘short-term’ and ‘long-term’ premia.     

Money non-neutrality in a Rational Belief Equilibrium with financial assets

Summary. In Rational Beliefs Equilibria money is generically non-neutral. Given the expectational perspective proposed by the Theory of Rational Belief Equilibrium, we show that one of the most important factors in the emergence of money non-neutrality is played by Endogenous Uncertainty. This, in contrast to the Rational Expectations results of money neutrality and policy ineffectiveness, leads to a scenario in which monetary policy has an impact on the real economy and price volatility. The heterogeneity of beliefs together with the distribution and intensity of agents' states of optimism/pessimism can amplify the real effect of monetary policy and/or generate endogenous fluctuations in the economy which are not explained by any exogenous shock. We claim that money non-neutrality is mostly an expectations driven phenomenon. Indeed, additional assumptions of asymmetry of information and/or unanticipated monetary policy are not needed to explain the real effect of monetary policy as it is customary in the New Classical Theory. Received: May 30, 2000; revised version: December 28, 2000     

Liquidity shocks and equilibrium liquidity premia

We study an equilibrium in which agents face surprise liquidity shocks and invest in liquid and illiquid riskless assets. The random holding horizon from liquidity shocks makes the return of the illiquid security risky. The equilibrium premium for such risk depends on the constraint that agents face when borrowing against future income; it is insignificant without borrowing constraint, but can be very high with borrowing constraint. Illiquidity, therefore, can have large effects on asset returns when agents face liquidity shocks and borrowing constraints. This result can help us understand why some securities have high liquidity premia, despite low turnover frequency.     

Diverse beliefs and time variability of risk premia

Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief on risk premia. Individual belief is taken as a fundamental primitive state variable. Market belief is observable; it is central to the empirical evaluation and we show how to measure it. Our asset pricing model is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive equilibrium asset prices and implied risk premium. Our approach permits a closed form solution of prices; hence we trace the exact effect of market belief on the time variability of asset prices and risk premia. We test empirically the theoretical conclusions. Our main result is that, above the effect of business cycles on risk premia, fluctuations in market belief have significant independent effect on the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3- and 6-month Treasury Bills (T-Bills). The annual mean risk premium on holding such assets for 1?C12?months is about 40?C60 basis points and we find that, on average, the component of market belief in the risk premium exceeds 50% of the mean. Since time variability of market belief is large, this component frequently exceeds 50% of the mean premium. This component is larger the shorter is the holding period of an asset and it dominates the premium for very short holding returns of less than 2?months. As to the structure of the premium we show that when the market holds abnormally favorable belief about the future payoff of an asset the market views the long position as less risky hence the risk premium on that asset declines. More generally, periods of market optimism (i.e. ??bull?? markets) are shown to be periods when the market risk premium is low while in periods of pessimism (i.e. ??bear?? markets) the market??s risk premium is high. Fluctuations in risk premia are thus inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant.     

Changes in Investors' Market Attention and Near-Term Stock Market Returns

We use Google Search volume to track changes investors' positive and negative market attention. Our results support the hypothesis that this information reflects investors' optimistic and pessimistic anticipation and can be used to predict near-term future returns. We find that changes in negative search term volume of “market crash” and “bear market” and changes in positive search term volume “market rally” explain near-term stock returns. Changes in investors' attention are partly related to past stock market returns, implying that investors are prone to pay attention to possible price reversals. These measures of market attention are potential gauges of investor sentiment.     

Another Look at the Equity Risk Premium Puzzle

The model of Mehra and Prescott (1985, J. Econometrics, 22, 145–161) implies that reasonable coefficients of risk‐aversion of economic agents cannot explain the equity risk premium generated by financial markets. This discrepancy is hitherto regarded as a major financial puzzle. We propose an alternative model to explain the equity premium. For normally distributed returns and for returns far away from normality (but still light tailed), realistic equity risk premia do not imply puzzlingly high risk aversions. Following our approach, the ‘equity premium puzzle’ does not exist. We also consider fat‐tailed return distributions and show that Pareto tails are incompatible with constant relative risk aversion.     

Regional stock market integration in Singapore: A multivariate analysis

This paper evaluates the time-varying integration of the Singapore stock market in the ASEAN-5 region based on a conditional version of the International Capital Asset Pricing Model (ICAPM) with c-DCC-FIAPARCH parameters. This model allows for dynamic changes in the degree of market integration, regional market risk premium, regional exchange-rate risk premium, and domestic market risk premium. Our findings show several interesting facts. First, the time-varying degree of integration in the Singapore market is satisfactorily explained by the level of trade openness and the term premium of US interest rates, which have recently tended to increase, however these markets remain substantially segmented from the world market. Second, the local market risk premium is found to explain a significant proportion of the total risk premium for emerging market returns. Our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity markets. Our results are also of interest for both policymakers and investors, with respect to regional development policies and dedicated portfolio investment strategies in the ASEAN-5 region.     

Asset prices and business cycles with costly external finance

This paper asks whether the asset pricing fluctuations induced by the presence of costly external finance are empirically plausible. To accomplish this, we incorporate costly external finance into a dynamic stochastic general equilibrium model and explore its implications for the properties of the returns on key financial assets, such as stocks, bonds and risky loans. We find that the mean and volatility of the equity premium, although small, are significantly higher than those in comparable adjustment cost models. However, we also show that these results require a procyclical financing premium, a property that seems at odds with the data.     

A Model of Financial Markets with Endogenously Correlated Rational Beliefs

This paper studies how communication amongst agents influences the equilibria of a financial economy. We set up a standard overlapping generations model with assets, while allowing for heterogeneous beliefs. The paper explicitly describes how communication causes the beliefs of the agents to be correlated. In particular, it is shown that communication may generate large fluctuations even if the unconditional probability beliefs themselves are independent. Because of the complex nature of the problem, we use simulations to examine the characteristics of the equilibria Part of the results presented in this paper is based on my Ph.D. thesis at Stanford University. I gratefully acknowledge the inspiration obtained from innumerable discussions with Mordecai Kurz about this subject over the years. Also, I appreciate comments from Kenneth J. Arrow and Peter J. Hammond as well as from the participants of the workshop at Stanford University, University of Tokyo and the 1st Illinois workshop in Economic Theory (University of Illinois at Urbana-Champaign) and the anonymous referee     

Predictor imperfection: international evidence

Pástor and Stambaugh (2009) demonstrate that the relationship between predictors and equity premium is imperfect in US market using a new model named predictive system. This article extends their study by providing international evidence of predictor imperfection using samples from G7 countries. Our results show that predictor imperfection is ubiquitous in all G7 countries and that investors’ prior beliefs about the relationship between predictors and equity premium play a significant role in predictor’s explanatory power.     

Aggregation of heterogenous beliefs,asset pricing,and risk sharing in complete financial markets

Given a competitive equilibrium in complete asset markets, we propose a method that aggregates heterogeneous individual beliefs into a single “market probability,” which, if commonly shared by investors, generates the same marginal valuation of assets by the market as well as by each individual investor. As a result of the aggregation process, the market portfolio may have to be scalarly adjusted, upward or downward, a reflection of an aggregation bias due to the diversity of beliefs. From a dual viewpoint, the standard construction of an expected utility-maximizing aggregate investor designed to represent the economy in equilibrium, is shown to be also valid in the case of heterogeneous beliefs, modulo the above scalar adjustment of the market portfolio, thereby generating an Adjusted version of the Consumption based Capital Asset Pricing Model (ACCAPM). We analyze how the allocation of aggregate and individual risks relates to deviations of individual beliefs from the aggregate market probability. Finally, we identify the channels through which the distribution of beliefs and other microeconomic characteristics (incomes, attitudes toward risk) across investors impact the pricing of risky assets an may contribute to explaining the equity premium puzzle.     

How does a pay-as-you-go system affect asset returns and the equity premium?

When applying a differences-in-differences approach, equity returns and the equity premium are both estimated to be more than four percentage points higher after the introduction of a pay-as-you-go (PAYGO) system. In a realistically calibrated model, the PAYGO system is also found to increase the returns and the premium, although the effects are smaller than in the data. Intuitively, the system lowers asset prices, which in turn increases the importance of dividend risk. Since only equity is subject to dividend risk, equity returns become more volatile relative to bond returns.     

The conditional influence of term spread and pattern changes on future equity returns

We extend previous research examining the relation between interest rates and equity returns using a multivariate analysis of covariance model with a dynamic yield curve and conditioned term spread. We find yield pattern changes predict economic equity returns; that the long end-of-yield curve is a strong determinant factor; and, in contrast to previous research, we find no relation between a decrease in the short rate and equity returns. However, the conditional term spread captures a significant positive return indicating that the degree of decline in the short rate relative to the long rate is of more importance than the term spread alone.     

Global financial crisis and dependence risk analysis of sector portfolios: a vine copula approach

We use regular vine (r-vine), canonical vine (c-vine) and drawable vine (d-vine) copulas to examine the dependence risk characteristics of three 20-stock portfolios from the retail, manufacturing and gold-mining equity sectors of the Australian market in periods before, during and after the 2008–2009 global financial crisis (GFC). Our results indicate that the retail portfolio is less risky than the manufacturing counterpart in the crisis period, while the gold-mining portfolio is less risky than both the retail and manufacturing sector portfolios. Both the retail and gold stocks display a higher propensity to yield positively skewed returns in the crisis periods, contrary to the manufacturing stocks. The r-vine is found to best capture the multivariate dependence structure of the stocks in the retail and gold-mining portfolios, while the d-vine does it for the manufacturing stock portfolio. These findings could be used to develop dependence risk- and investment risk-adjusted strategies for investment, rebalancing and hedging which more adequately account for the downside risk in various market conditions.     

Coordination and correlation in Markov rational belief equilibria

Summary This paper studies the effect of correlation in the rational beliefs of agents on the volatility of asset prices. We use the technique of generating variables to study stable and non-stationary processes needed to characterize rational beliefs. We then examine how the stochastic interaction among such variables affects the behavior of a wide class of Rational Belief Equilibria (RBE). The paper demonstrates how to construct a consistent price state space and then shows the existence of RBE for any economy for which such price state space is constructed. Next, the results are used to study the volatility of asset prices via numerical simulation of a two agents model. If beliefs of agents are uniformly dispersed and independent, we would expect heterogeneity of beliefs to have a limited impact on the fluctuations of asset prices. On the other hand, our results show that correlation across agents can have a complex and dramatic effect on the volatility of prices and thus can be the dominant factor in the fluctuation of asset prices. The mechanism generating this effect works through the clustering of beliefs in states of different levels of agreement. In states of agreement the conditional forecasts of the agents tend to fluctuatetogether inducing more volatile asset prices. In states of disagreement the conditional forecasts fluctuatein diverse directions tending to cancel each other's effect on market demand and resulting in reduced price volatility.This research was supported, in part, by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the Research Incentive Fund of Stanford University. The authors thank Carsten K. Nielsen and Ho-Mou Wu for valuable discussions on an earlier draft. Carsten K. Nielsen also made an important contribution to the development of Section 3.     

Gurus and belief manipulation

We analyze a model with two types of agents: standard agents and gurus, i.e. agents who have the ability to influence the other investors. Gurus announce their beliefs and act accordingly. Gurus are strategic: they take into account the impact of their announced beliefs on the other agents, hence on prices. Standard agents observe gurus' performances, choose a guru and follow her/his recommendations. Prices are determined through a classical Walras mechanism. The competition among gurus for attracting followers among standard agents is governed by the level of accuracy of their predictions. The strategic behavior leads to belief subjectivity and heterogeneity among the gurus even when gurus' initial beliefs coincide with the objective belief. Optimism as well as pessimism can both emerge. We find a positive correlation across the agents between pessimism and risk tolerance. The representative agent belief, or the consensus belief is pessimistic. As a consequence of the pessimistic bias at the aggregate level, the risk premium is greater than in the standard rational expectations equilibrium. We show on an example that this impact is significative. In a multi-asset framework, the impact is stronger on the riskier assets.     

Heterogeneity of First-order Risk Aversion and the Equity Premium

I show that stockholders and non-stockholders can coexist in equilibrium even if securities markets are perfect and complete. This is due to a heterogeneous safety inclination, which is defined as heterogeneity in first-order risk aversion (Segal and Spivak, 1990). A static two-security market model is analysed by the mean–standard deviation approach, where safety inclination is described by the degree of the marginal rate of substitution between the mean and the standard deviation at a certain point. In equilibrium, aggregate shocks may be concentrated on stockholders, which may lead to a high equity premium.
JEL Classification Numbers: D81, E44.     

基于投资者异质性信念的证券定价模型——对我国股票市场价格的实证检验

投资者异质性信念的相互作用影响着证券价格,证券市场上的各种证券需求与供给关系,往往表现为投资者各种不同信念的对抗和交融。本文以悲观信念（看多）和乐观信念（看空）之间的相互作用为例,研究了异质性信念对资产均衡定价的影响,并以我国股票市场的机构投资者信念为对象进行了实证检验,得出我国股票市场投资者信念与证券价格相互作用的结论。本文的建议是在投资过程中,准确分析市场中投资者的异质性信念结构,尤其是资金雄厚的机构投资者的信念结构至关重要。