Endogenous Uncertainty and Market Volatility

Endogenous Uncertainty is that component of economic risk and market volatility which is propagated within the economy by the beliefs and actions of agents. The theory of Rational Belief (see Kurz [1994]) permits rational agents to hold diverse beliefs and consequently, a Rational Belief Equilibrium (in short, RBE) may exhibit diverse patterns of Endogenous Uncertainty. This paper shows that most of the observed volatility in financial markets is generated by the beliefs of the agents and the diverse market puzzles which are examined in this paper, such as the equity premium puzzle, are all driven by the structure of market expectations. To make the case for this theory we present a single RBE model, which builds on developments in Kurz and Beltratti [1997] and Kurz and Schneider [1996], with which we study a list of phenomena that have been viewed as "anomalies" in financial markets. The model is able to predict 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 Forward Discount Bias in foreign exchange markets. We also conjecture that an adaptation of the same model to markets with derivative assets will predict the appearance of "smile curves" in derivative prices. The common economic explanation for these phenomena is the existence of heterogeneous agents with diverse but correlated beliefs. Given such diversity, some agents are optimistic and some pessimistic. We develop a simple model which allows agents to be in these two states of belief but the identity of the optimists and the pessimists fluctuates over time since at any date any agent may be in these two states of belief. In this model there is a unique parameterisation under which the model makes all the above predictions simultaneously. That is, although the parameter space of the RBE is large, all parameterisations outside a small neighbourhood of the parameter space fail significantly to reproduce some subset of variables under consideration. Any parameter choice in this small neighbourhood 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. This higher intensity has a decisive effect on the market: it increases the demand for riskless assets, decreases the equilibrium riskless rate and increases the equity premium. In simple terms, the large equity premium and the lower 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 relative impact of these two groups of agents who are, at any moment of time, in the two states of belief is a direct consequence of the rationality of belief conditions and in that sense it is unique to an RBE. As for the correlation among the beliefs of agents, the paper shows that the dynamics of asset prices are strongly affected by such correlation. The pattern of correlation which was used in the model can be explained intuitively in terms of its effect on the dynamics of prices. The model correlation causes periods of price rises (i.e. bull markets) to develop slower than periods of decline (i.e. bear markets) hence the model dynamics does not permit prices to shoot directly from the bottom to the top but the opposite is possible and takes the form of market crashes. Note: Both the RBE model developed in this paper as well as the associated programs used to solve it are available to the public on Professor Kurz's web page at http://www.stanford.edu/~mordecai/Rational Expectations, Rational Beliefs, Rational Belief Equilibrium (RBE), Endogenous uncertainty, States of belief, Stock price, Discount bond, Equity premium, Market volatility, GARCH, Forward Discount Bias.

Risk Premia, diverse belief and beauty contests

We present a theoretical and empirical evaluation of the role of market belief in the structure of risk premia. To that end we employ a familiar asset pricing model for which we develop in detail the belief structure. The novelty in this development is the treatment of individual and market beliefs as Markov state variables. Moreover, the market belief is observable and the paper explains how we extract it from the data. The advantage of our formulation is that it permits a closed form solution of equilibrium prices hence we can trace the exact effect of market belief on the time variability of equilibrium risk premia. We present a model of asset pricing with diverse beliefs. We then explore the conditions under which diverse beliefs arise. We then derive the equilibrium asset pricing and the risk premium which the model implies. Since asset prices are affected by the dynamics of market belief, the component of market risk which is determined by the belief of agents is thus termed “Endogenous Uncertainty.” The theoretical conclusions are tested empirically for investments in the futures markets, the bond markets. Our main theoretical and empirical result is that fluctuations in the market belief about state variables are a dominant factor determining the time variability of risk premia. More specifically, we show that when the market holds abnormally favorable belief about future payoffs of an asset the market views the long position as less risky and hence the risk premium on that asset declines. This means that fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is very strong and empirically very dominant. The strong effect of market belief on market risk premia offers two additional perspectives. First, it offers an additional way of showing (for those who have any doubt) that fundamental factors affect market dynamics but perceptions have equally important effect on volatility. Second, that market belief is actually an observable data which can be used for a deeper understanding of the basic causes of stochastic volatility and time variability of risk premia.Risk premium; heterogenous beliefs; market state of belief; asset pricing; Bayesian learning; updating beliefs; Rational Beliefs

The role of expectations in economic fluctuations and the efficacy of monetary policy

We show diverse beliefs is an important propagation mechanism of fluctuations, money non neutrality and efficacy of monetary policy. Since expectations affect demand, our theory shows economic fluctuations are mostly driven by varying demand not supply shocks. Using a competitive model with flexible prices in which agents hold Rational Belief (see Kurz (1994)) we show that (i) our economy replicates well the empirical record of fluctuations in the U.S. (ii) Under monetary rules without discretion, monetary policy has a strong stabilization effect and an aggressive anti-inflationary policy can reduce inflation volatility to zero. (iii) The statistical Phillips Curve changes substantially with policy instruments and activist policy rules render it vertical. (iv) Although prices are flexible, money shocks result in less than proportional changes in inflation hence the aggregate price level appears "sticky" with respect to money shocks. (v) Discretion in monetary policy adds a random element to policy and increases volatility. The impact of discretion on the efficacy of policy depends upon the structure of market beliefs about future discretionary decisions. We study two rationalizable beliefs. In one case, market beliefs weaken the effect of policy and in the second, beliefs bolster policy outcomes and discretion could be a desirable attribute of the policy rule. Since the central bank does not know any more than the private sector, real social gain from discretion arise only in extraordinary cases. Hence, the weight of the argument leads us to conclude that bank´s policy should be transparent and abandon discretion except for rare and unusual circumstances. (vi) An implication of our model suggests the current effective policy is only mildly activist and aims mostly to target inflation

The Role of Expectations in Economic Fluctuations and the Efficacy of Monetary Policy

We show diverse beliefs is an important propagation mechanism of fluctuations, money non neutrality and efficacy of monetary policy. Since expectations affect demand, our theory shows economic fluctuations are mostly driven by varying demand not supply shocks. Using a competitive model with flexible prices in which agents hold Rational Belief (see Kurz (1994)) we show that (i) our economy replicates well the empirical record of fluctuations in the U.S. (ii) Under monetary rules without discretion, monetary policy has a strong stabilization effect and an aggressive anti-inflationary policy can reduce inflation volatility to zero. (iii) The statistical Phillips Curve changes substantially with policy instruments and activist policy rules render it vertical. (iv) Although prices are flexible, money shocks result in less than proportional changes in inflation hence the aggregate price level appears “sticky” with respect to money shocks. (v) Discretion in monetary policy adds a random element to policy and increases volatility. The impact of discretion on the efficacy of policy depends upon the structure of market beliefs about future discretionary decisions. We study two rationalizable beliefs. In one case, market beliefs weaken the effect of policy and in the second, beliefs bolster policy outcomes and discretion could be a desirable attribute of the policy rule. Since the central bank does not know any more than the private sector, real social gain from discretion arise only in extraordinary cases. Hence, the weight of the argument leads us to conclude that bank’s policy should be transparent and abandon discretion except for rare and unusual circumstances. (vi) An implication of our model suggests the current effective policy is only mildly activist and aims mostly to target inflation.Monetary policy rules, Money non neutrality, Business cycles, Market volatility, Propagation mechanism, Capacity utilization, Heterogenous beliefs, Over confidence, Rational Belief, Optimism, Pessimism, Non stationarity, Empirical distribution

Endogenous Uncertainty and the Non-neutrality of Money

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 \ufb02uctuations. 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 \ubf\ufb02utters, real output sputters\ubf. We show that Endogenous Uncertainty and the distribution of market beliefs are the major explanatory variables of such \ufb02uctuations. 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 in\ufb02ation and recessions can be substantially aggravated by the distribution of market beliefs

Endogenous Uncertainty and the Non-neutrality of Money

We study the implications of the Theory of Rational Beliefs to monetary policy. A two-agent OLG model based on Lucas' model is proposed to study such issue. We show that monetary policy in a Rational Beliefs environment can have an important e ect on the characteristics of eco- nomic fluctuations. In Rational Beliefs Equilibria (RBE) money is generi- cally non-neutral unlike Rational Expectations Equilibria (REE) in which money is neutral and monetary policy is ine ective. Without structural knowledge by agents, individuals who hold rational beliefs make decisions based on their di ering expectations. In such an economy 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. Endogenous Uncertainty, the internally propagated uncertainty about en- dogenous variables such as beliefs and actions of other agents and prices, is the major cause of such fluctuations. The rational mistakes of agents in RBE can amplify or reverse the effect of an expansionary monetary policy leading to higher or lower impact on prices than under REE. Distribution of beliefs among agents can have a persistent effect on the long term price level volatility and, given that agents are risk averse and given the presence of endogenous uncertainty, in a RBE the wage rate is higher in expected value than would be forthcoming under REE. Under Rational Expectations monetary policy has no effect because agents neutralize such effect by predicting correctly the effect of the pol- icy. Under Rational Beliefs it is shown instead that price fluctuations and recessions can be substantially aggravated by the structure of beliefs

Money Non-neutrality in a Rational Belief Equilibrium with Financial Assets.

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

Risk Premia, diverse belief and beauty contests

We present a theoretical and empirical evaluation of the role of market belief in the structure of risk premia. To that end we employ a familiar asset pricing model for which we develop in detail the belief structure. The novelty in this development is the treatment of individual and market beliefs as Markov state variables. Moreover, the market belief is observable and the paper explains how we extract it from the data. The advantage of our formulation is that it permits a closed form solution of equilibrium prices hence we can trace the exact effect of market belief on the time variability of equilibrium risk premia. We present a model of asset pricing with diverse beliefs. We then explore the conditions under which diverse beliefs arise. We then derive the equilibrium asset pricing and the risk premium which the model implies. Since asset prices are affected by the dynamics of market belief, the component of market risk which is determined by the belief of agents is thus termed “Endogenous Uncertainty.” The theoretical conclusions are tested empirically for investments in the futures markets, the bond markets. Our main theoretical and empirical result is that fluctuations in the market belief about state variables are a dominant factor determining the time variability of risk premia. More specifically, we show that when the market holds abnormally favorable belief about future payoffs of an asset the market views the long position as less risky and hence the risk premium on that asset declines. This means that fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is very strong and empirically very dominant. The strong effect of market belief on market risk premia offers two additional perspectives. First, it offers an additional way of showing (for those who have any doubt) that fundamental factors affect market dynamics but perceptions have equally important effect on volatility. Second, that market belief is actually an observable data which can be used for a deeper understanding of the basic causes of stochastic volatility and time variability of risk premia

Risk Premia, Diverse Belief and Beauty Contests

We present a theoretical and empirical evaluation of the role of market belief in the structure of risk premia. To that end we employ a familiar asset pricing model for which we develop in detail the belief structure. The novelty in this development is the treatment of individual and market beliefs as Markov state variables. Moreover, the market belief is observable and the paper explains how we extract it from the data. The advantage of our formulation is that it permits a closed form solution of equilibrium prices hence we can trace the exact effect of market belief on the time variability of equilibrium risk premia. We present a model of asset pricing with diverse beliefs. We then explore the conditions under which diverse beliefs arise. We then derive the equilibrium asset pricing and the risk premium which the model implies. Since asset prices are affected by the dynamics of market belief, the component of market risk which is determined by the belief of agents is thus termed Endogenous Uncertainty. The theoretical conclusions are tested empirically for investments in the futures markets, the bond markets. Our main theoretical and empirical result is that fluctuations in the market belief about state variables are a dominant factor determining the time variability of risk premia. More specifically, we show that when the market holds abnormally favorable belief about future payoffs of an asset the market views the long position as less risky and hence the risk premium on that asset declines. This means that fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is very strong and empirically very dominant. The strong effect of market belief on market risk premia offers two additional perspectives. First, it offers an additional way of showing (for those who have any doubt) that fundamental factors affect market dynamics but perceptions have equally important effect on volatility. Second, that market belief is actually an observable data which can be used for a deeper understanding of the basic causes of stochastic volatility and time variability of risk premia

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 state variable. Market belief is observable, it is central to the empirical evaluation and we show how to extract it from the data.The asset pricing model we use is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive the equilibrium asset pricing and the 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 and beyond 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-month and 6-month Treasury Bills. The annualized mean risk premium on holding such assets for 1-12 months is about 40-60 basis points and, on average, we find that the component of market belief in the risk premium at a random date 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. \u201cbull\u201d markets) are shown to be periods when the market risk premium declines while in periods of pessimism (i.e. \u201cbear\u201d markets) the market\u2019s risk premium rises. Hence, fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant