Heterogeneous Expectations and Bond Markets

This paper presents a dynamic equilibrium model of bond markets, in which two groups of agents hold heterogeneous expectations about future economic conditions. Our model shows that heterogeneous expectations can not only lead to speculative trading, but can also help resolve several challenges to standard representative-agent models of the yield curve. First, the relative wealth fluctuation between the two groups of agents caused by their speculative positions amplifies bond yield volatility, thus providing an explanation for the "excessive volatility puzzle" of bond yields. In addition, the fluctuation in the two groups' expectations and relative wealth also generates time-varying risk premia, which in turn can help explain the failure of the expectation hypothesis. These implications, essentially induced by trading between agents, highlight the importance of incorporating heterogeneous expectations into economic analysis of bond markets.

The economics of global environmental risk

This chapter focusses on global environmental risks such as climate change, an issue that must be confronted as we move into the future. It proposes sound principles of risk management that make sense in today's society generally, going beyond their role of averting and hedging climate risks. This chapter is about these and related questions. In attempting to answer them, it deals with different aspects of the theory of risk-bearing. I explain current responses to global change, focusing on the new challenges: human-induced or endogenous risks, including potentially catastrophic risks, which are not adequately treated by traditional economic analysis. In summary, we are dealing with risks that have two major new characteristics: they are endogenous and potentially catastrophic. In addition, climate risks have three more conventional features: they are poorly understood, correlated and irreversible. In all cases, this chapter proposes ways to advance our understanding of the problems. This chapter proposes ways to evaluate decisions under endogenous and potentially catastrophic risks, and incorporates often neglected features of correlated, poorly understood and irreversible risks. The analysis proposed here opens new ways of thinking and at the same time poses new challenges. At the end I indicate new areas of research.risk; global environment; climate change; endogenous risk; catastrophic risk; risk management; mathematical modeling; endogenous uncertainty; policy

Information Aggregation in a Catastrophe Futures Markets

We experimentally examine a reinsurance market in which participants have differing information regarding the probability distribution over losses. The key question is whether the market equilibrium reflects traders maximizing value with respect to their different priors, or whether the equilibrium is one based on a common belief incorporating all participants’ information. When assuming subjects are expected value maximizers, we reject both full information aggregation and no information aggregation equilibria. We discover, as in past individual choice insurance experiments, that buyers under-assess the probabilities of large loss states, or alternatively, subjects assign larger utility values to losses than to comparable gains. After accounting for these decision theoretic concerns, the non-aggregation of information hypothesis explains the data better than full information aggregation.

Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs.

The aim of the paper is to analyze the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus probability belief, as well as a consensus consumer, are shown to be valid modulo an aggregation bias, which takes the form of a discount factor. In classical cases, the consensus probability belief is a risk tolerance weighted average of the individual beliefs, and the discount factor is proportional to beliefs dispersion. This discount factor makes the heterogeneous beliefs setting fundamentally different from the homogeneous beliefs setting, and it is consistent with the interpretation of beliefs heterogeneity as a source of risk. We then use our construction to rewrite in a simple way the equilibrium characteristics (market price of risk, risk premium, risk-free rate) in a heterogeneous beliefs framework and to analyze the impact of beliefs heterogeneity. Finally, we show that it is possible to construct specific parametrizations of the heterogeneous beliefs model that lead to globally higher risk premia, lower risk-free rates, and risk premia that are lower for assets with higher belief dispersion.Beliefs Heterogeneity; Consensus Consumer; Pessimism; Optimism; Risk Premium;

Consensus consumer and intertemporal asset pricing with heterogeneous beliefs

The aim of the paper is to analyze the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus probability belief, as well as a consensus consumer, are shown to be valid modulo an aggregation bias, which takes the form of a discount factor. In classical cases, the consensus probability belief is a risktolerance weighted average of the individual beliefs, and the discount factor is proportional to beliefs dispersion. This discount factor makes the heterogeneous beliefs setting fundamentally different from the homogeneous beliefs setting, and it is consistent with the interpretation ofbeliefs heterogeneity as a source of risk.We then use our construction to rewrite in a simple way the equilibrium characteristics (market price of risk, risk premium, risk-free rate) in a heterogeneous beliefs framework and to analyze the impact of beliefs heterogeneity. Finally, we show that it is possible to construct specific parametrizations of the heterogeneous beliefs model that lead to globally higher risk premia and lower risk-free rates.risk premium; beliefs heterogeneity; optimism; pessimism; consensus consumer

Isoelastic Agents and Wealth Updates in Machine Learning Markets

Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alpha-mixtures, with a particular form of mixing component relating to each agent's wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Speculation in Financial Markets: A Survey

This survey covers the microeconomic theory of speculation in financial markets, since the development of the economics of uncertainty. It starts with a description of Walrasian exchange economies, both in general equilibrium –the Arrow-Debreu model and its extensions– and in partial equilibrium. Speculation, it is explained, is an incomplete-market phenomenon. It proceeds by analyzing more general voluntary trade environments, with a focus on whether or not differences in information are a valid source for belief heterogeneity. The role of common priors in the no-trade theorem is discussed. Finally, heterogeneous priors models are considered.

Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility

Our objective is to identify the trading strategy that would allow an investor to take advantage of "excessive" stock price volatility and "sentiment" fluctuations. We construct a general-equilibrium model of sentiment. In it, there are two classes of agents and stock prices are excessively volatile because one class is overconfident about a public signal. As a result, this class of overconfident agents changes its expectations too often, sometimes being excessively optimistic, sometimes being excessively pessimistic. We determine and analyze the trading strategy of the rational investors who are not overconfident about the signal. We find that, because overconfident traders introduce an additional source of risk, rational investors are deterred by their presence and reduce the proportion of wealth invested into equity except when they are extremely optimistic about future growth. Moreover, their optimal portfolio strategy is based not just on a current price divergence but also on their expectation of future sentiment behavior and a prediction concerning the speed of convergence of prices. Thus, the portfolio strategy includes a protection in case there is a deviation from that prediction. We find that long maturity bonds are an essential accompaniment of equity investment, as they serve to hedge this "sentiment risk."