Heterogeneous agents,the financial crisis and exchange rate predictability

We construct an empirical heterogeneous agent model which optimally combines forecasts from fundamentalist and chartist agents and evaluates its out-of-sample forecast performance using daily data covering an overall period from January 1999 to June 2014 for six of the most widely traded currencies. We use daily financial data such as level, slope and curvature yield curve factors, equity prices, as well as risk aversion and global trade activity measures in the fundamentalist agent's predictor set to obtain a proxy for the market's view on the state of the macroeconomy. Chartist agents rely upon standard momentum, moving average and relative strength index technical indicators in their predictor set. Individual agent specific forecasts are constructed using a flexible dynamic model averaging framework and are then aggregated into a model combined forecast using a forecast combination regression. We show that our empirical heterogeneous agent model produces statistically significant and economically sizeable forecast improvements over a random walk benchmark.     

A Strategic Asset Pricing Model for Relative Performance Concern

We propose a strategic asset pricing model for the relative performance concern with heterogeneous beliefs in the framework of Nash equilibrium. In our model, the presence of heterogeneous beliefs generates the upward pressure on the stock market volatility and gives rise to the separation of agents’ perceived Sharpe ratios. We show that if one of the agents temporarily wins the market, the presence of relative performance concern will reduce the impacts of the winner and make the investors who have been edged out of the market more inclined to return. Besides, the sufficiently strong concern of relative performance will bring investors the extreme aversion to losing and get them to trade similarly.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Risk premia,asset price bubbles,and monetary policy

We develop a dynamic general equilibrium asset pricing model with heterogeneous beliefs to study the effects of monetary policy on prices, risk premia, asset price bubbles, and financial stability. We propose a new framework for monetary policy with respect to bubbles. Because bubble risk premia arise from an interaction between disagreements among investors and dynamic trading constraints, under a non-accommodative monetary policy, liquidity adjusted risk and bubble risk premia increase. What matters for policy is the trading constrained fraction/mass of agents that disagree about fundamentals (i.e. optimists/pessimists). Accommodative policy can lead to a larger fraction of trading constrained agents that disagree, larger bubbles, and increased systemic risk. An implication of our results is that accommodative monetary policy in response to the Covid-19 crisis does not increase systemic risk due to asset price bubbles, as long as the policy keeps inflation under control.     

Market selection with learning and catching up with the Joneses

We study the market selection hypothesis in complete financial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and learning mechanism, risk aversion, impatience and ‘catching up with the Joneses’ preferences. We develop new techniques for studying the long-run behavior of such economies, based on Strassen’s functional law of the iterated logarithm. In particular, we explicitly determine an agent’s survival index and show how the latter depends on the agent’s characteristics. We use these results to study the long-run behavior of the equilibrium interest rate and the market price of risk.     

Shorting in Speculative Markets

In models of trading with heterogeneous beliefs following Harrison-Kreps, short selling is prohibited and agents face constant marginal costs-of-carry. The resale option guarantees that prices exceed buy-and-hold prices and the difference is identified as a bubble. We propose a model where risk-neutral agents face asymmetric increasing marginal costs on long and short positions. Here, agents also value an option to delay, and a Hamilton-Jacobi-Bellman equation quantifies the influence of costs on prices. An unexpected decrease in shorting costs may deflate a bubble, linking financial innovations that facilitated shorting of mortgage-backed securities to the collapse of prices.     

Far from the madding crowd: collective wisdom in prediction markets

We investigate market selection and bet pricing in a repeated prediction market model. We derive the conditions for long-run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true probabilities, nor are they always nearer to the truth than the beliefs of all surviving agents. This implies that, in general, prediction market prices are not maximum likelihood estimators of the true probabilities. However, when more than one agent survives, the average price emerging from a prediction market approximates the true probability with lower information loss than any individual belief.     

Model Uncertainty and Option Markets with Heterogeneous Beliefs

This paper provides option pricing and volume implications for an economy with heterogeneous agents who face model uncertainty and have different beliefs on expected returns. Market incompleteness makes options nonredundant, while heterogeneity creates a link between differences in beliefs and option volumes. We solve for both option prices and volumes and test the joint empirical implications using S&P500 index option data. Specifically, we use survey data to build an Index of Dispersion in Beliefs and find that a model that takes information heterogeneity into account can explain the dynamics of option volume and the smile better than can reduced‐form models with stochastic volatility.     

Belief Dispersion in the Stock Market

We develop a dynamic model of belief dispersion with a continuum of investors differing in beliefs. The model is tractable and qualitatively matches many of the empirical regularities in a stock price and its mean return, volatility, and trading volume. We find that the stock price is convex in cash‐flow news and increases in belief dispersion, while its mean return decreases when the view on the stock is optimistic, and vice versa when pessimistic. Moreover, belief dispersion leads to higher stock volatility and trading volume. We demonstrate that otherwise identical two‐investor heterogeneous‐beliefs economies do not necessarily generate our main results.     

Asset pricing with heterogeneous beliefs and relative performance

We propose an equilibrium asset pricing model in which agents with heterogeneous beliefs care about relative performance. We find that the concern with relative performance leads agents to trade more similarly, a development that has two effects. First, similar trading directly decreases volatility. Second, similar trading decreases the impact of dominant agents. The second effect dominates the first when agents expect large differences between their final performances, and vice versa when agents expect small differences between their final performances. Compared with the case in which agents are unconcerned about relative performance, the stock return volatility is higher when the second effect dominates, and lower when the first effect dominates. This paper also demonstrates that the concern about relative performance influences investors’ holdings, stock prices and risk premia.     

Dynamic financial contracting with persistent private information

We study a dynamic agency model where the agent privately observes the firm's cash flows that are subject to persistent shocks. We characterize the policy dynamics and implement the optimal contract by financial securities. Because bad performance distorts investors' beliefs downward, the agent has less incentive to misrepresent information. The agent's compensation is less than what he can divert and is convex in performance. As private information becomes more persistent, (i) the agent is compensated more by stock options; (ii) firm credit limits vary more with history, dropping after bad performance; (iii) the firm is financially constrained for longer time.     

Nominal Interest Rates and Loan Volume with Heterogeneous Beliefs

The large volume of loan transactions suggests widely divergent beliefs among borrowers and lenders, but most modern term structure theories make no prediction about volume because they assume homogeneous agents. Within these rational expectations, representative agent theories, loans are not only in zero net supply; they are also in zero gross supply. Here, the shape of the average term structure, the bias in forward interest rates, and the volume of transactions are discussed in a heuristic setting with heterogeneity and incomplete rationality. A reconciliation of heterogeneity with continuous–time term structure theory is attempted, but the results are not encouraging. Empirical data are consistent with the importance of heterogeneous beliefs.     

Where are the sources of stock market mispricing and excess volatility?

Using a simple dividend model, we illustrate and synthesize the sources of stock market mispricing and excess volatility based upon two hypotheses—inflation illusion and heterogeneous beliefs. Our theoretical framework posits that equity mispricing arises when investors have subjective expectations about discount rates or dividend growth rates. We then analyze the sources of equity mispricing and market excess volatility under a VAR framework. Empirically, we find that both inflation illusion and heterogeneous beliefs explain equity mispricing. However, heterogeneous beliefs play a more important role in explaining stock mispricing in the long run. We also find that heterogeneous beliefs cause excess volatility, but inflation illusion does not. Therefore, dispersion in investors’ beliefs is a better explanation of stock market mispricing than the investors’ inability to properly discount future cash flows.     

Competitive risk sharing contracts with one-sided commitment

This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. We demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment effectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogoff [1989. Sovereign debt: is to forgive to forget? American Economic Review 79, 43-50]. From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved.     

Interest rate linkages within the EMS and bank credit supply

The exchange rates between the currencies of European Monetary System (EMS) members are essentially fixed between narrow bands mandated by the Exchange Rate Mechanism (ERM). the intent of such a fixed rate regime is to enhance policy co-ordination within the EMS. However, it has instead led to German policy dominance within the system according to several recent studies. We examine the optimal dynamic credit policy of a bank in an EMS country that is subject to such German ‘dominance’. Our stochastic control model reveals conditions under which German monetary policies can influence domestic bank lending behaviour. It also suggests that banks may be able to hedge such risk exposure by increasing in size. the model offers ‘credit supply' based explanations for recent regulatory reforms in Europe towards unified banking and the attempts of several EMS members to de-link their policies from that of the German Bundesbank.     

Dynamic regulation of quality

We develop a dynamic regulation model of quality provision where maintenance efforts and quality shocks have a durable impact. When the regulator contracts with a sequence of agents, asymmetric information can lead to overprovision of quality, reflecting a dynamic rent extraction effect. When the regulator contracts with a single agent, the efficiency of their relationship depends on the regulator’s ability to transfer rents across periods. Hiring a single agent with unlimited liability is socially preferable to hiring a sequence of agents, even when no commitment is feasible. By contrast, shorter franchises are socially preferable if the agent has limited liability.     

A financial CCAPM and economic inequalities

This paper considers a wealth heterogeneous multi-agent (MA) financial pricing CCAPM model. It is based on the following observations: (a) A distinction between what agents are willing to pay for consumption and what they actually pay. The former is a function of a number of factors including the agent’s wealth and risk preferences and the latter is a function of all other agents’ aggregate consumption or equivalently, their wealth committed to consumption. (b) Unlike traditional pricing models that define a representative agent underlying the pricing model, this paper assumes that each agent is in fact ‘Cournot-gaming’ a market defined by all other agents. This results in a decomposition of an n-agents game into n games of two agents, one a specific agent and the other a synthetic agent (a proxy for all other agents), on the basis of which an equilibrium consumption price solution is defined. The paper’s essential results are twofold. First, a Martingale pricing model is defined for each individual agent expressing the consumer willingness to pay (his utility price) and the market price—the price that all agents pay for consumption. In this sense, price is unique defined by each agent’s ‘Cournot game’ Agents’ consumption are then adjusted accordingly to meet the market price. Second, the pricing model defined is shown to account for agents wealth distribution pointing out that all agents valuations are a function of their and others’ wealth, the information they have about each other and other factors which are discussed in the text. When an agent has no wealth or cannot affect the market price of consumption, then this pricing model is reduced to the standard CCAPM model while any agent with an appreciable wealth compared to other agents, is shown to value returns (and thus future consumption) less than wealth-poor agents. As a result, this paper will argue that even in a financial market with an infinite number of agents, if there are some agents that are large enough to affect the market price by their decisions, such agents have an arbitrage advantage over the poorer agents. The financial CCAPM MA pricing model has a number of implications, some of which are considered in this paper. Finally, some simple examples are considered to highlight the applicability of this paper to specific financial issues.     

Heterogeneous Beliefs, the Term Structure and Time-varying Risk Premia

This paper demonstrates theoretically and empirically that one possible economic explanation of the dynamics of the term structure of interest rates is the time-varying heterogeneous beliefs about future economic conditions. Assuming that each agent forms heterogeneous expectations about both his income shock and others’ beliefs about their income shocks each period, the paper illustrates that heterogeneous beliefs generate time-varying risk premia of the term structure in a closed-form solution. Motivated by this theory, several empirical tests are conducted using the cross-sectional mean and dispersion of belief indices that are extracted as the differences between non-judgemental econometric forecasts based on diffusion indices in Stock and Watson (J Bus Econ Stat, 2002) and professional survey forecasts. It is shown that (a) an increase in the mean belief about inflation steepens the yield curve, (b) the mean and dispersion of interest rate beliefs help explain the mean and the stochastic volatility of the term structure, suggesting that time-varying risk premia may be explained by endogenous uncertainty caused by heterogeneous beliefs in the economy.I am indebted to Mordecai Kurz, Timothy Cogley and Narayana Kocherlakota for constant support and extensive discussions that inspired this work. I would like to thank Randall Moore for providing the Blue Chip financial forecast data. The financial support from the Smith Richardson Foundation to the Stanford Institute for Economic Policy Research is gratefully acknowledged.     

Incomplete Information, Heterogeneity, and Asset Pricing

We consider a pure exchange economy where the drift of aggregateconsumption is unobservable. Agents with heterogeneous beliefsand preferences act competitively on financial and goods markets.We discuss how equilibrium market prices of risk differ acrossagents, and in particular we discuss the properties of the marketprice of risk under the physical (objective) probability measure.We propose a number of specifications of risk aversions andbeliefs where the market price of risk is much higher, and theriskless rate of return lower, than in the equivalent full informationeconomy (homogeneous and heterogeneous preferences) and thuscan provide an(other) answer to the equity premium and risk-freerate puzzles. We also derive a representation of the equilibriumvolatility and numerically assess the role of heterogeneityin beliefs. We show that a high level of stock volatility canbe obtained with a low level of aggregate consumption volatilitywhen beliefs are heterogeneous. Finally, we discuss how incompleteinformation may explain the apparent predictability in stockreturns and show that in-sample predictability cannot be exploitedby the agents, as it is in fact a result of their learning processes.     

An evolutionary CAPM under heterogeneous beliefs

Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This paper incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better-performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume.