We propose a theory of asset pricing based on heterogeneous agents who continually adapt their expectations to the market that these expectations aggregatively create. And we explore the implications of this theory computationally using our Santa Fe artificial stock market. Asset markets, we argue, have a recursive nature in that agents ’ expectations are formed on the basis of their anticipations of other agents ’ expectations, which precludes expectations being formed by deductive means. Instead traders continually hypothesize—continually explore—expectational models, buy or sell on the basis of those that perform best, and confirm or discard these according to their performance. Thus individual beliefs or expectations become endogenous to the market, and constantly compete within an ecology of others ’ beliefs or expectations. The ecology of beliefs co-evolves over time. Computer experiments with this endogenous-expectations market explain one of the more striking puzzles in finance: that market traders often believe in such concepts as technical trading, “market psychology, ” and bandwagon effects, while academic theorists believe in market efficiency and a lack of speculative opportunities. Both views, we show, are correct, but within different regimes. Within a regime where investors explore alternative expectational models at a low rate, the market settles into the rational-

This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the trade-off between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and cross-sectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar-* Department of Economics, Harvard University, Cambridge, Massachusetts

This paper provides one potential explanation for the rise, persistence and eventual fall of internet stock prices. Specifically, we appeal to a model of heterogenous agents with varying degrees of beliefs about asset payoffs who are subject to short sales constraints. In this framework, it is possible that "optimistic" investors overwhelm "pessimistic" ones, leading to prices not reflecting fundamental values about cash flows. Empirical support for this explanation is provided by exploring the behavior of internet stock prices during the period January 1998 to November 2000. In particular, we document four important elements to our story: (i) the high level of internet stock prices given their underlying fundamentals, (ii) responses of stock prices to a shift towards potentially optimistic investors, (iii) empirical results consistent with shorting being at its maximum possible level for internet stocks, and (iv) the eventual fall, or bubble bursting, of intemet stocks being tied to the increase in the number of sellers to the market via expiration of lockup agreements.

Abslract. The article considers the possibility that asset prices might deviate from intrinsic values based on market fundamentals. Three broad categories of theory are surveyed: (a) growing bubbles (b) fads and (c) information bubbles. 'Sunspot' theories are also discussed. The paper covers both theory and evidence, and directions for future research are discussed.

The widespread use and proven pro tability of technical trading rules in nancial markets has long been a puzzle in academic nance. In this paper we show, using an agent-based model of an evolving stock market, that widespread technical trading can arise due to a multi-person prisoners' dilemma in which the inclusion of technical trading rules to a single agent's repertoire of rules is a dominant strategy. The use of this dominant strategy by all traders in the market creates a symmetric Nash equilibrium in which wealth earned is lower and the volatility of prices is higher than in the hypothetical case in which all agents rely only on fundamental rules. Our explanation of this lower wealth and higher volatility is that the use of technical trading rules worsens the accuracy of the predictions of all agents' market forecasts by contributing to the reinforcement of price trends, augmenting volatility, and increasing the amount of noise in the market.

A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date-stamping the origination and collapse of economic exuberance, and providing valid confidence intervals for explosive growth rates. The method involves the recursive implementation of a right-side unit root test and a sup test, both of which are easy to use in practical applications, and some new limit theory for mildly explosive processes. The test procedure is shown to have discriminatory power in detecting periodically collapsing bubbles, thereby overcoming a weakness in earlier applications of unit root tests for economic bubbles. An empirical application to Nasdaq stock price index in the 1990s provides confirmation of explosiveness and date-stamps the origination of financial exuberance to mid-1995, prior to the famous remark in December 1996 by Alan Greenspan about irrational exuberance in financial

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset’s market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the ”no free lunch with vanishing risk” and ”no dominance” assumptions. We propose a new theory for bubble birth which involves a nontrivial modification of the classical framework. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles, (ii) European call options and discounted forward prices can have bubbles, but the magnitude of their bubbles must equal the magnitude of the asset’s price bubble, (iii) with no dividends, American call prices must always equal an otherwise identical European call’s price, regardless of bubbles, (iv) European put-call parity in market prices must always hold, regardless of bubbles, and (v) futures price bubbles can exist and they are independent of bubbles in the underlying asset’s price. These results imply that in a market satisfying NFLVR and no dominance, in the presence of an asset price bubble, risk neutral valuation can not be used to match call option prices. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.

A recursive regression methodology is used to analyze the bubble characteristics of various financial time series during the subprime crisis. The methods provide a technology for identifying bubble behavior and consistent dating of their origination and collapse. Seven relevant financial series are investigated, including three financial assets (the Nasdaq index, home price index and asset-backed commercial paper), two commodities (the crude oil price and platinum

useful comments and suggestions. They should, of course, be absolved from any remaining errors or inaccuracies. The views expressed in the paper are those of the In recent years, there has been much re-assessment and re-evaluation by academic economists of the Efficient Markets Hypothesis. The traditional view, stressing the ability of speculative markets to keep asset prices in line with economic fundamentals, has been challenged by an approach more sympathetic to the role of self-fulfilling expectations, psychology, herd behaviour and other seemingly irrational influences on asset prices. Greater appreciation of the institutional features of real-world asset markets also distinguishes this modern approach. The paper summarises this influential and rapidly-growing body of theoretical literature on asset price formation.

We estimate a dynamic asset pricing model characterized by heterogeneous boundedly rational agents. The fundamental value of the risky asset is publicly available to all agents, but they have different beliefs about the persistence of deviations of stock prices from the fundamental benchmark. An evolutionary selection mechanism based on relative past profits governs the dynamics of the fractions and switching of agents between different beliefs or forecasting strategies. A strategy attracts more agents if it performed relatively well in the recent past compared to other strategies. We estimate the model to annual US stock price data from 1871 until 2003. The estimation results support the existence of two expectation regimes, and a bootstrap F-test rejects linearity in favor of our nonlinear two-type heterogeneous agent model. One regime can be characterized as a fundamentalists regime, because agents believe in mean reversion of stock prices toward the benchmark fundamental value. The second regime can be characterized as a chartist, trend following regime because agents expect the deviations from the fundamental to trend. The fractions of agents using the fundamentalists and trend following forecasting rules show substantial time variation and switching between predictors. The model offers an explanation for the recent stock prices run-up. Before the 90s the trend following regime was active only occasionally. However, in the late 90s the trend following regime persisted and created an extraordinary deviation of stock prices from the fundamentals. Recently, the activation of the mean reversion regime has contributed to drive stock prices back closer to their fundamental valuation.