Restrictions that a class of general equilibrium models place upon the average returns of equity and Treasury bills are found to be strongly violated by the U.S. data in the 1889-1978 period. This result is robust to model specification and measurement problems. We conclude that, most likely, an equilibrium model which is not an Arrow-Debreu economy will be the one that Simultaneously rationalizes both historically observed large average equity return and the small average risk-free return. 1.

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-

Implicit in the prices of traded financial assets are Arrow-Debreu prices or, with continuous states, the state-price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitrage-free method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility "smiles" for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.

Abstract: This paper examines the joint time series of the S&P 500 index and near-the-money short-dated option prices with an arbitrage-free model, capturing both stochastic volatility and jumps. Jump-risk premia uncovered from the joint data respond quickly to market volatility, becoming more prominent during volatile markets. This form of jump-risk premia is important not only in reconciling the dynamics implied by the joint data, but also in explaining the volatility “smirks” of cross-sectional options data.

This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their `beliefs' in each period in a boundedly rational way, according to a `fitness measure' such as past realized profits. Price fluctuations are thus driven by an evolutionary dynamics between different expectation schemes (`rational animal spirits'). Using a mixture of local bifurcation theory and numerical methods, we investigate possible bifurcation routes to complicated asset price dynamics. In particular, we present numerical evidence of strange, chaotic attractors when the intensity of choice to switch prediction strategies is high.

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

As a consequence of optimal investment choices, a firm’s assets and growth options change in predictable ways. Using a dynamic model, we show that this imparts predictability to changes in a firm’s systematic risk, and its expected return. Simulations show that the model simultaneously reproduces: ~i! the time-series relation between the book-to-market ratio and asset returns; ~ii! the cross-sectional relation between book-to-market, market value, and return; ~iii! contrarian effects at short horizons; ~iv! momentum effects at longer horizons; and ~v! the inverse relation between interest rates and the market risk premium. RECENT EMPIRICAL RESEARCH IN FINANCE has focused on regularities in the cross section of expected returns that appear anomalous relative to traditional models. Stock returns are related to book-to-market, and market value. 1 Past returns have also been shown to predict relative performance, through the documented success of contrarian and momentum strategies. 2 Existing explanations for these results are that they are due to behavioral biases or risk premia for omitted state variables. 3 These competing explanations are difficult to evaluate without models that explicitly tie the characteristics of interest to risks and risk premia. For example, with respect to book-to-market, Lakonishok et al. ~1994! argue: “The point here is simple: although the returns to the B0M strategy are impressive, B0M is not a ‘clean ’ variable uniquely associated with eco-

This paper presents a dynamic asset-pricing model under asymmetric information. Investors have different information concerning the future growth rate of dividends. They rationally extract information from prices as well as dividends and maximize their expected utility. The model has a closed-form solution to the rational expectations equilibrium. We find that existence of uninformed investors increases the risk premium. Supply shocks can affect the risk premium only under asymmetric information. Information asymmetry among investors can increase price volatility and negative autocorrelation in returns. Less-informed investors may rztionally behave like price chasers.

Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This chapter provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the method of undetermined coefficients. This chapter contains nothing substantially new. Instead, the chapter simplifies and unifies existing approaches to make them accessible for a wide audience, showing how to log-linearizing the nonlinear equations without the need for explicit di erentiation, how to use the method of undetermined coefficients for models with a vector of endogenous state variables, to provide a general solution by characterizing the solution with a matrix quadratic equation and solving it, and to provide frequency-domain techniques to calculate the second order properties of the model in its HP-filtered version without resorting to simulations. Since the method is an Euler-equation based approach rather than an approach based on solving a social planners problem, models with externalities or distortionary taxation do not pose additional problems. MATLAB programs to carry out the calculations in this chapter are made available. This chapter should be useful for researchers and Ph.D. students alike.

Recent imperfect capital market theories predict the presence of asymmetries in the variation of small and large firms' risk over the economic cycle. Small firms with little collateral should be more strongly affected by tighter credit market conditions in a recession state than large, better collateralized ones. This paper adopts a flexible econometric model to analyse these implications empirically. Consistent with theory, small firms display the highest degree of asymmetry in their risk across recession and expansion states and this translates into a higher sensitivity of these firms' expected stock returns with respect to variables that measure credit market conditions. Recent imperfect capital market theories (e.g., Bernanke and Gertler (1989), Gertler and Gilchrist (1994), Kiyotaki and Moore (1997)) predict that changing credit market conditions can have very different effects on small and large firms' risk. Agency costs induced by asymmetry in the information held by firms and their creditors make...