Recent empirical research in finance has uncovered two families of pervasive regularities: underreaction of stock prices to news such as earnings announcements, and overreaction of stock prices to a series of good or bad news. In this paper, we present a parsimonious model of investor sentiment, or of how investors form beliefs, which is consistent with the empirical findings. The model is based on psychological evidence and produces both underreaction and overreaction for a wide range of parameter values. � 1998 Elsevier Science S.A. All rights reserved. JEL classification: G12; G14

We model a market populated by two groups of boundedly rational agents: “newswatchers” and “momentum traders.” Each newswatcher observes some private information, but fails to extract other newswatchers’ information from prices. If information diffuses gradually across the population, prices underreact in the short run. The underreaction means that the momentum traders can profit by trendchasing. However, if they can only implement simple (i.e., univariate) strategies, their attempts at arbitrage must inevitably lead to overreaction at long horizons. In addition to providing a unified account of under- and overreactions, the model generates several other distinctive implications.

We examine long-run firm performance following open market share repurchase announcements, 1980-1990. We find that the average abnormal four-year buy-and-hold return measured after the initial announcement is 12.1%. For ‘value ’ stocks, companies more likely to be repurchasing shares because of undervaluation, the average abnormal return is 45.3%. For repurchases announced by ‘glamour ’ stocks, where undervaluation is less likely to be an important motive, no positive drift in abnormal returns is observed. Thus, at least with respect to value stocks, the market errs in its initial response and appears to ignore much of the information conveyed through repurchase announcements.

Various theories have been proposed to explain momentum in stock returns. We test the gradual-information-diffusion model of Hong and Stein (1999) and establish three key results. First, once one moves past the very smallest stocks, the profitability of momentum strategies declines sharply with firm size. Second, holding size fixed, momentum strategies work better among stocks with low analyst coverage. Finally, the effect of analyst coverage is greater for stocks that are past losers than for past winners. These findings are consistent with the hypothesis that firm-specific information, especially negative information, diffuses only gradually across the investing public. SEVERAL RECENT PAPERS HAVE DOCUMENTED that, at medium-term horizons ranging from three to 12 months, stock returns exhibit momentum-that is, past winners continue to perform well, and past losers continue to perform poorly. For example, Jegadeesh and Titman (1993), using a U.S. sample of NYSE/ AMEX stocks over the period from 1965 to 1989, find that a strategy that buys past six-month winners (stocks in the top performance decile) and shorts past six-month losers (stocks in the bottom performance decile) earns approximately one percent per month over the subsequent six months. Not only is this an economically interesting magnitude, but the result also appears to be robust: Rouwenhorst (1998) obtains very similar numbers in a

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios. THE SINGLE FACTOR CAPITAL ASSET PRICING MODEL ~CAPM! of Sharpe ~1964! and Lintner ~1965! has come under recent scrutiny. Tests indicate that the crossasset variation in expected returns cannot be explained by the market beta alone. For example, a growing number of studies show that “fundamental” variables such as size, book-to-market value, and price to earnings ratios

1980 and 1995 an internationally diversified portfolio of past medium-term Winners outperforms a portfolio of medium-term Losers after correcting for risk by more than one percent per month. Return continuation is present in all twelve sample countries and lasts on average for about one year. Return continuation is negatively related to firm size, but is not limited to small firms. The international momentum returns are correlated with the U.S. which suggests that exposure to a common factor may drive the profitability of momentum strategies. Many papers have documented that average stock returns are related to past performance. Jegadeesh and Titman (1993) document that over medium-term horizons performance persists: firms with higher returns over the past three months to one year continue to outperform firms with low past returns over the same period. By contrast, DeBondt and Thaler (1985,1987) document return reversals over longer horizons. Firms with poor three- to five-year past performance earn higher average returns than firms that performed well in the past. There has been an extensive literature on whether these return patterns reflect an improper response by markets to information, or that they can be explained by market microstructure biases or by 1

Value stocks have higher returns than growth stocks in markets around the world. For the period 1975 through 1995, the difference between the average returns on global portfolios of high and low book-to-market stocks is 7.68 percent per year, and value stocks outperform growth stocks in twelve of thirteen major markets. An international capital asset pricing model cannot explain the value premium, but a two-factor model that includes a risk factor for relative distress captures the value premium in international returns. INVESTMENT MANAGERS CLASSIFY FIRMS that have high ratios of book-to-market equity ~B0M!, earnings to price ~E0P!, or cash flow to price ~C0P! as value stocks. Fama and French ~1992, 1996! and Lakonishok, Shleifer, and Vishny ~1994! show that for U.S. stocks there is a strong value premium in average returns. High B0M, E0P, or C0P stocks have higher average returns than low B0M, E0P, or C0P stocks. Fama and French ~1995! and Lakonishok et al. ~1994! also show that the value premium is associated with relative distress.

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 addresses the following basic capital budgeting question: Suppose that crosssectional differences in stock returns can be predicted based on variables other than beta (e.g., book-to-market), and that this predictability reflects market irrationality rather than compensation for fundamental risk. In this setting, how should companies determine hurdle rates? I show how factors such as managerial tune horizons and financial constraints affect the optimal hurdle rate. Under some circumstances, beta can be useful as a capital budgeting tool, even if it is of no use in predicting stock returns.