Market e#ciency survives the challenge from the literature on long-term return anomalies. Consistent with the market e#ciency hypothesis that the anomalies are chance results, apparent overreaction to information is about as common as underreaction, and post-event continuation of pre-event abnormal returns is about as frequent as post-event reversal. Most important, consistent with the market e#ciency prediction that apparent anomalies can be due to methodology, most long-term return anomalies tend to disappear with reasonable changes in technique. # 1998 Elsevier Science S.A. All rights reserved.

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.

In a financially integrated global market, the conditionally expected return on a portfolio of securities from a particular country is determined by the country's world risk exposure. This paper measures the conditional risk of 17 countries. The reward per unit of risk is the world price of covariance risk. Although the tests provide evidence on the conditional mean variance efficiency of the benchmark portfolio, the results show that countries' risk exposures help explain differences in performance. Evidence is also presented which indicates that these risk exposures change through time and that the world price of covariance risk is not constant.

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

The value premium in U.S. stock returns is robust. The positive relation between average return and book-to-market equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers. A three-factor risk model explains the value premium better than the hypothesis that the book-tomarket characteristic is compensated irrespective of risk loadings. Firms with high ratios of book value to the market value of common equity have higher average returns than firms with low book-to-market ratios (Rosenberg, Reid, and Lanstein (1985)). Because the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) does not explain this pattern in average returns, it is typically called an anomaly. There are four common explanations for the book-to-market (BE/ME) anomaly. One says that the positive relation between BE/ME and average return (the so-called value premium) is a chance result unlikely to be observed out of sample (Black (1993), MacKinlay (1995)). Out-of-s...

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.

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We estimate and test the conditional version of an International Capital Asset Pricing Model using a parsimonious multivariate GARCH process. Since our approach is fully parametric, we can recover any quantity that is a function of the first two conditional moments. Our findings strongly support a model which includes both market and foreign exchange risk. However, both sources of risk are only detected when their prices are allowed to change over time. The evidence also indicates that, with the exception of the U.S. equity market, the premium for bearing currency risk often represents a significant

We investigate the portfolio choices of mean-variance-optimizing investors who use sample evidence to update prior beliefs centered on either risk-based or characteristic-based pricing models. With dogmatic beliefs in such models and an unconstrained ratio of position size to capital, optimal portfolios can differ across models to economically significant degrees. The differences are substantially reduced by modest uncertainty about the models ’ pricing abilities. When the ratio of position size to capital is subject to realistic constraints, the differences in portfolios across models become even less important, nonexistent in some cases.

INTRODUCTION The CBOE Market Volatility Index (VIX) is an average of S&P 100 option (OEX) implied volatilities. As such, it represents a market- consensus estimate of future stock market volatility. 1 The computation and dissemination of VIX on a real-time basis offers practitioners and academics an important new source of information. Practitioners, for This research was supported by the Futures and Options Research Center at the Fuqua School of Business, Duke University. We gratefully acknowledge the helpful comments and suggestions of Fischer Black, Mark Rubinstein, and two anonymous referees. We also thank participants at the University of Pennsylvania, the University of Texas at Dallas, and the University of Waterloo/KPMG Peat Marwick Thorne seminars, as well as attendees of the 1993 Conference on Financial Innovation: 20 Years of Black/Scholes and Merton (Duke University) and the 1994 Berkeley Program in Finance, Ojai Valley, California. Since OEX options are the mos