This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962–1997 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, whereas the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.

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Understanding volatility in emerging capital markets is important for determining the cost of capital and for evaluating direct investment and asset allocation decisions. We provide an approach that allows the relative importance of world and local information to change through time in both the expected returns and conditional variance processes. Our time-series and cross-sectional models analyze the reasons that volatility is different across emerging markets, particularly with respect to the timing of capital market reforms. We find that capital market liberalizations often increase the correlation between local market returns and the world market but do not drive up local market volatility.

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

We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describt tbe process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: 1) positive correlation between conditional volatility and volume, 2) large price movements are followed by high volume, 3) conditioning on lagged volume substantially attenuates the "leverage " effect, and 4) after conditioning on lagged volume, there is a positive risk/return relation.

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

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Abstract: This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of cross-sectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: 1) an increase in trading volume relative to trend over the prior six months; and 2) positive returns over the prior thirty-six months. The first finding is consistent with the model of Hong and Stein (1999), which predicts that negative asymmetries are more likely to occur when there are large differences of opinion among investors. The latter finding fits with a number of theories, most notably Blanchard and Watson’s (1982) rendition of stockprice bubbles. Analogous results also obtain when we attempt to forecast the skewness of the aggregate stock market, though our statistical power in this case is limited.

This paper uses the Specific-to-General methodological approach that is widely used in science, in which problems with existing theories are resolved as the need arises, to illustrate a number of important developments in the modelling of univariate and multivariate financial volatility. Twenty frequently arising issues in analysing timevarying univariate and multivariate conditional volatility and stochastic volatility are discussed. In view of some of these difficulties, including the number of parameters to be estimated, and the computational complexities associated with multivariate conditional volatility models and both univariate and multivariate stochastic volatility models, automated inference is argued to be unhelpful to modelling in empirical financial econometrics. Some suggestions for future research are also presented. *The author wishes to acknowledge helpful discussions with Manabu Asai, Massimiliano

It has been previously documented that individual firms stock return volatility rises after stock prices fall. This paper finds that this statistical relation is largely due to a positive contemporaneous relation between firm stock returns and firm stock return volatility. This positive relation is strongest for both small fnms and firms with little financial leverage. At the aggregate level, the sign of this contemporaneous relation is reversed. The reasons for the difference between the aggregate- and firm-level relations are explored.