Correlations between U.S. stocks and the aggregate U.S. market are much greater for downside moves, especially for extreme downside moves, than for upside moves. We develop a new statistic for measuring, comparing, and testing asymmetries in conditional correlations. Conditional on the downside, correlations in the data differ from the conditional correlations implied by a normal distribution by 11.6%. We find that conditional asymmetric correlations are fundamentally different from other measures of asymmetries, such as skewness and co-skewness. We find that small stocks, value stocks, and past loser stocks have more asymmetric movements. Controlling for size, we find that stocks with lower betas exhibit greater correlation asymmetries, and we find no relationship between leverage and correlation asymmetries. Correlation asymmetries in the data reject the null hypothesis of multivariate normal distributions at daily, weekly, and monthly frequencies. However, several empirical models with greater flexibility, particularly regime-switching models, perform better at capturing correlation asymmetries.

We develop a stock market model with differences of opinion and short-sales constraints. When breadth is low—i.e., when few investors have long positions—this signals that the short-sales constraint is binding tightly, and that prices are high relative to fundamentals. Thus reductions in breadth should forecast lower returns. Using data on mutual fund holdings, we find that stocks whose change in breadth in the prior quarter is in the lowest decile of the sample underperform those in the top decile by 6.38% in the twelve months after formation. Adjusting for size, book-to-market, and momentum, the figure is 4.95%.

We develop a series of cross-sectional regression specifications 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, consistent with the model of Hong and Stein (NBER Working Paper, 1999), and (2) positive returns over the prior 36 months, which fits with a number of theories, most notably Blanchard and Watson's (Crises in Economic and Financial Structure. Lexington Books, Lexington, MA, 1982, pp. 295–315) rendition of stock-price 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.