Using nonparametric techniques, we develop a methodology for estimating and testing conditional alphas and betas and long-run alphas and betas, which are the averages of conditional alphas and betas, respectively, across time. The estimators and tests can be implemented for a single asset or jointly across portfolios. The traditional Gibbons, Ross, and Shanken (1989) test arises as a special case of no time variation in the alphas and factor loadings and homoskedasticity. As applications of the methodology, we estimate conditional CAPM and multifactor models on book-to-market and momentum decile portfolios. We reject the null that long-run alphas are equal to zero even though there is substantial variation in the conditional factor loadings of these portfolios.

We investigate the leverage of hedge funds in the time series and cross-section. Hedge fund leverage is counter-cyclical to the leverage of listed financial intermediaries and decreases prior to the start of the financial crisis in mid-2007. Hedge fund leverage is lowest in early 2009 when the market leverage of investment banks is highest. Changes in hedge fund leverage tend to be more predictable by economy-wide factors than by fund-specific characteristics. In particular, decreases in funding costs and increases in market values both forecast increases in hedge fund leverage. Decreases in fund return volatilities predict future increases in leverage.

Using only the definition of returns, together with a transversality assumption, we demonstrate that given a dividend process, any one of three variables—expected return, return volatility, and the price–dividend ratio—completely determines the other two. By parameterizing only one of these processes, common empirical specifications place strong, and sometimes counter-factual, restrictions on the dynamics of the other variables. Our findings lend insight into the nature of the risk–return relation and the predictability of stock returns.

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.

Stocks with recent past high idiosyncratic volatility have low future average returns around the world. Across 23 developed markets, the difference in average returns between the extreme quintile portfolios sorted on idiosyncratic volatility is -1.31% per month, after controlling for world market, size, and value factors. The effect is individually significant in each G7 country. In the United States, we rule out explanations based on trading frictions, information dissemination, and higher moments. There is strong covariation in the low returns to high-idiosyncratic-volatility stocks across countries, suggesting that broad, not easily diversifiable factors lie behind this phenomenon.