A stylized theoretical model with stochastic volatility suggests the existence of a trade-off between returns and volatility-of-volatility. Using the VVIX, a measure of the option-implied volatility of the volatility index, we confirm this prediction and detect that time-varying aggregate volatility-of-volatility commands an economically substantial and statistically significant negative risk premium. We find that a two-standard-deviation increase in aggregate volatility-of-volatility factor loadings is associated with a decrease in average annual returns of about 11%. These results are robust to controlling for aggregate volatility, jump risk, and several other characteristics and factor sensitivities, as well as various additional tests.

We study the relation between hedge fund equity holdings and measures of informational efficiency of stock prices derived from intraday transactions as well as daily data. Our findings support the role of hedge funds as arbitrageurs who reduce mispricing in the market. Hedge funds invest in stocks that are relatively inefficiently priced, and the price efficiency of these stocks improves after hedge funds increase their holdings. Hedge fund ownership contributes more to efficient pricing than ownership by other types of institutional investors. However, stocks held by hedge funds experienced large declines in price efficiency during several liquidity crises.Received July 27, 2016; editorial decision January 07, 2017 by Editor Wayne Ferson.

We use bootstrap simulations to examine the properties of long-horizon U.S. stock market returns. We document the rate at which continuously compounded market returns converge toward normal distributions as we extend the horizon from 1 month to 30 years, and the rate at which dollar payoffs converge toward lognormal. We also verify that, though largely irrelevant at short horizons, uncertainty about the expected market return has a substantial impact on uncertainty about long-horizon payoffs.

Using hedge funds’ holdings of IPO stocks, we find that stocks with abnormally high hedge fund holdings, based on stock and deal characteristics, yield abnormal returns. Moreover, hedge funds are able to sell IPO stocks in a timely fashion before long-run underperforming periods start, suggesting that hedge funds possess information advantages in IPO stocks. Finally, we address the question of where hedge funds may have obtained their information advantages. Hedge funds earn higher abnormal returns in “connected” stocks when their prime brokers also serve as IPO underwriters, indicating that such connections enable hedge funds to make more informed investment decisions in IPO stocks. Received December 31, 2014; editorial decision May 27, 2017 by Editor Wayne Ferson.

We nest multiple volatility components, fat tails, and a U-shaped pricing kernel in a single option model and compare their contribution in describing returns and option data. All three features lead to statistically significant model improvements. A U-shaped pricing kernel is economically most important and improves option fit by 17%, on average, and more so for two-factor models. A second volatility component improves the option fit by 9%, on average. Fat tails improve option fit by just over 4%, on average, but more so when a U-shaped pricing kernel is applied. Overall, these three model features are complements rather than substitutes: the importance of one feature increases in conjunction with the others.

Twitter posts covering 1,082 firms from November 2008 to June 2011 reveal that sentiment in nonlocal Twitter posts is negatively related to future returns, and this negative relation is due to nonlocal posts favoring overpriced stocks, which earn lower subsequent returns. In contrast, local posts do not exhibit this failing. Since nonlocal posts dominate social media, this result highlights the danger of a naive reliance on social media sentiment. The nonlocal disadvantage is larger for firms without public news and firms with higher information asymmetry, suggesting that richer information constrains the exuberance of nonlocal investors.

We show that an increase in a stock’s breadth of institutional ownership or turnover is followed by a significant, but temporary, increase in its CAPM beta estimate and a decrease in its CAPM alpha. The increasing effect of breadth of ownership on beta estimates is mainly driven by short-term investors. These transitory trading-activity-driven components of beta estimates contribute to the empirical failure of the CAPM and the large returns to long-short portfolios that bet against beta. Relations between ownership breadth, turnover, and betas, which we document, help explain the puzzling fact that, on average, betas increase after seasoned equity offerings and stock splits and decrease after stock repurchases.Received November 26, 2015; editorial decision February 17, 2017 by Editor Jeffrey Pontiff.

We evaluate the performance of various methods for estimating factor returns in an approximate factor model. Differences across estimators are most pronounced when there is cross-sectional heteroscedasticity or when cross-sectional sample sizes, n, have fewer than 4,000 assets. Estimators incorporating either cross-sectional or time-series heteroscedasticity outperform the other estimators when those types of heteroscedasticity are present. The differences are most pronounced when the cross-sectional sample is small. Received December 2, 2015; editorial decision May 16, 2017 by Editor Jeffrey Pontiff.

A simple general equilibrium production economy matches moments of the value premium and equity premium. Value firms have low productivity, but will eventually produce high cash flows. The present value of these temporally distant cash flows is especially sensitive to equity premium movements. The value premium is the reward for bearing this sensitivity. Capital adjustment costs are important. Without these costs, value firms would disinvest heavily, leading to high cash flows today, low cash-flow growth going forward, and little exposure to discount rate shocks. Empirical evidence verifies that value firms have higher cash-flow growth and supports other predictions.

Do stocks bear a crash risk premium? We examine the empirical performance of the tail index measure from Kelly and Jiang (2014). We find that the tail index explains the cross-section of the discount rate component of returns, but not the cash-flow component. Moreover, in the time series the tail index is uncorrelated with theoretically motivated measures of aggregate uncertainty and systemic risk. In contrast, the tail index Granger causes and is Granger caused by the level of the term structure, and the slope of the term structure Granger causes tail risk. Received June 22, 2016; editorial decision December 23, 2017 by Editor Raman Uppal.