We conduct a comprehensive comparison of market beta estimation techniques. We study the performance of several historical, time-series model, and option-implied estimators for estimating realized market beta. Thereby, we find the hybrid methodology of Buss and Vilkov to consistently outperform all other approaches. In addition, all other approaches, including fully implied and dynamic conditional beta, based on generalized autoregressive conditional heteroskedasticity (GARCH) models, are dominated by a simple beta estimate based on historical (co-)variances and an approach based on the Kalman filter. Our conclusions remain unchanged after performing several robustness checks.

Researchers and practitioners face many choices when estimating an asset's sensitivities toward risk factors, i.e., betas. Using the entire U.S. stock universe and a sample period of more than 50 years, we find that a historical estimator based on daily return data with an exponential weighting scheme as well as simple shrinkage adjustments yield the best predictions for future beta. Adjustments for asynchronous trading, macroeconomic conditions, or regression-based combinations, on the other hand, typically yield very high prediction errors and fail to create market-neutral anomaly portfolios. Finally, we document a robust link between stock characteristics and beta predictability.

When using high-frequency data, the conditional capital asset pricing model (CAPM) can explain asset-pricing anomalies. Using conditional betas based on daily data, the model works reasonably well for a recent sample period. However, it fails to explain the size anomaly as well as three out of six of the anomaly component excess returns. Using high-frequency betas, the conditional CAPM is able to explain the size, value, and momentum anomalies. We further show that high-frequency betas provide more accurate predictions of future betas than those based on daily data. This result holds for both the time-series and the cross-sectional dimensions. This paper was accepted by Karl Diether, finance.

A stylized theoretical model with stochastic volatility suggests the existence of a trade-off between returns and volatility-of-volatility. Using the VVIX index as empirical measure, 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 a two-standard deviation increase in aggregate volatility-of-volatility factor loadings to be associated with a decrease in average annual returns of about 11%. This phenomenon cannot be explained by aggregate volatility, jump risk, and several other characteristics and factor sensitivities, or by a crisis effect.

We examine the pricing of tail risk in international stock markets. We find that the tail risk of different countries is highly integrated. Introducing a new World Fear index, we find that local and global aggregate market returns are mainly driven by global tail risk rather than local tail risk. World fear is also priced in the crosssection of stock returns. Buying stocks with high sensitivities to World Fear while selling stocks with low sensitivities generates excess returns of up to 2.72% per month.