We propose a new decomposition of the realized covariance matrix into components based on the signs of the underlying high-frequency returns. Under an asymptotic setting in which the sampling interval goes to zero, we derive the asymptotic properties of the resulting realized semicovariance...

Equal compensation across assets for the same risk exposures is a bedrock of asset pricing theory and empirics. Yet real-world frictions can violate this equality and create high-Sharpe ratio opportunities. We develop new methods for asset pricing with cross-sectional heterogeneity in...

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR,...