Abstract
High-frequency events are valuable source of statistics on rare events. We show that the difference between the upside tail volatility and downside tail volatility of intraday price dynamics carries a significant fraction of the time-series variation in returns. We term this difference the tail asymmetry risk premium. To isolate the tail asymmetry risk premium, we develop a new approach for decomposing realized volatility. We use a vector autoregressive (VAR) model to uncover that the tail asymmetry risk premium is the sole part of the realized volatility that predicts a nontrivial part of the subsequent month's market return. Using intraday S&P 500 index returns from 1986 to 2010, our analysis suggests that the tail asymmetry risk premium is a strong predictor of monthly market returns and is robust against other well-known price measures such as the variance risk premium or the price dividend ratio.