Disentangling Continuous Volatility from Jumps in Long-Run Risk–Return Relationships

Realized variance can be broken down into a continuous volatility and a jump components. We show that these two components have very different degrees of power of prediction on future long-term excess stock market returns. Namely, continuous volatility is a key driver of medium to long-term risk–return relationships. In contrast, jumps do not predict future medium or long-term excess returns. We use inference methods that are robust to persistent predictors in a multi-horizon setup. Specifically, we use a rescaled Student-t to test for significant risk–return relationship and simulate its exact behavior under the null in the case of multiple regressors with different levels of persistence. We also perform tests of equality of the risk–return relationship at multiple horizons. We do not find evidence against a proportional relationship between long-term continuous volatility and future returns.