Segregating Continuous Volatility from Jumps in Long-Run Risk-Return Trade-Offs

Abstract

We provide a multi-horizon characterization of the strength of the relationship between market realized variance components, namely continuous volatility and jump, and future market excess return. Building on quadratic variation theory, we find that continuous volatility is a key driver of medium/long-run risk-return trade-offs while jumps lack predictive power to explaining the time variation in medium/long-term excess return. We use inference methods that are robust to persistent predictor in a multi-horizon setup. Specifically, we show that rescaled versions of the usual test statistics converge to non-degenerate distributions in our local-to-unity framework. This study yields evidence supporting a proportional risk-return linkage when jumps are extracted from the quadratic variation activity.

Keywords: stock return predictability, continuous volatility, jumps, long-run, realized volatility

JEL Classification: G12