Conditional Covariance of Risky and Risk-Free Assets

This paper examines how the covariance between stock and bond returns changes with respect to market volatility. First, we establish a set of stylized facts that describe the qualitative nature of this relationship, and the existence of a Tail Risk in the conditional distribution. We construct an asset pricing model that replicates and explains this relationship in the context of a CRRA utility maximization model. The empirical strategy used is a non-parametric approach to the task of conditional covariance measurement. We observe that covariances between stock and bond returns are decreasing with respect to market volatility up to a certain point, after which they begin increasing. This non-monotonic relationship is a consequence of how this covariance is driven by two opposing forces that we derive in the theoretical model: macroeconomic risk, which drives covariances up, and asset reallocation, which drives covariances down.