Understanding Negative Risk-Return Trade-offs

Abstract

Recent literature documents a hump-shaped response where equity and variance risk premia initially decrease with stock market variance before subsequently increasing. I find that large volatility spikes are the primary drivers behind these patterns. Once isolating away the impact of these spikes, market volatility significantly and positively predicts both risk premia, with coefficients that decay almost exponentially, aligning with leading asset pricing theories. A nested-model test suggests that these spikes may indicate structural breaks rather than transitory jumps. I develop a tractable belief-formation model, in which two types of volatility shocks, transitory and structural, drive a recency-biased parameter learner to react differently. The model successfully captures the time-varying relations between volatility and risk premia, and many other stylized facts, including a time-invariant positive correlation between equity and variance risk premium, a robust leverage effect, and negative observations of short-horizon equity and variance risk premia at crisis onsets. The model has other empirical support.

Keywords: Equity Premium, Variance Risk Premium, Time-Varying and Time-Invariant Predictability, Parameter Learning, Parameter Breaks

JEL Classification: G00, G10, G12, G13