Understanding Negative Risk-Return Trade-offs

Abstract

Recent literature documents a puzzle where monthly equity and variance risk premia initially decrease with realized volatility before subsequently increasing. I classify volatility news in the data into three types: small transitory shocks, large transitory jumps, and large persistent structural shocks. In 30 years of data from 1990 to 2019, 9 large structural shocks occurring across 42 months almost entirely explain the puzzle. When these months are excluded, (realized and implied) volatility predicts both risk premia with exponentially decreasing coefficients, remarkably consistent with standard asset pricing theories. I explain the evidence within a model in which two types of volatility shocks, transitory and structural, drive a fading-memory parameter learner and risk premia to react differently in equilibrium.

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

JEL Classification: G00, G10, G12, G13