Bear Beta or Speculative Beta?—Reconciling the Evidence on Downside Risk Premium

Abstract

This article develops a new approach to explain why risk factors constructed from index option returns are priced in the stock market. We decompose an option-based factor into three main components and identify the one responsible for the beta–return relationship. Applying this method to the bear risk factor proposed by Lu and Murray reveals that the negative correlation between bear betas and stock returns does not reflect systematic risk premia. Instead, it represents an anomaly closely related to the betting-against-beta puzzle. We trace the root of this anomaly to disagreement concerning the aggregate stock market. Our work reconciles the conflicting evidence concerning downside risk by showing that neither ex-post nor ex-ante downside risk is priced in the cross-section of stocks while making a methodological contribution that facilitates more accurate interpretation of option-based risk factors in future research.