On the Estimation of Systematic Downside Risk

Abstract

This paper discusses the appropriate methodology for the estimation of systematic downside risk. I find that the Hogan & Warren (1974) approach is the only one of several specifications of downside beta, that is consistent with both the original downside risk framework, as defined by Markowitz (1959), and state-preference theory. Empirically, the HW downside beta dominates both its unconditional counterpart and the alternative specifications of downside beta, suggesting that the role of downside risk has been greatly underestimated in the past literature. Additionally, as opposed to unconditional beta, HW downside beta (i) predicts significantly larger slopes and non-significant intercepts in portfolio cross-sectional tests that are consistent with theory and (ii) is not subsumed by size and changes in market value of equity, that drive the priced component of book-to-market [Gerakos and Linnainmaa (2012)]. The results indicate that downside beta has increased ability in capturing distress risk, which can account for its superior empirical performance.

Keywords: Downside risk, Downside beta, Asset pricing

JEL Classification: C21, G11, G12