Does the Tail Wag the Market : Measuring and Pricing Systematic Tail Risk in the Cross-Section of U.S Equity Returns

Sammanfattning

We examine the systematic tail risk pricing puzzle by replicating the measures used by Stoja et al. (2023), in which the tail beta fails to earn a cross-sectional premium, whereas the simpler tail dependence measure does, contradicting predictions from behavioural finance and safety-first theory. We use NYSE equity data from 1981 to 2026 to test whether this puzzle reflects investor indifference to the magnitude of crashes or a measurement artifact. The analysis utilizes Fama-MacBeth regressions, a common-features test, and a copula-based tail-dependence measure. The results show that the puzzle replicates and that the components of the tail beta measure exhibit offsetting dynamics with the copula measure earning a significant premium. The evidence supports the interpretation that the failure of the tail beta measure is driven by a measurement artifact.