Hybrid Tail Risk and Expected Stock Returns: When Does the Tail Wag the Dog?

Abstract

We introduce a new, hybrid measure of stock return tail covariance risk, motivated by the under-diversified portfolio holdings of individual investors, and investigate its cross-sectional predictive power. Our key innovation is that this covariance is measured across the left tail states of the individual stock return distribution, not across those of the market return as in standard systematic risk measures. We document a positive and significant relation between hybrid tail covariance risk (H-TCR) and expected stock returns, with an annualized premium of 9%, in contrast to the insignificant or negative results for purely stock-specific or systematic tail risk measures.