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

Abstract

This paper introduces a new, hybrid measure of covariance risk in the lower tail of the stock return distribution, motivated by the under-diversified portfolio holdings of individual investors, and investigates its performance in predicting the cross-sectional variation in stock returns over the sample period July 1963-December 2009. Our key innovation is that the covariance is measured across the states of the world in which the individual stock return is in its left tail, not across the corresponding tail states for the market return as in standard systematic risk measures. The results indicate a positive and significant relation between what we label hybrid tail covariance risk (H-TCR) and expected stock returns, in contrast to the insignificant or negative results for purely stock-specific or standard systematic tail risk measures. A trading strategy that goes long stocks in the highest H-TCR decile and shorts stocks in the lowest H-TCR decile produces average raw and risk-adjusted returns of 6% to 8% per annum, consistent with results from a cross-sectional regression analysis that controls for a battery of known predictors.