Nonparametric Tail Risk, Stock Returns and the Macroeconomy

Abstract

This paper introduces a new tail risk measure based on the risk-neutral excess expected shortfall of a cross-section of stock returns. We propose a novel way to risk neutralize the returns without relying on option price information. Empirically, we illustrate our methodology by estimating a tail risk measure over a long historical period based on a set of size and book-to-market portfolios. We find that a risk premium is associated with long-short strategies with portfolio sorts based on tail risk sensitivities of individual securities. Our tail risk index also provides meaningful information about future market returns and aggregate macroeconomic conditions. Results are robust to the cross-sectional information selected to compute the tail risk measure.

Keywords: Tail Risk, Risk Factor, Risk-Neutral Probability, Prediction of Market Returns, Economic Predictability

JEL Classification: G12, G13, G17