Moving Beyond the Mean: Explaining the Cross-Sectional Tails with Firms’ Characteristics

Abstract

Empirical asset pricing focuses on the average cases. We propose a complementary approach to analyze the cross-section of returns based on quantile regression. With data from the U.S. market, we show that market-beta, size, book-to-market ratio, investment, momentum and liquidity have a different effect across the entire conditional distribution of market returns. Our results emphasize the need to consider carefully what factors are relevant to understand asset price movement under risk regimes relatively distant from the average representation described by a pricing equation, depending on whether one’s attitude to risk is focused on the winners’ or the losers’ tail. In short, not all explanatory variables serve all purposes, while some are better for pricing other are for risk analysis.

Keywords: factor models, asset characteristics, tail-risks, quantile regression