Rethinking Asset Pricing with Quantile Factor Models

Abstract

Traditional empirical asset pricing focuses on the average cases. We propose a new approach to analyze the cross-section of the returns. We test the predictive power of market-beta, size, book-to-market ratio, profitability, investment, momentum, and liquidity, across the whole conditional distribution of market returns. Our results indicate that the relevant characteristics to explain the winners􀂶 tail, the losers􀂶 tail and the center of the distribution, in a given period, differ. Indeed, some characteristics can be discarded from our specification if our main interest is to model expected extreme losses (such as traditional momentum), and some others should be kept even if they do not seem particularly significant for the average scenario, because they become significant at the tails (such as size). Book-to-market is mainly a left tail factor, in the sense that it explains to a greater extent the loser􀂶s tail than either the center or the tail of the winners. On the contrary, liquidity and investment are right-tail factors, because they explain in greater proportion the winners􀂶 tail than the rest of the distribution. Market beta is relevant throughout the whole cross-section, but affect winners and losers in diametrically opposite ways (the effect is positive on the right tail and negative on the left tail). We show that the practice of adding characteristics to our pricing equation should be clearly informed by our particular interests regarding the cross-sectional distribution of the returns, that is, whether we are more interested in a certain fragment of the distribution than in other parts. Our results emphasize the need to consider carefully what factors to include in the pricing equation, which depends on the dynamics that one wants to understand and even on one attitude towards risk. In short, not all factors serve all purposes