Robust Measurement of Size and Book-to-Market Premia

Abstract

In this paper we use the quantile regression to analyze size and book-to-market effects on the conditional distribution of stock returns. In contrast with Knez and Ready (1997), the quantile regression can obtain more robust results without trimming informative extremes. We find that size and book-to-market exhibits asymmetric effects on return quantiles. Comparing with Fama and French (1992), the negative relation between size and returns only occurs in stocks that performs well above the average (winners). However, the robust measurements show that size has positive effects on returns. The book-to-market premium has similar influences on return quantiles and is a more consistent risk factor than size does. We also find that the size and book-to-market effects on the tails of the return distribution may have changed since 1982. Our results provide practical implications on momentum strategies.