Risk factor extraction with quantile regression method

Firm characteristics based risk factors constitute a large part of the asset pricing literature. These characteristic based factors are constructed using the extreme quantiles of the sorted portfolios based on the firm characteristic in question. Yet to date, there is no consensus on a systematic approach to determine the optimal quantile used for extracting firm characteristic based risk factors. In addition, it is a stylised fact that asset prices exhibit heteroscedastic behavior, and counting on the extreme portfolios to extract the characteristic factors can produce unexpected result. In this study, we use quantile regressions to determine the optimal quantiles used in portfolios sorts to extract characteristic based risk factors used in asset pricing. Quantile regressions are well-suited to identify the quantiles needed to extract firm characteristic based factors, especially when the firm characteristic based factors and stock returns relationship is non-linear. More over, quantile regressions presents the quantile-by-quantile risk-return coefficients, thereby verifying the behavior of the extreme quantiles used in the factor construction. By examining the relationship between common characteristic based factors and stock returns in 23 developed countries, we observed that the optimal quantiles used to construct the common factors may differ between factors, but is similar across the North American, Asia-Pacific and Europe regions.