Evaluation of portfolio returns in fama-french model using quantile regression under asymmetric laplace distribution

Abstract

© Springer International Publishing Switzerland 2015. We applied the method of quantile regression under asymmetric Laplace distribution to predicting stock returns. Specifically, we used thismethod in the Fama and French three-factor model for the five industry portfolios to estimate the beta coefficient, which measure risk in the portfolios management analysis at given levels of quantile. In many applications, we are concerned with the changing effects of the covariates on the outcome across the quantiles of the distribution. Inference in quantile regression can be proceeded by assigning an asymmetric Laplace distribution for the error term. Finally, we use the method to measures the volatility of a portfolio relative to the market, size and value premium. It should be noted that a complete study of quantile regression models with various error distributions is of great interests for applications.