Testing and comparing conditional risk‐return relationship with a new approach in the cross‐sectional framework

Abstract

This paper presents an innovative approach in examining the conditional relationship between beta and returns for stocks traded on S&P 500 for the period from July 2001 to June 2011. We challenge other competitive models with portfolios formed based on the book value per share and betas using monthly data. A novel approach for capturing time variation in betas whose pattern is treated as a function of market returns is developed and presented. The estimated coefficients of a nonlinear regression constitute the basis of creating a two factor model. Our results indicate that the proposed specification surpasses alternative models in explaining the cross-section of returns. The implications of this study show that the proposed new risk factors that found to be significant both in time series and cross-section analyses provide valuable information in better understanding the characteristics of returns, targeting the reinforcement of stock market efficiency, and the capital allocation procedure.