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

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.