Payment For Risk: Constant Beta Vs. Dual‐Beta Models

Abstract

Fama and French’s (1992) assertion that investors receive premium payments for risk associated with the book value to market price (BE/ME) and size and not for holding beta risk has sparked a lively debate concerning risk factors that are priced in the market. Howton and Peterson (1998) use a dual‐beta model to test the Fama and French conclusions. They conclude that the significant relationship between beta and returns depends on the use of the dual‐beta model. This work, however, ignores the results reported by Pettengill, Sundaram, and Mathur (PSM, 1995). PSM find a significant relation between a constant risk beta and returns when data are segmented between up and down markets, but do not consider the impact of size and BE/ME. In this paper we show that the PSM (1995) market segmentation procedure alone provides a sufficient condition to identify a significant relation between beta and returns in the presence of size and BE/ME. Dual market betas may be relevant in explaining risk and return. However, the market segmentation procedure of PSM (1995) is the critical condition for finding a significant relationship between returns and betas.