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

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.