Cross-sectional regression of returns on betas and portfolio grouping procedures Online publication date: Sat, 07-Jun-2014
by Jungshik Hur; Raman Kumar; Vivek Singh
International Journal of Business and Systems Research (IJBSR), Vol. 8, No. 1, 2014
Abstract: This paper shows that the deviation of the estimated coefficient of beta from the market risk premium in cross-sectional regression of returns on betas is a direct consequence of the cross-sectional relation between the estimated alphas and betas. Therefore, the portfolio grouping procedure results in systematic cross-sectional relationship between the alphas and betas, causing a deviation in the estimated coefficient of beta in either direction. When firm size is used as the only portfolio grouping variable (Table AI in Fama and French, 1992), the estimated alphas and betas across portfolios are positively related, causing the estimated coefficient of beta to be upwardly biased. However, when beta is used as the only portfolio grouping variable (Table 2 in Kothari et al., 1995), the estimated alphas and betas across portfolios are negatively related, causing the estimated coefficient of beta to be downward biased. We show that forming portfolios on alphas and betas independently can adequately control for this deviation.
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