Modified Beta and Cross-Sectional Stock Returns

There exist many anomalous relationships between firm characteristics and average asset returns which are inconsistent with the predictions of the Capital Asset Pricing Model (CAPM). The size and value effects are two such well known empirical anomalies (see Fama and French, 1992, 1993). The size effect posits that firms with low market capitalizations have higher average returns than firms with high market capitalizations, whereas the value effect demonstrates that firms with high book-to-market ratios have higher average returns than firms with low book-to-market ratios. Both of these observations are at odds with the maintained hypothesis of the CAPM, as the CAPM beta alone cannot explain these anomalies.In this paper we show that the failure of the CAPM beta may lie in the fact that the standard beta across all markets does not account for up and down market scenarios individually. We estimate equity betas in up versus down markets in time series regressions, and we then compare the predictive power for cross-sectional asset returns of the CAPM beta, beta from up markets, beta from down markets, and two modified betas based on scaling the CAPM beta by the Up/Down betas. The CAPM beta scaled by the ratio of Up beta to Down beta (or Modified beta) outperforms the traditional CAPM beta with respect to predictive power in Fama-French tests. It also outperforms in those cross-sectional tests when partitioning into up and down markets, as in Pettengill, Sundaram, and Mathur (1995)