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Unlike previous studies, this paper finds a consistent and highly significant relationship between beta and cross-sectional portfolio returns. The key distinction between our tests and previous tests is the recognition that the positive relationship between returns and beta predicted by the Sharpe-Lintner-Black model is based on expected rather than realized returns. In periods where excess market returns are negative, an inverse relationship between beta and portfolio returns should exist. When we adjust for the expectations concerning negative market excess returns, we find a consistent and significant relationship between beta and returns for the entire sample, for subsample periods, and for data divided by months in a year. Separately, we find support for a positive payment for beta risk.
Pettengill et al. (Wed,) studied this question.