JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS OL 30. NO. 1 MARCH 1995 The Conditional relation between Beta and Returns Glenn N. Pettengill, Sridhar Sundaram, and Ike Mathur* Abstract 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 egative market excess returns, we find a consistent and signifi lationship 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 1. Introduction The Sharpe-Lintner-Black(SLB)model, which is predicated on the assump- ion of a positive risk-return tradeoff, asserts that the expected return for any asset is a positive function of only three variables: beta( the covariance of asset return and market return), the risk-free rate, and the expected market return. This as sertion implies that an asset s responsiveness to general market movements is the only variable to cause systematic differences in returns between assets Empirical tests of this assertion, using average realized returns to proxy for expected returns and an index of equity security returns as a proxy for market returns, initially supported the validity of the SLB model(e.g, Fama and Mac- Beth(1973)). The usefulness of beta as the single measure of risk for a security has, however, been challenged by at least three arguments. First, research has challenged the notion that beta is the most efficient measure of systematic risk for individual securities. Thus, some researchers have argued in favor of measuring ystematic responsiveness to several macroeconomic variables(e. g, Chen, Roll, 5087: Mathur, College of Business and Administration, Southern llinois University at Carbondale, Carbondale, IL 62901, respectively. The authors thank Marcia Comett, Dave Davidson, John Doul Roger Huang, Santosh Mohan, Jim Musumeci, Lilian Ng, Edgar Norton, Nanda rangan, Andy Szak mary, participants of the Southwest Finance Symposium at the University of Tulsa, JFQA Managing Editor Jonathan Karpoff, and JFQA Referees Michael Pinegar and Alan Shapiro for he ments on earlier drafts of the paper. The authors also thank Shari Garnett and Pauletta Avery for their sistance in preparing the manuscript