![]() Average returns on small (low ME) stocks are too high given their β estimates, and average returns on large stocks are too low.Īnother contradiction of the SLB model is the positive relation between leverage and average return documented by Bhandari (1988). He finds that market equity, ME (a stock's price times shares outstanding), adds to the explanation of the cross-section of average returns provided by market βs. ![]() The most prominent is the size effect of Banz (1981). There are several empirical contradictions of the Sharpe-Lintner-Black (SLB) model. The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market βs (the slope in the regression of a security's return on the market's return), and (b) market βs suffice to describe the cross-section of expected returns. The central prediction of the model is that the market portfolio of invested wealth is mean-variance efficient in the sense of Markowitz (1959). T he asset-pricing model of Sharpe (1964), Lintner (1965), and Black (1972) has long shaped the way academics and practitioners think about average returns and risk.
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