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The capital asset pricing model (CAPM) has played a significant role in modern portfolio theory for decades. The innovative work of Sharpe (1964), Lintner (1965), Mossin (1966) and Black (1972) brought together a model that ‘embodies a theory of what can be inferred about expected returns when markets are in equilibrium, homogeneous expectations prevail and when all investors pursue a mean-variance optimizing objective’ (Van Rensburg & Robertson 2003:7). However, literature has shown that there are several empirical contradictions of the so-called SharpeLintner-Black (SLB) model, brought about by the assumptions that expected returns are a positive linear function of market betas and that market betas are sufficient to describe the cross-section of expected returns (Fama & French 1992). The most prominent contradiction of the SLB model is reported by Banz (1981), who found that the size effect contributes to the ability of market betas to explain the cross-section of average returns. Another contradiction can be found in the work of Bhandari (1988), who reported a positive relationship between average returns and leverage. Although the SLB model assumes that leverage risk should already be captured by the market beta, Bhandari (1988) found that including leverage in a model (which already accounts for market size and beta) improves the explanation of average share returns. Further studies also found evidence to support the book-to-market ratio (B/M); the price-to-earnings ratio (P/E); the return-on-equity ratio (ROE); the DuPont model to overcome the shortcomings of the ROE ratio (Berzkalne & Zelgalve 2014; Traub 2001); the dividend yield (DY); the implied dividend growth rate; the cash-flow-to-price ratio; and the price-to-net asset value (NAV) ratio as additional ‘blanket’ proxies for unnamed risk factors that can enhance the explanation of average share returns (see, for example, Asness, Porter & Stevens 2000; Auret & Cline 2011; Auret & Sinclaire 2006; Basiewicz & Auret 2010; Basu 1983; Chan, Hamao & Lakonishok 1991; Fama & French 2017; Hoffman 2012; Hou, Karolyi & Kho 2011; Johannes, Korteweg & Polson 2014; Lakonishok, Shleifer Background: Using financial ratios is considered to be important when making informed judgments about investment portfolios. However, the ‘ideal’ set of ratios is an elusive notion on which the literature has failed to reach any consensus.

Re-examining the ability to explain future South African banking share returns: A data envelopment analysis approach