This paper examines properties of mean-variance inefficient proxies with respect to producing a linear relation between expected returns and betas. The numerical results of a Monte Carlo simulation show that in the CAPM slightly inefficient, positively weighted proxies cause an almost perfect linear expected return - beta relation. Moreover, we show that a strong linearity among a predefined subset of assets exists. These implications are important for the interpretation of empirical tests as well as for asset pricing and for the improvement of proxies' benchmark properties. In contrast to current literature the results suggest that the CAPM's pricing error is small when slightly inefficient, positively weighted proxies are used.