The market portfolio may be mean/variance efficient after all

Numerous studies have examined the mean/variance efficiency of various market proxies by employing sample parameters and have concluded that these proxies are inefficient. These findings cast doubt about the capital asset pricing model (CAPM), one of the cornerstones of modern finance. This study adopts a reverse-engineering approach: given a particular market proxy, we find the minimal variations in sample parameters required to ensure that the proxy is mean/variance efficient. Surprisingly, slight variations in parameters, well within estimation error bounds, suffice to make the proxy efficient. Thus, many conventional market proxies could be perfectly consistent with the CAPM and useful for estimating expected returns.