Mean-variance versus naïve diversification: The role of mispricing

Abstract

We compare the equal-weight naïve 1/N portfolio with mean-variance strategies from the perspective of mispricing (alpha) and provide three new findings. First, we analytically show that the 1/N rule approaches the ex ante mean-variance efficient portfolio in the absence of mispricing. With mispricings, mean-variance strategies can overcome the difficulty brought by the imprecise parameter estimates and outperform 1/N by exploiting the mispricing. Second, with mispricings the 1/N rule is unlikely to outperform mean-variance strategies even when N is large, since mean-variance strategies have more opportunities to exploit mispricings. Third, minimum-variance strategies do not exploit mispricings and underperform the 1/N rule.