This paper expands upon "Toward Maximum Diversification", a 2008 paper by Choueifaty and Coignard (Journal of Portfolio Management 35(1), 40-51). We present new mathematical properties of the diversification ratio and most diversified portfolio (MDP), and investigate the optimality of the MDP in a mean-variance framework. We also introduce a set of "portfolio invariance properties", providing the basic rules an unbiased portfolio construction process should respect. In the light of these rules, theMDPis then compared with popular methodologies (equal weights, equal risk contribution, minimum variance), and their performance is investigated over the past decade, using the MSCI World as the reference universe. We believe that the results obtained in this paper show that the MDP is a strong candidate for being the undiversifiable portfolio, and as such delivers investors the full benefit of the equity premium.