In this paper, we evaluate the performance of different mean-variance portfolios, relative to the na?ve "1/n portfolio", that is investing equally on each of n assets. A similar research was already conducted by Victor DeMiguel, Lorenzo Garlappi, and Raman Uppal in the paper "Optimal versus Naive Diversification: How Inefficient Is the 1/n Portfolio Strategy?". Nevertheless, we show that using a risk calibration and different test statistic to measure portfolio performance, we reach very different conclusions. We indeed show that Markowitz does outperform the na?ve 1/n portfolio and we present a method to maximize the out-of-sample performance of the Markowitz portfolio. We also show that when we add some maximum rebalancing constraints on the asset weights, the Markowitz model still outperforms the 1/n portfolio, and in addition becomes very robust. Finally, we apply this constrained mean-variance method to show that any portfolio can be improved upon.