Regime switching models have been assuming a central role in financial applications because of their well-known ability to capture the presence of rich non-linear patterns in the joint distribution of asset returns. This paper examines how the presence of regimes in means, variances, and correlations of asset returns translates into explicit dynamics of the Markowitz mean-variance frontier. In particular, the paper shows both theoretically and through an application to international equity portfolio diversification that substantial differences exist between bull and bear regime-specific frontiers, both in statistical and in economic terms. Using Morgan Stanley Capital International (MSCI) investable indices for five countries/macro-regions, it is possible to characterize the mean-variance frontiers and optimal portfolio strategies in bull periods, in bear periods, and in periods where high uncertainty exists on the nature of the current regime. A recursive back-testing exercise shows that between 1998 and 2010, adopting a switching mean-variance strategy may have yielded considerable risk-adjusted payoffs, which are the largest in correspondence to the 2007-2009 financial crisis.