We consider the global portfolio of privatized state assets from 1985 to 2012 in the non-parametric decision-making context of Stochastic Dominance Efficiency for broad classes of investor preferences. We estimate all possible portfolios in the context of Strategic vs non-Strategic and Cyclical vs non-Cyclical asset allocations that dominate the market benchmark and provide a complete efficiency ranking. The optimal solutions are computed using linear and mixed integer programming formulations. Dominant portfolios tend to overweight non-Cyclical and non-Strategic assets, while rotation may take place across business cycles. Bayesian investment style return attribution analysis, based on Monte Carlo Integration, suggests that Growth drives returns during the first business cycle, rotating to a balanced mix of styles with Size and Debt Leverage during the second business cycle and finally to Size during the last business cycle. Value is found to be the least influential style in all periods.