An optimal weighting scheme is proposed to construct economic, political and financial risk indices in emerging markets using an approach that relies on consistent tests for stochastic dominance efficiency. These tests are considered for a given risk index with respect to all possible indices constructed from a set of individual risk factors. The test statistics and the estimators are computed using mixed integer programming methods. We derive an economic, political and financial risk ranking of emerging countries. Finally, an overall risk index is constructed. One main result is that the financial risk is the leading contributor to sovereign risk in emerging markets followed by the economic and political risks.