We propose a novel regime-switching model to study correlation asymmetries in international equity markets. We decompose returns into frequent-but-small diffusion and infrequent-but-large jumps and derive an estimation method for many countries. We find that correlations due to jumps, not diffusion, markedly increase in bad markets, leading to correlation breaks during crises. Our model provides a better description of correlation asymmetries than do GARCH, copula, and stochastic volatility models. Good and bad regimes are persistent. Regime changes are detected rapidly, and risk diversification allocations are improved. Asset allocation results in- and out-of-sample are superior to other models, including the 1/N strategy. Received September 26, 2015; accepted May 25, 2016 by Editor Wayne Ferson.