This paper investigates the presence of Markov regimes in the conditional heteroskedastic dynamics for US excess stock and bond returns. We find strong evidence in favor of a three-state models. However, persistence and predictability in the stock-bond covariance tends to be weak. We find that the three-state model outperforms a number of benchmarks in out-of-sample prediction tests concerning means, variances, and covariances. In fact, when the three-state model is used to support mean-variance portfolio selection decisions in a recursive, out-of-sample experiments, we report that it gives the best overall performance in a number of dimensions, including realized Sharpe ratios and certainty equivalent measures.