We estimate a number of multivariate regime switching VAR models on a long monthly U.S. data set for eight variables that include excess stock and bond returns, the real T-bill yield, predictors used in the finance literature (default spread and the dividend yield), and three macroeconomic variables (inflation, industrial production growth, and a measure of real money growth). Heteroskedasticity may be accounted for by making the covariance matrix a function of the regime. We find evidence of

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... ur regimes and of timevarying covariances. We show that the best in-sample fit is provided by a four state model in which the VAR(1) component fails to be regime-dependent. We interpret this as evidence that the dynamic linkages between financial markets and the macroeconomy have been stable over time. The four-state model can be helpful in forecasting applications and provides one-step ahead predicted Sharpe ratios. JEL codes: E44, G12, C32, C52. Elizabeth La Jeunesse provided excellent research assistance. We thank two anonymous referees for stimulating comments and helpful suggestions. We are also indebted to session partecipants at the European Financial Management Association in Madrid (July 2005). It is now clear that the EMH may be consistent with predictability. In synthesis, the random walk obtains only under special assumptions or after appropriately scaling the asset prices. The EMH implies the existence of a relationship between asset returns and all variables that contain information on the fundamental pricing operator (the stochastic discount factor).