The paper first characterizes the predictable components in excess rates of returns on major equity and foreign exchange markets using lagged excess returns, dividend yields, and forward premiums as instruments. Vector autoregressions (VARs) demonstrate one‐step‐ahead predictability and facilitate calculations of implied long‐horizon statistics, such as variance ratios. Estimation of latent variable models then subjects the VARs to constraints derived from dynamic asset pricing theories. Examination of volatility bounds on intertemporal marginal rates of substitution provides summary statistics that quantify the challenge facing dynamic asset pricing models.