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We study the currency risk premium and the forward premium bias in a two‐country New Keynesian model with production, no physical capital, and recursive utility. Monetary policy follows an interest rate feedback rule and exogenous total factor productivity (TFP) growth follows a long‐run risk process with stochastic volatility, which we estimate from data. With cross‐country heterogeneity in TFP and monetary policy, reasonable currency risk premia emerge under complete and incomplete markets but the forward premium bias is trivial. We diagnose the challenge faced by this fairly standard production model to explain the forward premium bias.