This paper investigates how oil price shocks affect the trade balance and terms of trade in a two country DSGE model. We show that the response of the external sector depends critically on the structure of financial market risk-sharing. Under incomplete markets, higher oil prices reduce the relative wealth of an oil-importing country, and induce its non-oil terms of trade to deteriorate, and its non-oil trade balance to improve. The magnitude of the non-oil terms of trade response hinges on structural parameters that affect the divergence in wealth effects across oil importers and exporters, including the elasticity of substitution between oil and other inputs in production, and the discount factor. By contrast, cross-country wealth differences effectively disappear under complete markets, with the implication that oil shocks have essentially no effect on the non-oil terms of trade or the non-oil trade balance.