We document a robust negative relationship between bilateral RER volatility and bilateral FDI flows in the European Union. We then extend the standard international business cycle model to allow for domestic and foreign ownership of physical capital stock to be less than perfect substitutes. This allows the model to have meaningful predictions about the behavior of gross FDI flows. We characterize the conditions under which lower RER volatility coincides with larger bilateral FDI flows. We also show, both theoretically, and using numerical simulations, that the magnitude of the relationship between the RER volatility and FDI flows depends crucially on one parameter: the elasticity of substitution between domestic and foreign ownership of capital stock used in production. Our results suggest the existence of a new channel through which a reduction in RER volatility can be welfare improving: more efficient allocation of capital across countries (capital diversity).