Entangled Risks in Incomplete FX Markets

We study the implications of risk entanglements on international financial (FX) markets. Risk entanglement is a refinement of incomplete markets that some risks in asset markets cannot be singly traded. We show that in FX markets with entangled risks (i) there exist multiple pricing-consistent exchange rates, (ii) every exchange rate is affected by idiosyncratic risks, and (iii) exchange rates can be smooth while stochastic discount factors (SDFs) are volatile and almost uncorrelated. These results are in stark contrast to the case of complete markets or incomplete markets without risk entanglements