Entangled Risks in Incomplete FX Markets

Abstract

We introduce the concept of risk entanglement in a preference-free setting to jointly explain the exchange rate volatility, cyclicality, and currency risk premia in the data. Risk entanglement specifies a subset of incomplete market models, in which nondiffusive or nonlog-normal shocks to exchange rates are not fully spanned by asset returns. When risks are entangled, there exist multiple pricing-consistent exchange rates, but none of them are equal to the ratio of the stochastic discount factors (SDFs) or their projections. Decoupling the exchange rate from the SDFs allows us to address key FX market patterns that are puzzling in international finance.