Does Incomplete Spanning Help to Explain Exchange Rates?

We assume that domestic (foreign) agents, when investing abroad, can only trade in the foreign (domestic) risk-free rates. In a preference-free environment, we derive the exchange rate volatility and risk premia in any such incomplete spanning model, as well as a measure of exchange rate cyclicality. We find that incomplete spanning lowers the volatility of exchange rate, increases the risk premia but only by creating exchange rate predictability, and does not affect the exchange rate cyclicality.