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.

Fixing the investment horizon, the returns to currency carry trades decrease as the maturity of the foreign bonds increases. Across developed countries, the local currency term premia, which increase with the maturity of the bonds, offset the currency risk premia. Similarly, in the time-series, the predictability of foreign bond returns in dollars declines with the bonds’ maturities. Leading no-arbitrage models in international finance do not match the downward term structure of currency carry trade risk premia. We derive a simple preference-free condition that no-arbitrage models need to reproduce in the absence of carry trade risk premia on long-term bonds.