Fixing the investment horizon, the returns to currency carry trades decrease as the maturity of the foreign bonds increases, because the local currency term premia offset the currency risk premia. The time series predictability of foreign bond returns in dollars similarly declines with the bonds' maturities. Leading no-arbitrage models in international finance cannot match the downward term structure of currency carry trade risk premia. To match these findings, we find that long-run U.I.P. has to hold on average in dynamic no-arbitrage asset pricing models.