Compared to the predictions of exchange rate models with complete spanning in financial markets, actual exchange rates are puzzlingly smooth and only weakly correlated with macro-economic fundamentals. This paper derives an upper bound on the effects of incomplete spanning in international financial markets. We introduce stochastic wedges between the exchange rate's rate of appreciation and the difference between the marginal utility growth rates of the countries' stand-in investors without violating the foreign investors' Euler equations for the domestic risk-free assets. The wedges always lower the volatility of no-arbitrage exchange rates and can help to match the volatility of exchange rates in the data, provided that the wedges are as volatile as the maximum Sharpe ratio, but the wedges cannot deliver exchange rates that are uncorrelated with macro-fundamentals without largely eliminating currency risk premia.
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