Hanno Lustig, Stanford University and NBER, and Adrien Verdelhan, MIT and NBER

Does Market Incompleteness Help to Explain Exchange Rates?

Exchange rates are puzzlingly smooth and only weakly correlated with macro-economic fundamentals compared to the predictions of exchange rate models with complete spanning. This paper derives an upper bound on the effects of incomplete spanning in international financial markets.Lustig and Verdelhan introduce stochastic wedges between log exchange rate changes and the difference in the countries' log pricing kernels without violating the foreign investors' Euler equations for the domestic risk-free assets. The wedges reconcile the volatility of no-arbitrage exchange rates with the data, provided that the volatility of the wedges is approximately as large as the maximum Sharpe ratio, but these same wedges cannot deliver exchange rates that simultaneously match currency risk premia and the exchange rates' correlation with fundamentals in the data.