This paper explores the hypothesis that high volatility of real and nominal exchange rates may be due to the fact that local currency pricing eliminates the pass-through from changes in exchange rates to consumer prices. Exchange rates may be highly volatile because in a sense they have little effect on macroeconomic variables. The paper shows the ingredients necessary to construct such an explanation for exchange rate volatility. In addition to the presence of local currency pricing, we need a) incomplete international financial markets, b) a structure of international pricing and product distribution such that wealth effects of exchange rate changes are minimized, and c) stochastic deviations from uncovered interest rate parity. Together, it is shown that these elements can produce exchange rate volatility that is much higher than shocks to economic fundamentals, and `disconnected' from the rest of the economy in the sense that the volatility of all other macroeconomic aggregates are of the same order as that of fundamentals.