However, because of economic weakness and credit strains, coupled with the demand for Treasuries by the Fed, quantitative easing instead moves U.S. interest rates in the opposite direction, falling rather than rising. From the standpoint of interest rate parity, capital market equilibrium then requires the U.S. dollar to depreciate immediately, by a sufficient amount to set up the expectation of future appreciation in order to offset the shortfall of U.S. interest rate returns.
In short, quantitative easing is likely to induce what the late MIT economist Rudiger Dornbusch described as "exchange rate overshooting" - a large and abrupt shift in the spot exchange rate that occurs in order to align long-term equilibrium in the market for goods and services with short-term equilibrium in the capital markets.
This adjustment is depicted in the diagram below. In response to the monetary shock, a modest but long-term depreciation in the dollar (a rise in the U.S. dollar price of foreign currency) is required, depicted by the blue line. However, since nominal interest rates in the U.S. actually decline, ongoing equilibrium in the capital market requires that the U.S. dollar must be expected to appreciate over time by enough to offset the lost interest. As a result, quantitative easing is likely to result in an abrupt "jump depreciation" of the U.S. dollar (that is, a spike in the value of foreign currencies).
Frankly, I've always thought Dornbush's use of the word "overshooting" was unfortunate, because it implies that the exchange rate move is an overreaction, when that is not at all the case. Overshooting refers to the tendency of the spot exchange rate to move beyond its long-term PPP value, but this move is in fact approprate, efficient, and required in order to align the returns that investors can expect in each currency. So it is important to avoid misinterpretation - the policy of quantitative easing is likely to force a large adjustment on the U.S. dollar because the Federal Reserve is choosing to lay a heavier hand on the Treasury bond market than would result from economic conditions alone. The resulting shift in interest rates and long-term inflation prospects combine to dramatically reduce the attractiveness of the U.S. dollar. A significant and relatively abrupt devaluation is then required, in an amount sufficient to set up expectations of a U.S. dollar appreciation over time.
Japan has given us a great example of an economy that has expanded its debt to GDP 3+X without inflation and currency weakness. I'd not be suprised to see little inflation in the US over the next dozen yrs, 30-yr treasuries near 2% & the US$ flat to the Euro.