My colleague, Charles Engel, has a new paper entitled The Real Exchange Rate, Real Interest Rates, and the Risk Premium, in which he tries to identify what characteristics an exchange rate model must possess in order to explain two stylized facts.
…The well-known interest parity puzzle in foreign exchange markets finds … the high interest rate country tends to have the higher expected return in the short run. The second stylized fact concerns evidence that when a country’s relative real interest rate rises above its average, its currency tends to be stronger than average in real terms.
The first stylized fact pertains to forward rate bias, or equivalently the fact that ex post uncovered interest parity doesn’t hold, discussed in these posts  . Engel sums up the results of the paper:
This paper produces evidence that confirms these empirical regularities for the exchange rates of the G7 countries (Canada, France, Germany, Italy, Japan and the U.K.) relative to the U.S. However, these findings, taken together, constitute a previously unrecognized puzzle regarding how cumulative excess returns or foreign exchange risk premiums affect the level of the real exchange rate. Theoretically, a currency whose assets are perceived to be risky prospectively — looking forward from the near to the distant future — should be weaker, ceteris paribus. The evidence cited implies that when a country’s relative real interest rate is high, the country’s securities are expected to yield an excess return over foreign securities in the short run; but, because the high-interest rate currency tends to be stronger, over longer horizons the foreign asset is expected to yield an excess return. This behavior of excess returns in the foreign exchange market poses a challenge for conventional theories of the foreign exchange risk premium.
In brief, when one country’s interest rate is high, its currency tends to be stronger than average in real terms, it tends to keep appreciating for awhile, and then depreciates back toward its long-run value. But leading models of the forward-premium anomaly do not account for the behavior of the level of the real exchange rate: they predict that the high-interest rate currency will be weaker than average in real terms and appreciate over both the short- and long-run. A risk-based explanation for the empirical regularities requires a story of some sort of reversal of the risk premium – the securities of the high-interest rate country must be relatively riskier in the short-run, but expected to be less risky than the other country’s securities in the more distant future. It may be difficult to rationalize this pattern by focusing on the risk premium required by a single agent in each economy, as many theoretical models do. Instead, a full explanation may require interaction of more than one type of agent and perhaps also requires introducing some sort of “stickiness” in the financial markets — delayed reaction to news, slow adjustment of expectations, liquidity constraints, momentum trading, or other sorts of imperfections.
The entire paper is here.