The PPP puzzle refers to the wide swings of nominal exchange rates around their long‐run equilibrium values whereas the excess return puzzle represents the persistent deviation of the domestic‐foreign interest rate differential from the expected change in the nominal exchange rate. Using the I(2) cointegrated VAR model, much of the excess return puzzle disappears when an uncertainty premium in the foreign exchange market, proxied by the persistent PPP gap, is introduced. Self‐reinforcing feedback mechanisms seem to cause the persistence in the Swiss‐US parity conditions. These results support imperfect knowledge based expectations rather than so‐called “rational expectations”.