We theoretically examine under which assumptions the impossible trinity holds. We also focus on the most recent Swiss experience and ask, if the SNB gained monetary independence by switching from a fixed to a floating exchange rate system in January 2015. The theoretical examination shows that the impossible trinity holds under the following assumptions: Equality of domestic and foreign real interest rates, the quantity theory of money holds, and that the relative PPP is fulfilled. The empirical analysis reveals that relative PPP does not hold for the Swiss case and it was necessary for the SNB to adopt its monetary policy in accordance with the ECB's expansive monetary policy. The paper shows that for a small open economy, such as Switzerland, it does not play a role for its monetary policy independence whether the central bank implements a fixed or a floating exchange rate system.