This paper investigates the effects of Switzerland's real effective exchange rate (REER) on its current account. Using dynamic empirical methods, we focus on exchange rate movements that are unrelated to real and monetary developments, i.e., those more likely to be driven by the Swiss franc's safe-haven proprieties or unexpected exchange rate policy decisions. The paper's key result is that the Swiss headline current account has been largely inelastic to the exchange rate at the business cycle frequency. Three factors explain this somewhat counterintuitive result. A) A negative but short-lived effect on the trade balance is partly offset by a positive effect on net investment income. B) Large and often volatile net exports of nonmonetary gold blur the aggregate reaction. C) Improved terms-of-trade largely offset the negative effect on the (real) goods trade balance, as import prices tend to fall by more than export prices. The limited sensitivity of the current account, however, does not mean that the Swiss economy is insensitive to the exchange rate. Our results confirm that consumer prices, as well as corporate profits in particularly exposed sectors, decline significantly following an appreciation. These results suggest that an appreciation of the Swiss franc likely doesn't reduce Switzerland's current account quickly but rather tightens monetary conditions, reduces GDP, and hampers prospects in the longer term.