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China and Switzerland have recently experienced foreign exchange reserve accumulation far in excess of what would be implied by the literature on optimal reserves. Using a dynamic general equilibrium model, we show that the credible expectation of an upper limit to how many reserves a country is willing to accumulate would lead to a balance-of-payments anti-crisis. This is characterized by an accelerated pre-crisis accumulation of foreign exchange reserves, followed by a collapse of the monetary target that is instantaneous under exchange rate targeting and gradual under price level targeting. We argue that Switzerland has recently experienced such an event.