From September 2011 to January 2015, the Swiss National Bank (SNB) implemented a minimum exchange rate regime (i.e. a one-sided target zone) vis-à-vis the euro to fight deflationary pressures in the aftermath of the Great Financial Crisis. During this period of unconventional monetary policy, the SNB faced mounting criticism from the media and the public on the sizable balance sheet risks that it was incurring. Motivated by this episode, I present a structural model embedded within the target zone framework developed by Krugman (1991) that allows monetary authorities to determine ex-ante the maximum size of foreign exchange market interventions that are expected to be necessary to implement and maintain a one-sided target zone. An empirical application of the proposed model to the aforementioned episode reveals that it is well suited to explain the actual size of these interventions and that, in January 2015, the SNB's euro purchases might indeed have been large without the abandonment of the minimum exchange rate regime, which is consistent with the official statements of the SNB in the aftermath of that episode.