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Why did the Swiss National Bank fix the EUR/CHF exchange rate at CHF 1.20?
It's not. If you look at the page you link to and change dates, it's clear the rate changes a bit. 120.15 120.1 per hundred. The Swiss can keep the 1.200 as a target and if it's higher, sell agingst the euro to bring it down, if lower, buy. If the swiss experienced a serious financial crisis and their currency fell, they may not have the power to control it, if the rest of the world said it was worth less, you can be sure it will fall.