Shows that the adoption of automated market makers (AMM) is severely limited for pairs of coins with high volatility. This is due to the large arbitrage rents which can be extracted from liquidity providers when deviations of AMM spot prices from fair value exchange rates become prominent. The paper shows that these rents can be so high, it causes a liquidity freeze if token pairs are highly volatile. The authors demonstrate that a pricing curve with larger convexity reduces arbitrage rents, but also decreases trading activities. The empirical study in the paper confirms the model implications that deposit inflows are negatively correlated with exchange rate volatility, and positively correlated with trading volume.