An Economic Model of a Decentralized Exchange with Concentrated Liquidity

We provide an economic model of a decentralized exchange (DEX) that allows investors to concentrate liquidity within exogenously specified price intervals (e.g., Uniswap V3). We demonstrate that providing liquidity for a risky vs. risk-free asset pair within any price interval is analogous to investing in a portfolio composed of the risky asset and the risk-free asset. The associated portfolio weights evolve dynamically such that the risky asset portfolio weight declines from unity to zero as the risky asset price increases. Notably, we establish that DEX liquidity provision is always a sub-optimal investment in the absence of trading fees, even when loss-versus-rebalancing costs are negligible. Relatedly, we show that any level of positive trading fees supports a unique level of equilibrium liquidity provision for each DEX price interval. We provide a simple approximation of the equilibrium liquidity provision for each interval which can be useful for empirical work