Inefficiency of CFMs: Hedging Perspective and Agent-Based Simulations

We investigate whether the fee income from trades on the CFM is sufficient for the liquidity providers to hedge away the exposure to market risk. We first analyse this problem through the lens of continuous-time financial mathematics and derive an upper bound for not-arbitrage fee income that would make CFM efficient and liquidity provision fair. We then evaluate our findings by performing multi-agent simulations by varying CFM fees, market volatility, and rate of arrival of liquidity takers. We observe that, on average, with volatility set to realistic values, fee income generated from liquidity provision is insufficient to compensate for market risk. In case where the underlying pair volatility is very low the fee income exceeds market risk cost.