Liquidity Providers Face a Trade-Off Between Fees and Loss in Concentrated AMMs

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Abstract

1. Introduction

2. Constant function markets and concentrated liquidity

• Constant function markets
• Concentrated liquidity market

3. The wealth of liquidity providers in CL pools

• Position value
• Fee income
• Fee income: pool fee rate
• Fee income: spread and concentration risk
• Fee income: drift and asymmetry
• Rebalancing costs and gas fees

4. Optimal liquidity provision in CL pools

• The problem
• The optimal strategy
• Discussion: profitability, PL, and concentration risk
• Discussion: drift and position skew

5. Performance of strategy

• Methodology
• Benchmark
• Performance results

6. Discussion: modelling assumptions

• Discussion: related work

7. Conclusions And References

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Conclusions

We studied the dynamics of the wealth of an LP in a CPM with CL who implements a selffinancing strategy that dynamically adjusts the range of liquidity. The wealth of the LP consists of the position value and fee revenue. We showed that the position value depreciates due to PL and the LP widens her liquidity range to minimise her exposure to PL. On the other hand, the fee revenue is higher for narrow ranges, but narrow ranges also increase concentration risk. We derived the optimal strategy to provide liquidity in a CPM with CL when the LP maximises expected utility of terminal wealth. This strategy is found in closed-form for log-utility of wealth, and it shows that liquidity provision is subject to a profitability condition. In particular, the potential gains from fees, net of gas fees and concentration costs, must exceed PL. Our model shows that the LP strategically adjusts the spread of her position around the reference exchange rate; the spread depends on various market features including tthe volatility of the rate, the liquidity taking activity in the pool, and the drift of the rate.

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:::info Authors:

1. Alvaro Cartea ´
2. Fayc¸al Drissia
3. Marcello Monga

:::

:::info This paper is available on arxiv under CC0 1.0 Universal license.

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