Key Takeaways
This paper gives a simple but very general definition of ‘price stability’ for a class of markets that includes the popular constant function market makers (CFMMs) such as Uniswap, Curve, and Balancer, used extensively in decentralized finance (DeFi).
It shows that the definition of price stability elucidated in this paper is deeply connected to the curvature of the trading function used in the CFMM, making the folk intuition that “flatter CFMMs are more price stable” more concrete.
It also shows that this definition gives sufficient conditions for the profitability of liquidity providers, and, similar to the classical market microstructure literature, gives bounds on the edge of informed traders and bounds on the losses of liquidity providers.
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