Liquidity Provider Returns in Geometric Mean Markets

Understand

Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted) geometric mean.

• This paper extends several results known for constant-weight G3Ms to the general case of G3Ms with time-varying and potentially stochastic weights.
• These results include the returns and no-arbitrage prices of liquidity pool (LP) shares that investors receive for supplying liquidity to G3Ms.
• Using these expressions, we show how to create G3Ms whose LP shares replicate the payoffs of financial derivatives.