  Automated market makers (AMM) have grown to obtain significant market share
within the cryptocurrency ecosystem, resulting in a proliferation of new
products pursuing exotic strategies for horizontal differentiation. Yet, their
theoretical properties are curiously homogeneous when a set of basic
assumptions are met. In this paper, we start by presenting a universal approach
to deriving a formula for liquidity provisioning for AMMs. Next, we show that
the constant function market maker and token swap market maker models are
theoretically equivalent when liquidity reserves are uniform. Proceeding with
an examination of AMM market microstructure, we show how non-linear price
effect translates into slippage for traders and impermanent losses for
liquidity providers. We proceed by showing how impermanent losses are a
function of both volatility and market depth and discuss the implications of
these findings within the context of the literature.
