A Balancer Pool is an automated market maker with certain key properties that cause it to function as a self-balancing weighted portfolio and price sensor.
Balancer turns the concept of an index fund on its head: instead of paying fees to portfolio managers to rebalance your portfolio, you collect fees from traders, who rebalance your portfolio by following arbitrage opportunities.
Balancer is based on a particular N-dimensional surface which defines a cost function for the exchange of any pair of tokens held in a Balancer Pool. This approach was first described by V. Buterin, generalized by Alan Lu, and proven viable for market making by the popular Uniswap dapp.
We independently arrived at the same surface definition by starting with the requirement that any trade must maintain a constant proportion of value in each asset of the portfolio. We applied an invariant-based modeling approach described by Zargham et al to construct this solution. We will prove that these constant-value market makers have this property.