A constant mean AMM keeps the weighted geometric mean of each asset in the pool remains constant. In a pool with three assets, the formula will be (x*y*z)^(⅓)=k.
Popularized by Balancer, the constant mean pricing equation enables a much higher degree of flexibility. Because of this, Balancer can support up to 8 different assets in a single pool versus 2 assets per pool such as in Uniswap.
As previously mentioned, one can consider a Uniswap pool a 50:50 portfolio of two assets that constantly rebalance to make sure the USD value of each side is equal. Constant mean AMMs take this up a few notches by introducing up to 8 assets and the ability to target different weights for each asset. This auto-rebalancing feature mimics the functionality of an index product.
Despite the improved flexibility, this primitive lacks traction. Part of the reasoning for this is the high amount of gas required associated with this model. If you’re sourcing liquidity from the same Balancer pool, gas isn’t too much higher than Uniswap v2. But, for larger trades where the optimal route is to go through 2 or more pools, gas consumption is much higher, which eats into a swap’s profitability. Balancer v2 on Polygon, where gas fees are much lower, mitigates some of these concerns.
