Balancer Pool is an Automated Market Maker (AMM) with certain properties that facilitate it to function as a self-balancing weighted portfolio and a price sensor. Balancer works as an index function (index consists of various stocks) and is composed of up to eight different crypto currencies. Balancer’s Pool value is derived through the percentage of each token present within and a weight chosen during the creation of pool.
Value Function: The Balancer’s exchange function is mainly dependent on a ‘surface’ defined by a function of weights and balances of pool known as Value function (V). The paper shows proof of how this surface determines spot price at each point in a way that the share of value of each token in a pool remains constant, independent of what exchanges are carried out.
Spot Price: Spot Price is defined by the weights and balances of each pair of tokens in a Pool. It is the ratio of normalized balances of tokens in terms of their weights. With this ratio, it is known that if weights are constant then the only element that can cause changes to Balancer Pool is change in balances. If the owner of the pool does not remove or add token from/to the pool, token balances could only be changed through trades.
The constant surface forces the prices of token bought (token o ), to increase and prices of the token sold (token i ) to decrease.
Arbitrage Opportunity
When the prices offered by balancer pool is different then the prices offered in external market, an arbitrageur can make profits until the prices are equal to the prices that are offered in external markets.
Effective Price
Above discussed is Spot Price which is a theoretical price for extremely small trades which would incur no slippage but in reality the Effective Price is derived by the amount being traded which causes prices to change. Effective price is the ratio of Amount of token bought by the trader (Ao) and the amount of token sold by the trader (Ai). When the traded amount is close to 0, effective price tends to move towards Spot price.
Pool Tokens
The pool aggregates the liquidity provided by several users. To freely deposit and withdraw assets from the pool, Pool Tokens are issued through the Balancer Protocol. Pool token represents the ownership of assets in the pool. The outstanding supply of pool tokens is directly proportional to the value function of the pool. So if the pool value function is increased by 10% due to increase in deposits by 10% then the outstanding supply of pool function is also increased by 10%. The reason for this is as the depositor is issued by 10% of new pool tokens in return to the deposits he made.
Methods to deposit/withdraw Assets to/from Pool
- All Asset Deposit/ Withdrawal: This follows the distribution of existing assets in the pool. If the deposit is 5% each of assets already in the pool, then the Value function (V) will increase by 5% and the depositor will be minted 5% of the current outstanding supply of pool token. A weighted Asset Withdrawal is the reverse operation where a pool token holder redeems pool tokens and in return, gets the proportional share of each of the assets held in the pool.
- Single Asset Deposit/ Withdrawal: It allows to get pool tokens from a shared pool by depositing a single asset to the shared pool, the only condition that needs to be met is that the pool should contain the Asset.
Single Asset Withdrawal is calculated as:
Source: https://www.thecoinrepublic.com/2023/10/12/balancer-white-paper-key-terms-you-should-know-about-this-amm/