At the time of writing the BAL / WETH 80/20 pools has the following traits:

• Swap fee: 0.05%

• BAL: 5,682,882

• WETH: 6,232.9054

• BPT: 2,891,832.103892

Let’s assume we want to invest 500 BAL, and proportionally this would prompt us to invest 0.548393 WETH to maintain the pool balance (see The Value Function section for reference). We know our amount in and balance in of each token. The ratio of Dk over Bk will be the same regardless of which token is chosen in proportional investments and withdrawals:

See the to see that this transaction is reversible.

Proportional deposits will yield newly minted Balancer Pool Tokens (BPT) for an investor. This function essentially states that the if the proportional amounts of all tokens deposited (Dk) in relation to the Balance of that given token (Bk) will yield that amount of the new total supply of pool tokens. The example in the whitepaper states that depositing 10% of each of the existing tokens in the pool an investor will receive 10% of the current BPT supply.

Equation:

Sample calculation:

Arbitrarily we will assume we are depositing 15% of the total balance meaning Dk divided by Bk will be 0.15

We will assume our total supply to be 10,000 BPTs at this time for the sake of simplicity. From here can make the following calculations:

Substituting 0.15 for our deposit over balance ratio and 10,000 for the supply value we can solve for the issued amount of pool tokens.

This shows that using the formula, based upon the number of tokens we deposit into a pool based upon the balance already we present we will be awarded a proportional number of pool tokens. These pool tokens are a user’s way to redeem their assets when the pool is exited.