Each stablecoin reserve in the pool has an ideal weight, w.
It determines what percentage of each reserve the pool wants to hold. If w = 0.5, then the ideal weight for that reserve will be 50% of the total reserves held by the pool.
The first Drachma pool deployed will be 50% m.USDC and 50% m.USDT
When a pool is “balanced,” actual weights are close to ideal weights, and the pool functions as a constant-sum market maker. The sum of all the balances remains unchanged before and after a swap.
Exchange between stablecoins will be 1:1 and there will be no slippage except for a fixed fee (see Section 2.D.)
β represents the depth of the 1:1 exchange.
The ideal weight (w) interacts with β, to determine the liquidity depth for that reserve.
Once the actual weight is more than β percent away from the ideal weight, transactions will begin to incur slippage. For example, if w = 0.5 and β = 0.75, then the token will encounter slippage if it is lower than 12.5% or larger than 87.5% of the pool. Therefore, the higher the value of β, the deeper the pool.
The rate at which price slippage increases (elasticity), once past β, is determined by the parameter ∆. The higher the value of ∆, the more rapidly slippage will increase. If ∆ = 0, then there will be no price slippage at any point.
While this may seem attractive, without price slippage even a small deviation from the peg will drain the pool of all its liquidity. Thus, no price slippage will actually make the pool less liquid, especially for stablecoins that deviate above the price peg. This exact phenomenon happened to mStable, a “meta” stablecoin basket with a no-slippage AMM. One of the reserve stablecoins, DAI, typically trades above its peg, and the results is that the mStable pool has a chronic DAI shortage.