How Does the ‘Constant Sum’ Formula Differ from the ‘Constant Product’ Formula in AMMs?
The Constant Product formula (x y=k) ensures that the product of the reserve quantities (x and y) remains constant, which results in a smooth but exponentially increasing price impact (slippage) for large trades. The Constant Sum formula (x+y=k) aims to keep the sum of the reserves constant, resulting in a linear, near-zero slippage price for trades.
This formula is primarily used for stablecoin pairs that should trade at a 1:1 ratio.
Glossar
Constant
Parameter ⎊ A fixed numerical input utilized within quantitative models governing options pricing or collateral calculations remains a critical element.
Stablecoin Pairs
Pairing ⎊ Stablecoin Pairs refer to the asset combinations in liquidity pools or trading venues where two different fiat-backed or algorithmically stabilized digital currencies are traded against each other, minimizing volatility exposure relative to volatile pairs.
Constant Sum Formula
Mechanism ⎊ The Constant Sum Formula, sometimes employed in specialized stablecoin AMMs, dictates that the sum of the reserves ($x + y = k$) remains fixed, implying a constant marginal price of one-to-one regardless of the trade size.
Price Impact
Execution Cost ⎊ Price Impact quantifies the immediate change in an asset's market price caused solely by the execution of a single trade, reflecting the inverse of available liquidity at the point of execution.
Constant Product Formula
Formula ⎊ The Constant Product Formula, a cornerstone of Automated Market Makers (AMMs) like Uniswap, dictates the relationship between the reserves of two tokens within a liquidity pool.