AMM Curves Compared

Why Multiple AMM Designs Exist

Different asset pairs have different trading characteristics. Two highly correlated stablecoins (USDC/USDT) should trade at ~1:1 with very tight spreads. Two volatile assets (ETH/BTC) need much wider price ranges. A token with a known fixed weight relationship to others needs yet another model. AMM (Automated Market Maker) designs have specialised over time to handle these different cases. Picking the right AMM for an asset pair has substantial impact on capital efficiency and trader experience.

Constant Product (Uniswap V2)

The original Uniswap V2 formula: x × y = k. The pool contains x units of token A and y units of token B; their product k stays constant after every trade. Mathematically elegant; works for any token pair; but capital is spread across the entire price range from 0 to infinity. Only a small portion of capital is 'doing work' near the current price. Gas-efficient and simple to integrate; the foundation of DeFi but increasingly displaced by more specialised designs.

Concentrated Liquidity (Uniswap V3, V4)

Uniswap V3 (May 2021) introduced concentrated liquidity. LPs specify a price range where their capital is active. Inside that range, capital is much more efficient — for stablecoin pairs concentrated near 1:1, V3 LPs can offer effective depth comparable to V2 pools with ~100x the capital. The catch: LP positions become directional bets. If price exits your range, you accumulate the 'losing' asset and stop earning fees. Active management is required for optimal returns.

• Different asset pairs need different AMM curves
• Constant product (V2): elegant, universal, but capital-inefficient
• Concentrated liquidity (V3, V4): efficient within a range, but requires active LP management
• Stable-swap (Curve): designed for highly correlated assets
• Weighted (Balancer): supports multi-asset pools with custom weights