Stableswap Invariant (Curve Finance)
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Last updated: March 2026
AI Quick Summary: Stableswap Invariant (Curve Finance) Summary
Term
Stableswap Invariant (Curve Finance)
Category
DeFi
Definition
The stableswap invariant is Curve Finance's AMM formula designed for trading assets with similar values (stablecoins, LSTs).
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The stableswap invariant is Curve Finance's AMM formula designed for trading assets with similar values (stablecoins, LSTs). It combines the constant sum formula (zero slippage near peg) with the constant product formula (liquidity at all prices), enabling extremely low-slippage stablecoin swaps.
Curve Finance's stableswap invariant, created by Michael Egorov, solved a major problem with using constant product AMMs for stablecoin pairs — the formula was capital inefficient for trading assets that should stay at roughly the same price.
**The math intuition:** - **Constant sum (x + y = k)**: Zero slippage at any volume, but runs out of liquidity when prices diverge - **Constant product (x*y = k)**: Infinite liquidity but high slippage near the current price - **Stableswap**: A hybrid that behaves like a constant sum formula near the peg and falls back to constant product when the peg breaks
**Amplification factor (A):** Curve uses an amplification factor A that controls how much the curve bends toward the constant sum formula. Higher A = more efficient near peg, but more dangerous if the peg breaks. Pool governors can adjust A over time.
**Why Curve dominates stablecoin liquidity:** - USDT/USDC/DAI trades on Curve have 10–50× lower slippage than on Uniswap v2 - Lower slippage → more volume → more fees for LPs - This created the "Curve flywheel" that made CRV emissions extremely valuable
**The 3pool (3CRV):** Curve's core USDT/USDC/DAI pool ("3pool") became the deepest stablecoin pool in DeFi and a benchmark for stablecoin health. When a stablecoin's 3pool balance becomes imbalanced (too much of one stablecoin), it signals potential depeg risk.
**Beyond stablecoins:** Curve's formula was later extended to "crypto pools" that use a different invariant for more volatile correlated assets (e.g., ETH/stETH, BTC/WBTC).
Frequently Asked Questions
Why does Curve have lower slippage than Uniswap for stablecoins?
Curve's stableswap invariant concentrates virtually all liquidity near the 1:1 peg price. For $1M USDC swapped to USDT in a well-funded Curve pool, slippage is less than 0.01%. The same trade on Uniswap v2 would have much higher slippage because x*y=k spreads liquidity across all price ranges. Curve v3 (crvUSD) further evolved the design.
What is the Curve Wars?
The Curve Wars refers to the competition among DeFi protocols to acquire veCRV (vote-escrowed CRV) to direct CRV emissions to their preferred liquidity pools. More CRV emissions to a pool → more LP rewards → more liquidity → lower slippage for the protocol's stablecoin. Convex Finance (CVX) became the dominant platform for aggregating CRV votes, making CVX a proxy for veCRV control.
What is the amplification factor in Curve and why does it matter?
The amplification factor A controls how much Curve's formula resembles the constant sum (zero slippage) vs. constant product (safe during depegs) formula. A higher A creates lower slippage but is more dangerous during depegs — if one asset loses value, the pool heavily concentrates in that asset before the price formula adjusts. Pool governors must balance efficiency vs. depeg risk when setting A.
Related Tools on Alpha Factory
Related Terms
Constant Product Formula (x*y=k)
The constant product formula x*y=k is the mathematical invariant underlying Uniswap v1/v2 and most early AMMs. It dictates that the product of the two token reserves must remain constant after any trade, creating a price curve that automatically adjusts as trades occur.
Concentrated Liquidity (Uniswap v3)
Concentrated liquidity allows AMM liquidity providers to allocate capital within a specific price range rather than across the entire price curve. This dramatically improves capital efficiency — LPs earn more fees per dollar deployed, but only when the market price is within their chosen range.
Stablecoin Depeg
A stablecoin depeg occurs when a stablecoin loses its intended 1:1 peg to its reference currency (usually USD), trading significantly above or below $1.00. Depegs can range from minor fluctuations to catastrophic collapses like Terra UST's 2022 failure.
veToken Model (Vote-Escrowed Tokens)
The veToken model locks governance tokens for a period of time to receive vote-escrowed tokens (veTokens) with enhanced voting power and boosted rewards. Pioneered by Curve Finance with veCRV, it aligns long-term token holders with protocol governance and reduces sell pressure.
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