StableSwap — efficient mechanism for Stablecoin liquidity

The five-minute read

One action, walked through

1. Providers deposit the stable assets in whatever shares the pool allows and receive pool tokens.
2. A trader swapping one dollar token for another moves along the flat part of the curve and pays a small fee, while A is large and balances are close.
3. If one asset's external price falls and traders keep selling it into the pool, balances tilt.
4. As the tilt grows, the invariant steepens. Further sales move the internal price more, which is the pool's way of stopping a complete drain.
5. Providers who withdraw during the tilt receive more of the impaired asset. The fee income is what they hoped would pay for that.

The argument, unpacked

What has to be true

• The assets are meant to track the same value most of the time. The curve is a bad fit for uncorrelated coins.
• Arbitrage against a redemption market exists. Without it the internal price is only a ratio of inventory.
• A is set by someone whose incentives a provider understands.
• Tokens do not rebase or charge hidden transfer fees that desynchronise the balances.

What happened after the paper

Curve deployed StableSwap for dollar stablecoins and later generalised it. Several depegs showed the warehouse risk in public, including events where the pool became a large holder of the impaired asset. The paper's math did what it said. The losses came from the peg assumption failing, which the design does not prevent.

What to check before you use the idea

• What is A, and who can change it?
• Is there a redemption market outside the pool for each asset?
• What does a provider hold if one asset gaps down by 20 percent?
• Is the internal price being used as proof that a token is worth a dollar?

Terms

Amplification

The parameter A. Higher means a flatter curve near equal balances.

Stable invariant

A blend of constant-sum and constant-product so pegged assets trade tightly until they diverge.

Depeg

One asset leaving the shared price. The pool then accumulates it, because that is where the flat curve is generous.

Warehouse risk

The provider's exposure to ending up holding more of the asset that failed.

The problem the paper names

A constant-product pool of two stablecoins quotes a meaningful spread even when both claim to be worth the same unit. That spread is a tax on the common case. A constant-sum pool quotes no spread and then goes bankrupt in inventory the moment the peg slips.

What the design proposes

• An amplification parameter blends a constant-sum region with a constant-product tail.
• The pool is for assets that share a unit of account, not for unrelated volatile pairs.
• The invariant is explicit. Changing the amplification changes the risk, and the paper treats it as a parameter with consequences.

How the mechanism is specified

• Near parity, a trader moves along a nearly flat price. Liquidity is concentrated where those traders are.
• Far from parity, the curve steepens so the pool does not sell the last of the stronger asset at the peg price.
• Later Curve gauges, voting and factory pools are not this note.

What this page does not treat as proven

• The math assumes the assets ought to be near parity. If that assumption is false, the flat region is a source of loss, not efficiency.
• Amplification is a risk setting. Higher is not 'better'.
• The paper is not a claim about any stablecoin's reserves.

Why a venture studio still reads it

This is the first document we ask for when a venture designs a pool of assets 'that should be worth the same'. If they cannot say what happens when the assets stop being worth the same, they have not finished the design.