Trading two assets that are both supposed to be worth a dollar requires different mathematics from trading assets whose relative value swings freely. Specialized pool designs exist for exactly this reason.
The standard curve assumes prices move
The most common automated market maker keeps the product of its two reserve balances constant. Buying one asset raises its price along a curve that never reaches zero or infinity.
That shape is appropriate when the assets have no fixed relationship, since the pool must quote a sensible price across every possible ratio.
Applied to two dollar-pegged tokens, it wastes capital. Most of the pool's reserves sit at price levels that will realistically never be reached.
Slippage appears where it should not
Under the standard curve, a trade large relative to the pool moves the price noticeably. Swapping a substantial quantity of one stablecoin for another produces a visibly worse rate.
Traders find that unacceptable because the two assets are meant to be interchangeable at parity. Any meaningful deviation defeats the purpose of the swap.
Compensating by making the pool enormous is possible but inefficient. It solves the symptom by immobilizing far more capital than the trading volume requires.
The stable curve flattens near parity
Pools designed for pegged assets use a formula that behaves almost like a constant sum near the balance point, quoting close to one-for-one across a wide range of ratios.
As the pool becomes badly imbalanced, the curve gradually reverts toward the standard shape. This protects reserves if one asset actually loses its peg.
The transition is controlled by an amplification parameter. Higher values flatten the curve further, improving normal trading while reducing protection during a depeg.
Concentrated liquidity achieves something similar
A different approach lets providers specify the price range in which their capital is active, concentrating it tightly around parity for stable pairs.
Within that band the pool behaves as though it were far larger, delivering the same tight pricing through position management rather than curve design.
The cost is active oversight. If the price leaves the chosen range, the position stops earning fees and sits entirely in one asset.
The design encodes an assumption
Every stable pool is built on the premise that its assets will trade near each other. When that premise breaks, the curve delivers the depegged asset cheaply to whoever acts first.
Liquidity providers in such pools are effectively holding a position that pays steadily while the peg holds and absorbs the loss when it does not.
Understanding the curve is therefore understanding the exposure. The mathematics is not neutral; it expresses a specific belief about how the assets should behave.