Learn · Crypto, from first principles
Automated market makers
Replace the order book with a formula and a pot of two assets. Prices come from a curve, and anyone can be the market maker.
A conventional exchange matches buyers against sellers through an order book. That requires continuous quoting by professional market makers, which requires identity, infrastructure and capital commitment. An automated market maker replaces all of it with a formula.
The constant product rule
Wealth Signal calculation
How a price emerges from a formula
A pool holds two assets, X and Y, and enforces X × Y = k, a constant. Suppose it holds 100 of X and 10,000 of Y, so k = 1,000,000. The implied price of X is 10,000 ÷ 100 = 100 Y.
Someone buys 10 X. The pool must keep k constant, so Y must rise to 1,000,000 ÷ 90 = 11,111. The buyer pays 1,111 Y for 10 X — an average of 111, not 100. The new implied price is 11,111 ÷ 90 = 123.
The trade moved the price. Larger trades move it more, and that is slippage.
A pool holds two assets, X and Y, and enforces X × Y = k, a constant. Suppose it holds 100 of X and 10,000 of Y, so k = 1,000,000. The implied price of X is 10,000 ÷ 100 = 100 Y.
Someone buys 10 X. The pool must keep k constant, so Y must rise to 1,000,000 ÷ 90 = 11,111. The buyer pays 1,111 Y for 10 X — an average of 111, not 100. The new implied price is 11,111 ÷ 90 = 123.
The trade moved the price. Larger trades move it more, and that is slippage.
What this buys
- Always quoting. The formula gives a price for any size at any moment. There is never an empty book.
- Anyone can supply. Deposit both assets in the current ratio and you earn a share of the fees. No permission, no minimum, no professional infrastructure.
- Any pair. A new token can have a market the moment someone funds a pool, which is why listing on a decentralised exchange requires no listing process.
Who sets the price
Fact
Arbitrage does, not the formula
The curve does not know what anything is worth. If the pool's implied price drifts from the wider market, arbitrageurs buy from whichever venue is cheaper until the gap closes. The pool tracks the market because it is profitable for outsiders to make it track. Remove the arbitrageurs and the pool price is meaningless — which is exactly the weakness exploited when a thin pool is used as a price oracle.
The curve does not know what anything is worth. If the pool's implied price drifts from the wider market, arbitrageurs buy from whichever venue is cheaper until the gap closes. The pool tracks the market because it is profitable for outsiders to make it track. Remove the arbitrageurs and the pool price is meaningless — which is exactly the weakness exploited when a thin pool is used as a price oracle.
Slippage and depth
Price impact depends on trade size relative to pool depth. A large trade against a thin pool executes at a far worse average price than the quoted one, and wallets display an estimate before you confirm. Setting a high slippage tolerance to force a trade through is a common way to lose money and an open invitation to sandwich attacks.
Beyond the constant product
- Stable-asset curves. For pairs expected to trade near parity — two dollar stablecoins — a flatter curve gives much lower slippage near the peg.
- Concentrated liquidity. Providers choose a price range to cover, greatly improving capital efficiency and requiring active management. It converts passive provision into something closer to a job.
- Weighted pools. More than two assets, in fixed proportions, functioning as a self-rebalancing index.
Interpretation
The achievement is real and the economics are widely misunderstood
An AMM is a working market maker with no operator, no credit relationship and no opening hours — a genuine invention. Supplying liquidity to one is not, however, a savings product. It is an options-like position that loses when prices move and earns fees in exchange. See impermanent loss, which is the single most under-explained concept in this field.
An AMM is a working market maker with no operator, no credit relationship and no opening hours — a genuine invention. Supplying liquidity to one is not, however, a savings product. It is an options-like position that loses when prices move and earns fees in exchange. See impermanent loss, which is the single most under-explained concept in this field.
If you only take one practical point: check pool depth before a large trade, and never raise slippage tolerance to make a failing trade succeed. The trade is failing for a reason.
Education, not advice. These lessons explain how things work. They do not tell you what
to buy, and Wealth Signal does not publish recommendations. Full disclaimer.