AMMs, liquidity pools & impermanent loss

An exchange with no order book, no market makers — just a formula.

Analyst · 10 min · Updated 2026-11-08

💡 The self-adjusting fruit stall

A stall holds 100 mangoes and 100 apples and follows one rule: mangoes × apples must stay at 10,000. Take 10 mangoes and you must add enough apples to keep the product at 10,000 — about 11.1 apples. The more mangoes people take, the more apples each next mango costs. That stall is an automated market maker.

The constant-product formula

A pool holds reserves x of token A and y of token B, and keeps x × y = k constant (before fees). The quoted price of A in B is y / x.

If you add Δx of A, you receive Δy = y − k / (x + Δx) of B (minus a fee, often 0.3%).

Price impact

Small trades barely move the price; trades that are large relative to the pool move it a lot. That's why shallow pools are dangerous: the price you see is not the price you'll get for size.

Liquidity providers (LPs)

LPs deposit both tokens and earn trading fees. But when prices move, arbitrage traders rebalance the pool, leaving LPs with more of the token that fell and less of the token that rose.

Impermanent loss (IL)

Compared with simply holding, an LP's value changes by IL = 2√r ÷ (1 + r) − 1, where r is the price ratio change.

It's "impermanent" only if prices return to where they started; otherwise it becomes very permanent. Fees may or may not compensate.

🧮 Practical example: swapping in a small pool

Key takeaways

• AMM pricing: x × y = k.
• Large trades vs shallow pools → big price impact.
• LPs earn fees but suffer impermanent loss.
• IL at 2× price move ≈ −5.7%.

Education only — not financial advice.