Impermanent Loss — Trading Wiki

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Published by TradeHQ. Site creator: Anuga Weerasinghe. This page has no recorded editorial review date; the About page explains the site's editorial approach.

What Impermanent Loss means

Impermanent loss compares the value of a liquidity-provider position with simply holding the original tokens. The difference depends on the pool design and relative prices; fees and incentives also matter.

In depth

For a fee-free, full-range constant-product pool initially balanced by value, compare the liquidity-provider position with holding the originally deposited assets. If their relative price changes by a factor r and arbitrage rebalances the pool, the relative value difference is 2×sqrt(r)/(1+r)−1 under these assumptions. At r=2 this is about −5.72%; at r=5 it is about −25.46%. This difference is a comparison with holding, not necessarily an absolute cash loss. Fees, incentives, concentrated ranges and token behavior change outcomes. Withdrawing does not create the earlier economic difference; a later price change can narrow or widen it.

Smart-contract and custody risks are additional.

Key points

• Value difference between LP position and simply holding the tokens
• In a simple fee-free constant-product pool, the relative value difference grows as paired-token prices diverge
• The value difference exists before withdrawal and can change with subsequent prices

Why it matters when you are learning

Compare liquidity provision with holding the same initial assets under a stated pool model. Fees, incentives and price changes all matter, alongside contract and withdrawal risks.

Worked exercise and its limits

For a fee-free full-range constant-product pool initially holding 1 token worth $100 and $100 cash, double the token price. Arbitrage gives about 0.7071 tokens and $141.42 cash, total $282.84 versus $300 holding: about 5.72% less. Fees, incentives and concentrated liquidity change the comparison.