Impermanent Loss
Impermanent loss is a temporary reduction in the value of assets held by a liquidity provider in an automated market maker (AMM) pool when the price of the deposited assets changes relative to each other.
Impermanent loss occurs when the price of tokens deposited in a [liquidity pool](/en/terms/liquidity-pool) changes relative to when they were deposited. This loss is 'impermanent' because the liquidity provider could, in theory, regain their initial value if the prices of the assets return to their original ratio. The loss is realized only when the liquidity provider withdraws their assets.
Impermanent loss is a core concept in the world of decentralized finance (DeFi), specifically within the context of Automated Market Makers (AMMs) like Uniswap and Curve. These AMMs allow users to trade tokens without intermediaries. Liquidity providers contribute tokens to a pool, and in return, they earn trading fees.
The magnitude of impermanent loss depends on the price divergence of the assets in the pool. The greater the price change, the larger the impermanent loss. While the impermanent loss can be substantial, liquidity providers also earn fees, which can offset or even exceed the loss. Understanding impermanent loss is crucial for anyone participating in DeFi liquidity pools.
graph LR
Center["Impermanent Loss"]:::main
Rel_automated_market_maker["automated-market-maker"]:::related -.-> Center
click Rel_automated_market_maker "/terms/automated-market-maker"
Rel_automated_market_maker_amm["automated-market-maker-amm"]:::related -.-> Center
click Rel_automated_market_maker_amm "/terms/automated-market-maker-amm"
Rel_decentralized_exchange_dex_order_book_aggregation["decentralized-exchange-dex-order-book-aggregation"]:::related -.-> Center
click Rel_decentralized_exchange_dex_order_book_aggregation "/terms/decentralized-exchange-dex-order-book-aggregation"
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🧠 Knowledge Check
🧒 Explain Like I'm 5
Imagine you lend two different toys to a friend, expecting to get them back plus some extra treats. If one toy suddenly becomes much more popular (valuable) than the other, your friend might trade them around, leaving you with more of the less popular toy when you get them back, making your collection worth less than if you'd just kept them.
🤓 Expert Deep Dive
The mathematical formulation of Impermanent Loss for a constant product AMM (like Uniswap V2) is derived from the invariant x y = k. Let x0 and y0 be the initial quantities of asset X and Y deposited, and P0 = y0 / x0 be the initial price. At a later time, let the price be P = y / x. The quantity of assets held by the LP after rebalancing is x = sqrt(k / P) and y = sqrt(k P). The value of the LP's holdings is V_lp = x P + y. The value of simply holding the initial assets is V_hold = x0 P0 + y0. Impermanent Loss is IL = (V_hold - V_lp) / V_hold. This can be expressed as a function of the price ratio r = P / P0. For example, if r = 2 (price doubles), IL ≈ 5.7%. If r = 3, IL ≈ 11.1%. If r = 0.5 (price halves), IL ≈ 5.7%. The formula highlights that IL increases quadratically with the price deviation. Edge cases include pools with very low liquidity where arbitrage can cause rapid price swings, exacerbating IL. Strategies to mitigate IL include providing liquidity in stablecoin pairs or utilizing AMMs with different bonding curves (e.g., Curve Finance's stableswap invariant).