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Impermanent loss

Impermanent Loss

What Is Impermanent Loss?

Impermanent loss refers to a temporary decline in the dollar value of assets deposited into a liquidity pool within an Automated Market Maker (AMM) protocol, compared to simply holding those assets outside the pool. This phenomenon is a key consideration within decentralized finance (DeFi), a rapidly evolving sector that aims to replicate traditional financial services using blockchain technology and smart contracts without intermediaries73, 74. Impermanent loss occurs when the price of deposited cryptocurrency assets changes relative to their value at the time of deposit. The greater the price divergence between the pooled assets, the larger the impermanent loss incurred by the liquidity provider70, 71, 72. This loss is termed "impermanent" because it only becomes realized if the assets are withdrawn from the pool before their prices return to the original ratio67, 68, 69.

History and Origin

The concept of impermanent loss is intrinsically linked to the emergence and growth of Automated Market Makers (AMMs) and decentralized exchanges (DEXs). Before AMMs, decentralized trading often faced challenges with liquidity, making it difficult to find willing buyers and sellers for every trade66. The idea of AMMs was introduced to address this by using mathematical formulas and liquidity pools to automate the pricing and trading process, removing the need for traditional order books64, 65.

A significant turning point for AMMs came with the launch of Uniswap in November 2018, pioneered by Hayden Adams. Uniswap introduced a novel automated pricing mechanism based on liquidity pools that quickly popularized the concept of automated market making within the nascent DeFi ecosystem60, 61, 62, 63. It was through the widespread adoption of such protocols that the effects of asset price divergence on liquidity providers became apparent, leading to the identification and study of impermanent loss. While the term "impermanent loss" became widely discussed with the rise of DeFi and AMMs, the underlying economic principle of opportunity cost has long existed in traditional finance.

Key Takeaways

  • Impermanent loss represents a temporary unrealized loss of value for liquidity providers in AMMs due to price divergence of deposited assets.
  • It occurs when the ratio of assets within a liquidity pool changes relative to their initial deposit ratio, often driven by arbitrage trading.
  • The "loss" is an opportunity cost, signifying that the value of the pooled assets is less than if they had simply been held in a wallet.
  • Impermanent loss can be offset, partially or entirely, by trading fees earned by the liquidity provider and other liquidity incentives.
  • The risk of impermanent loss is higher for pools containing highly volatility assets and lower for pools with correlated assets, such as stablecoins.

Formula and Calculation

Impermanent loss quantifies the difference in value between holding assets in a liquidity pool versus holding them individually. While precise calculations can be complex due to varying AMM algorithms and fees, a common formula for a 50/50 two-asset pool is:

Impermanent Loss=2price_ratio1+price_ratio−1\text{Impermanent Loss} = \frac{2 \sqrt{\text{price\_ratio}}}{1 + \text{price\_ratio}} - 1

Where:

  • price_ratio is the ratio of the asset prices at the time of withdrawal compared to the asset prices at the time of deposit. For example, if the initial price ratio of Asset A to Asset B was (P_0) and the current price ratio is (P_1), then price_ratio = (P_1 / P_0).56, 57, 58, 59

This formula calculates the percentage loss relative to simply holding the original assets. For instance, a 2x price change in one asset relative to the other would result in approximately a 5.7% impermanent loss53, 54, 55. Understanding this relationship is fundamental for anyone engaging in decentralized finance and portfolio management strategies.

Interpreting the Impermanent Loss

Interpreting impermanent loss involves understanding that it is primarily an unrealized loss until the liquidity is withdrawn from the pool51, 52. It highlights the difference in portfolio value a liquidity provider experiences compared to a scenario where they simply held their initial assets without providing liquidity. A positive impermanent loss value means the liquidity provider's position in the pool is worth less than if they had just held the assets. Conversely, if the assets' prices return to their original ratio before withdrawal, the impermanent loss can diminish or disappear entirely48, 49, 50.

The magnitude of impermanent loss is directly tied to the degree of price divergence between the two assets in the pool47. For highly correlated assets, such as two different stablecoins pegged to the same fiat currency, the impermanent loss risk is typically minimal because their relative prices rarely deviate significantly44, 45, 46. However, for asset pairs with high volatility, such as an altcoin paired with a major cryptocurrency, the potential for substantial impermanent loss is much greater42, 43.

Hypothetical Example

Consider an investor, Alice, who decides to provide liquidity to an ETH/DAI pool on a decentralized exchange. DAI is a stablecoin pegged to the U.S. dollar, while ETH is a volatile cryptocurrency.

  1. Initial Deposit: Alice deposits 1 ETH and 2,000 DAI into the pool when 1 ETH is valued at $2,000. Her total initial deposit value is $4,000.
  2. Price Change: The price of ETH increases to $3,000 on external markets. Due to the AMM's constant product formula, arbitrage traders will buy ETH from the pool using DAI until the pool's internal price reflects the external market price40, 41. This rebalances the pool, leading to Alice holding more DAI and less ETH than her initial deposit.
  3. New Pool Holdings: If Alice were to withdraw her liquidity now, she might receive, for example, 0.8 ETH and 2,400 DAI.
  4. Value Calculation:
    • Value if held (HODL): 1 ETH (($3,000)) + 2,000 DAI (($2,000)) = $5,000.
    • Value in pool (at new prices): 0.8 ETH ((0.8 \times $3,000 = $2,400)) + 2,400 DAI (($2,400)) = $4,800.
  5. Impermanent Loss: Alice's impermanent loss would be ( $5,000 - $4,800 = $200 ), or a ($200 / $5,000 = 4%) loss relative to simply holding her assets. This difference represents the impermanent loss she would incur if she withdrew her token holdings at this point.

Practical Applications

Understanding impermanent loss is crucial for participants in the decentralized finance ecosystem, particularly for those acting as liquidity providers. In practice, it influences decisions on which liquidity pools to engage with and how to manage exposure. For instance, LPs often choose pools with lower expected price divergence, such as those consisting of stablecoins or wrapped versions of the same asset, to mitigate impermanent loss risk37, 38, 39.

Furthermore, the [trading fees](https://diversification[1](https://cointelegraph.com/explained/what-is-impermanent-loss-and-how-to-avoid-it)[2](https://academy.binan[34](https://academy.binance.com/en/articles/impermanent-loss-explained), 35, 36ce.com/en/articles/impermanent-loss-explained), 34, 56, 78, 9, 10, [11](https://www.fxleaders.com/learn-crypto/defi/impermanent-los[31](https://nowpayments.io/blog/the-future-of-defi-in-payments-unlocking-new-opportunities-for-businesses), 32, 33s/)12, 13, 1415, [16](https://cointelegraph.com/explained/what-is-imperm[29](https://academy.binance.com/en/articles/impermanent-loss-explained), 30anent-loss-and-how-to-avoid-it)17, 18, 1920, 21, [22](https://academic.oup.com/jfr[26](https://www.ledger.com/academy/glossary/impermanent-loss), 27, 28/article/6/2/172/5913239)23, 24, 25