Impermanent Loss Definition:
Impermanent loss is a temporary loss liquidity providers face when asset prices in a pool changes compared to just holding the asset.
What Is Impermanent Loss
Impermanent loss is the temporary reduction in a liquidity provider's asset value compared to simply holding the assets when the price in a decentralized exchange (DEX) liquidity pool changes. This occurs in automated market makers (AMMs) like Uniswap, SushiSwap, and PancakeSwap. The loss is “impermanent” because it disappears if asset prices return to their original levels, but it becomes permanent if assets are withdrawn before the price stabilizes.
Key Takeaways
Impermanent loss can be reversed if prices return to original levels but becomes permanent if withdrawn early.
To calculate impermanent loss, use the impermanent loss formula: IL = 2 x sqrt(price ratio A x price ratio B) / (price ratio A + price ratio B) - 1
Impermanent loss is a DeFi concept, it occurs in decentralized exchanges (DEXs) using AMMs like Uniswap, SushiSwap, and PancakeSwap.
To avoid impermanent loss: use stablecoin pairs, active management, and hedging.
To reduce impermanent loss: use AMMs that adjust trading fees based on market volatility, have loss protection mechanisms, or concentrate liquidity within specific price ranges.
How Does Impermanent Loss Work?
Liquidity providers deposit assets into a pool in a fixed ratio (e.g., 50/50). If one asset's price changes relative to the other, the pool automatically adjusts the asset amounts, meaning the provider ends up with more of the lower-value asset and less of the higher-value asset. This often results in a lower total value than simply holding the assets outside the pool.
For example, if a provider deposits 1 ETH ($2,000) and 2,000 USDC into a pool, and ETH's price rises to $4,000, their share will be adjusted to 0.707 ETH and 2,828 USDC, worth $5,656 total instead of $6,000 if they had held the same amounts in a wallet. This difference is the impermanent loss.
If asset prices return to their original level, the total value of the provider's share is restored, effectively nullifying the impermanent loss. However, if they withdraw funds while the price is still different, the loss becomes permanent.
How Does Impermanent Loss Occur in Liquidity Pools?
- A liquidity provider deposits two assets (e.g., ETH and USDC) into an AMM pool at a fixed ratio.
- If ETH price rises, traders buy ETH and sell USDC, changing the pool's ratio.
- The provider's share of the pool now holds less ETH and more USDC than before.
- If withdrawn, the provider may receive assets of lower total value compared to just holding them.
Examples of Impermanent Loss
- XRP/USDT: A liquidity provider deposits $5,000 worth of XRP and USDT. When XRP's price increases by 60% in two weeks, the provider experiences a 2.69% impermanent loss due to the shifting token ratio.
- AVAX/ETH: A provider deposits AVAX and WETH into a liquidity pool. When AVAX drops 30% in value compared to WETH, the provider ends up with more AVAX and less WETH, leading to a 1.56% impermanent loss compared to simply holding the asset
- ADA/BTC: A liquidity provider supplies ADA and WBTC into a decentralized exchange. As ADA rises 50% in a month compared to WBTC, the provider **loses 2.02% **of potential gains due to impermanent loss.
How To Avoid Impermanent Loss
Trying to avoid impermanent loss completely can be limiting to the pair and liquidity pool options for the provider, but there are ways to do that:
- Use stablecoin pairs: Providing liquidity in pairs like USDC/DAI reduces price volatility risks.
- Provide liquidity on AMMs with protection: Some platforms like Bancor offer impermanent loss protection.
- Time withdrawals carefully: Waiting for asset prices to stabilize can help avoid losses.
How To Reduce Impermanent Loss
To hedge against impermanent loss, liquidity providers can use strategies that minimize exposure to volatility and maximize earnings from liquidity provision.
- Dynamic fees: Some AMMs, like Uniswap V3, increase transaction fees during high volatility. This compensates liquidity providers by generating higher returns when impermanent loss risk is elevated, helping to offset potential losses.
- Concentrated liquidity: Uniswap V3 allows setting a custom price range for liquidity, reducing exposure to extreme divergence.
- Low-volatility assets: Pairs with correlated assets experience lower divergence.
- Liquidity mining rewards: Earning extra incentives can counterbalance losses.
How To Calculate Impermanent Loss
Impermanent loss for a 50/50 pool can be calculated using the following formula:
Impermanent Loss = 2 x square root(A x B) / (A + B) - 1Where
A is the price change ratio of one asset in a pool, calculated as new price / old price, and B represents the price change of the other asset in that pool. The greater the change, the higher the loss.In a liquidity pool where one asset is a stablecoin, the calculation is more straightforward. For example:
- If an asset's price doubles, the impermanent loss is 5.72%.
- If the price triples, the loss increases to 13.4%.
- At a 4x price change, the loss reaches 20%.
Detailed Example #1: Calculating Impermanent Loss for ETH/USDC
Consider an AMM pool for ETH and USDC, where a liquidity provider deposits $1,000 worth of ETH and $1,000 worth of USDC — a total of $2,000 in a 50/50 pool. Later, ETH's price decreases by 30% (making its multiplier
A = 0.7, or 70% of the original price), while USDC remains fixed at $1 (B = 1). If the provider had simply held the tokens, the ETH would now be worth $700 (1,000 x 0.7) and the USDC would still be worth $1,000, resulting in a total hold value of $1,700. However, in the liquidity pool the assets are automatically rebalanced according to the constant product formula. To calculate the impermanent loss (IL) for a volatile asset paired with a stablecoin, we use the formula:IL = 2 x sqrt(A x 1) / (A + 1) - 1First, calculate the square root of A:
sqrt(0.7)is approximately 0.83666
Then, multiply by 2:
2 x 0.83666is approximately 1.67332
Next, sum the multipliers for ETH and USDC:
A + 1 = 0.7 + 1= 1.7
Now, divide the doubled square root by the sum:
1.67332 / 1.7is approximately 0.9843
This ratio indicates that the liquidity provider's position in the pool is worth about 98.43% of the hold value. Multiplying this ratio by the hold value of $1,700 gives a liquidity pool value of approximately** $1,674.33**. The difference between the **hold value ($1,700) **and the LP value ($1,673.32) is about $26.67, which corresponds to an **impermanent loss of roughly 1.57%. **This demonstrates how the rebalancing mechanism in AMMs leads to a slight underperformance compared to simply holding the assets when the price decreases by 30%.
Detailed Example #2: Calculating Impermanent Loss for VERSE/ETH
Consider an AMM pool where neither of the assets is a stablecoin, for instance, they are VERSE and ETH, and a liquidity provider deposits** $1,000 worth of VERSE** and $1,000 worth of ETH — a total of $2,000 in a 50/50 pool. Now imagine that over time, **VERSE's price increases by 40% (**making its multiplier
A = 1.4, or 140% of the original price) while ETH's price decreases by 20% (B = 0.8, or 80% of the original price). If the provider had simply held the tokens, the VERSE would now be worth $1,400 (1,000 x 1.4) and the ETH would be worth $800 (1,000 x 0.8), resulting in a total value of $2,200. But yet again the assets in the liquidity pool are automatically rebalanced. To calculate the impermanent loss (IL), we use the formula:IL = 2 x sqrt(A x B) / (A + B) - 1First, calculate the geometric mean:
√(1.4 x 0.8) = √1.12 ≈ 1.0583
Then, multiply by 2:
2 x 1.0583 ≈ 2.1166
Next, sum the multipliers:
1.4 + 0.8 = 2.2
Now, divide the doubled geometric mean by the sum:
2.1166 / 2.2 ≈ 0.9621
This ratio tells us that the liquidity pool position is worth about 96.21% of the hold value. Scaling to the total hold value, the LP position is valued at approximately $2,116.6 (
$2,200 x 0.9621). The difference between the hold value ($2,200) and the LP value ($2,116.6) is around $83.4, which corresponds to an impermanent loss of roughly 3.79%. This example illustrates how the rebalancing mechanism in AMMs leads to a slightly lower return compared to simply holding the assets when both VERSE and ETH experience significant price changes.Conclusion
Impermanent loss is a key risk for DeFi liquidity providers that could lead to a significant loss of profits, occurring when asset prices shift within an AMM pool. While it is unavoidable in volatile pairs, strategies like providing liquidity in stablecoin pools, hedging, and dynamic fees can help minimize its impact. Understanding impermanent loss and how to avoid it is crucial for anyone participating in DeFi liquidity provision.
