Introduction
Impermanent loss is a concept in decentralized finance that affects liquidity providers in automated market maker pools. It happens when the price of tokens inside a liquidity pool changes compared with their original deposit price.
The loss is called “impermanent” because it may disappear if the token prices return to their original ratio before the liquidity provider withdraws funds. However, if the provider withdraws after the price ratio has changed, the loss becomes realized.
How Impermanent Loss Occurs
In an AMM pool, liquidity providers deposit pairs of tokens such as ETH and USDT. The pool uses a pricing formula to maintain the relationship between the assets. A common formula is the constant product formula.
x = amount of token A in the pool
y = amount of token B in the pool
k = constant product
When the market price of one token changes, arbitrage traders buy or sell tokens in the pool until the pool price matches the external market price. This changes the ratio of tokens in the pool. As a result, liquidity providers may end up with fewer units of the asset that increased in price and more units of the other asset.
Deposit
You deposit two tokens into a liquidity pool.
Price Changes
One token rises or falls compared with the other token.
Arbitrage
Traders adjust the pool price to match the wider market.
New Ratio
Your share now contains a different balance of the two tokens.
Example: ETH and USDT Liquidity Pool
Assume a liquidity pool contains ETH and USDT. The original ETH price is $1,000. You deposit 1 ETH and 1,000 USDT into the pool, so your initial contribution is worth $2,000.
Initial Pool
10 ETH and 10,000 USDT.
Constant Product
10 × 10,000 = 100,000.
Your Deposit
1 ETH and 1,000 USDT.
Your Pool Share
10% of the pool.
Now suppose ETH rises from $1,000 to $2,000. Arbitrageurs trade with the pool until the pool price adjusts to the new market price.
Calculation: ETH Price Increases to $2,000
After ETH rises to $2,000, the pool must still satisfy the constant product rule:
y′ / x′ = 2,000
y′ = 2,000x′
x′ × 2,000x′ = 100,000
2,000x′² = 100,000
x′² = 50
x′ = √50 ≈ 7.071 ETH
y′ = 2,000 × 7.071 ≈ 14,142 USDT
Since your share is 10% of the pool, your new pool position is approximately:
| Item | Value | Explanation |
|---|---|---|
| ETH in your pool share | 0.7071 ETH | 10% of 7.071 ETH. |
| USDT in your pool share | 1,414.2 USDT | 10% of 14,142 USDT. |
| Pool value | 2,828.4 USDT | 0.7071 ETH × $2,000 + 1,414.2 USDT. |
| Value if held | 3,000 USDT | 1 ETH × $2,000 + 1,000 USDT. |
| Impermanent loss | -171.6 USDT or about -5.72% | The pool position is worth less than simply holding. |
On mobile, swipe the table horizontally if needed.
Formula for Impermanent Loss
Impermanent loss can also be calculated using a price ratio formula.
price ratio = new price / original price
In the ETH example:
IL = [ 2 × √2 / (1 + 2) ] − 1
IL = 2.8284 / 3 − 1
IL = 0.9428 − 1
IL = -0.0572
IL ≈ -5.72%
This matches the result from the pool balance calculation.
Why Liquidity Providers Must Understand This Risk
Liquidity providers earn trading fees, incentive tokens or yield farming rewards. These rewards may compensate for impermanent loss, but not always. The final result depends on token price movement, pool volume, fees, incentives and the timing of withdrawal.
Large Price Movement
The greater the price divergence between the two assets, the greater the impermanent loss.
Low Trading Fees
If trading fees are low, they may not offset the loss from price changes.
Volatile Tokens
Pools with highly volatile assets may have higher impermanent loss risk.
Withdrawal Timing
The loss becomes realized if you withdraw while the price ratio remains changed.
Key Takeaways
- ✓Impermanent loss occurs when the price ratio of assets in a liquidity pool changes.
- ✓AMM pools adjust balances through arbitrage and the constant product formula.
- ✓The more the token prices diverge, the higher the impermanent loss.
- ✓Trading fees and incentives can compensate LPs, but they do not guarantee profit.
- ✓If prices return to the original ratio before withdrawal, the loss may disappear.
Impermanent loss is one of the key risks every DeFi liquidity provider should understand before depositing into an AMM pool.
Continue Learning
After learning about impermanent loss, continue with other DeFi and blockchain topics.