Complete Guide to Impermanent Loss
What is Impermanent Loss
Impermanent Loss (IL) is the phenomenon where the value of assets deposited in a liquidity pool becomes lower than if you had simply held the same assets.
Due to the nature of AMMs, when prices change, the token ratio in the pool adjusts. During this process, LPs end up holding less of the token that increased in price and more of the token that decreased in price. The result is an effect of "automatically selling high and buying low."
The reason it's called "impermanent": the loss disappears if the price returns to its original level. However, if the price doesn't return before withdrawal, it becomes permanent loss.
The Mechanics of Impermanent Loss
How AMMs Work
The pool always maintains balance according to the constant product formula:
x × y = k
When prices change, arbitrageurs trade in the pool to match the market price. During this process, the token ratio in the pool changes.
Example: ETH Price Doubles
Initial State:
- Deposited: 1 ETH ($1,000) + 1,000 USDC = $2,000
- If simply held: 1 ETH + 1,000 USDC
ETH rises from $1,000 to $2,000:
According to the constant product formula:
- New pool ratio: 0.707 ETH + 1,414 USDC
- Pool value: 0.707 × $2,000 + 1,414 = $2,828
If simply held:
- 1 ETH × $2,000 + 1,000 USDC = $3,000
Impermanent Loss:
- Difference: $3,000 - $2,828 = $172
- Loss rate: 172 / 3,000 = 5.72%
Impermanent Loss by Price Change
Loss Rate Table
Impermanent loss based on price change ratio (for 50:50 pools):
| Price Change | Impermanent Loss |
|---|---|
| ±10% | 0.11% |
| ±25% | 0.62% |
| ±50% | 2.02% |
| ±75% | 3.79% |
| ±100% (2x) | 5.72% |
| ±200% (3x) | 13.40% |
| ±300% (4x) | 20.00% |
| ±400% (5x) | 25.46% |
Key Insights:
- IL increases sharply as price change grows
- Even with 2x change, IL is limited to about 5.7%
- However, with 5x change, loss exceeds 25%
Calculation Formula
Mathematically, impermanent loss is calculated as:
IL = 2 × √(price_ratio) / (1 + price_ratio) - 1
- price_ratio = current price / price at deposit
- Negative result indicates loss
Same in Both Directions
Impermanent loss occurs at the same rate regardless of whether the price goes up or down. Whether the price doubles or halves, the same 5.72% IL occurs.
Why "Impermanent"?
When Price Returns
If the price returns to the deposit level, the impermanent loss recovers to 0.
Scenario:
- At deposit: ETH $1,000, deposit 1 ETH + 1,000 USDC
- ETH rises to $2,000: IL 5.72%, position 0.707 ETH + 1,414 USDC
- ETH returns to $1,000: IL 0%, position 1 ETH + 1,000 USDC (+ fees)
The fees accumulated during the price movement become pure profit.
Converting to Permanent Loss
If the price differs from deposit time at withdrawal, the impermanent loss is "realized" and becomes permanent loss.
- IL is potential loss
- Withdrawal confirms the loss
- Waiting until price returns can recover the loss (though there's opportunity cost of time)
Fees and Impermanent Loss
Break-Even Analysis
LP's actual profit:
Actual Profit = Fee Income - Impermanent Loss
If fees exceed IL, it's net profit; otherwise, it's net loss.
Example:
- Deposit period: 1 year
- Fee APR: 20%
- Price change: 2x increase
- IL: 5.72%
Result:
- Fee income: +20%
- Impermanent loss: -5.72%
- Net profit: +14.28%
In this case, LP was advantageous. However, if fee income was less than 5%, simply holding would have been better.
APR Thresholds
Minimum APR needed for LP to profit based on expected price changes:
| Expected Price Change | Required Minimum APR |
|---|---|
| ±25% | ~0.6%+ |
| ±50% | ~2%+ |
| ±100% (2x) | ~5.7%+ |
| ±200% (3x) | ~13%+ |
Volatile token pairs in pools with low trading volume and APR are unfavorable for LPs.
Strategies to Minimize Impermanent Loss
1. Choose Highly Correlated Pairs
Asset pairs that move similarly have small relative price changes and thus low IL.
| Pool Type | Example | IL Risk |
|---|---|---|
| Stablecoin pair | USDC-USDT | Almost none |
| Pegged asset pair | ETH-stETH, BTC-WBTC | Very low |
| Same sector | ETH-MATIC (L1/L2) | Low to medium |
| Uncorrelated pair | ETH-UNI | Medium to high |
| High volatility pair | ETH-SHIB | High |
Lowest risk: Curve's stable pools (USDC-USDT-DAI)
2. Choose High-Volume Pools
High fee income offsets IL.
- Check volume/TVL ratio
- Major token pairs (ETH-USDC, etc.) are favorable
- Consider pools with incentives (but verify sustainability)
3. Accept Two-Way Exposure
LP positions provide exposure to both assets.
If you intended to hold both assets anyway, LP can be advantageous:
- Intended 50% ETH + 50% USDC → LP provides rebalancing + fees
- Intended 100% ETH → LP results in loss from IL
4. Price Range Management (V3)
In Uniswap V3's concentrated liquidity:
- Wide range: Mitigates IL, lower returns
- Narrow range: Amplifies IL, higher returns
Conservative approach favors wide range; active management allows narrow range.
5. Hedging
You can hedge price movements with futures or options. However, it's complex and incurs additional costs. Only practical for large LP positions.
When LP is Advantageous
Sideways Markets
When price moves up and down within a range:
- Impermanent loss periodically approaches 0
- Fees continue to accumulate
- Optimal environment for LP
When Volatility is Lower Than Expected
If the pool's APR is high but actual price movement is small, LP is favorable.
Long-Term Holding Intent
If you plan to hold both assets long-term anyway:
- IL is likely to be offset over time
- Fees accumulate meanwhile
- Rebalancing effect (automatic sell/buy)
When LP is Disadvantageous
One-Way Price Movement
When one token continuously rises:
- IL accumulates
- Quantity of the rising asset continues to decrease
- "Sell high, buy low" effect maximizes
Especially risky: Early altcoins that rise 10x, 100x
Sudden Volatility
When large price changes occur in short periods, fee income struggles to offset IL.
Decreasing Volume
Fee income decreases and can no longer offset IL.
Impermanent Loss Calculation Tools
Websites
- dailydefi.org/tools/impermanent-loss-calculator: Simple IL calculator
- APY.vision: Track IL of actual LP positions
- Revert Finance: Detailed Uniswap V3 analysis
Manual Calculation
In Google Sheets:
=2*SQRT(A1)/(1+A1)-1
Enter price_ratio (current price/deposit price) in A1
Frequently Asked Questions
Is IL a Real Loss?
It's a "loss compared to simply holding". The dollar value of your position usually increases (if price went up). However, you've missed gains you would have earned if you hadn't LPed.
Is IL Permanent?
It recovers if price returns. It's potential loss until withdrawal. However, if the price doesn't return, it becomes permanent loss.
Do Fees Always Offset IL?
No. Sufficient trading volume is required. If volume is low or price changes are large, IL can exceed fees.
Is IL Greater in V3 Than V2?
If you set a narrow range, IL is amplified. With a wide range, it's similar to V2. Concentrated liquidity means "higher returns, higher risk."
Summary
Impermanent loss is a structural characteristic of AMMs, causing losses compared to simply holding when prices change. The loss magnitude increases exponentially with the price change ratio, about 5.7% for a 2x change. By choosing highly correlated pairs, high-volume pools, and taking a long-term perspective, you can minimize IL. LP is only meaningful when fee income exceeds IL, which requires comparing the pool's APR with expected price movements.
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