What is Impermanent Loss?
Impermanent Loss (IL) is the difference between holding tokens in an automated market maker (AMM) liquidity pool versus holding them in your wallet.
Why it happens: AMMs maintain a constant product (x × y = k), so when one token's price changes, the pool automatically rebalances by trading to maintain the ratio. This rebalancing causes you to sell winners and buy losers.
When it matters: IL only applies to Strategy 1: ETH/USDC Liquidity Pool. The other strategies do not involve providing liquidity to two-sided pools.
It's "impermanent" because: If prices return to the original ratio, the loss disappears. However, if you withdraw at the new prices, the loss becomes permanent.
Impermanent Loss Formula
Where:
- price_ratio = (New Price of ETH) / (Original Price of ETH)
- IL = Loss as a decimal (negative value)
Convert to percentage: Multiply IL by 100
Example: If IL = -0.0572, then loss is -5.72%
Step-by-Step Example: ETH +50% Price Increase
Initial position value: $5,000 in ETH/USDC LP
This means: $2,500 in ETH (1.25 ETH) + $2,500 in USDC
price_ratio = $3,000 / $2,000 = 1.5
IL = 2 × 1.2247 / 2.5 - 1
IL = 2.4494 / 2.5 - 1
IL = 0.9798 - 1
IL = -0.0202 or -2.02%
$2,500 in ETH → $3,750 (ETH +50%)
$2,500 in USDC → $2,500 (no change)
Total: $6,250 (+25% overall gain)
If you held in LP:
Pool rebalances due to constant product formula
Your share is now worth: $6,250 × 0.9798 = $6,123.75
Impermanent Loss: $6,250 - $6,123.75 = -$126.25 (-2.02%)
+ Trading Fees Earned (30% APR over 1 year): +$1,500
= Net Gain: +$1,373.75
Conclusion: Despite 2.02% IL, the 30% APR from fees far exceeds the loss.
Key Insight: Fees vs. Impermanent Loss
Liquidity providers profit when fee income > impermanent loss. In Strategy 1 (ETH/USDC LP), you earn 30% APR from trading fees, which typically outweighs IL unless ETH makes extreme moves (>2x or <-50%).
For this assignment: Calculate IL for each scenario, then add the 30% APR to determine net returns.
Pre-Computed IL Table (Use This to Save Time)
| Price Change | Price Ratio | Impermanent Loss (%) | LP Value vs. HODL |
|---|---|---|---|
| ETH -75% | 0.25 | -20.00% | 80% of HODL value |
| ETH -50% | 0.50 | -5.72% | 94.28% of HODL value |
| ETH -25% | 0.75 | -1.44% | 98.56% of HODL value |
| ETH -10% | 0.90 | -0.23% | 99.77% of HODL value |
| No Change | 1.00 | 0.00% | 100% of HODL value |
| ETH +10% | 1.10 | -0.23% | 99.77% of HODL value |
| ETH +25% | 1.25 | -0.62% | 99.38% of HODL value |
| ETH +50% (Scenario A) | 1.50 | -2.02% | 97.98% of HODL value |
| ETH +100% | 2.00 | -5.72% | 94.28% of HODL value |
| ETH +200% | 3.00 | -13.40% | 86.60% of HODL value |
| ETH +300% | 4.00 | -20.00% | 80% of HODL value |
Scenario A: ETH +50%
Price Ratio: 1.5
IL: -2.02%
Calculation for $5,000 LP position:
With IL: $6,250 × 0.9798 = $6,123.75
IL Loss: -$126.25
+ Fee APR (30%): +$1,500
= Net: +$1,373.75
Scenario B: ETH Stable
Price Ratio: 1.0
IL: 0.00%
Calculation for $5,000 LP position:
With IL: $5,000 (no IL when price stable)
IL Loss: $0
+ Fee APR (30%): +$1,500
= Net: +$1,500
Scenario C: ETH -50%
Price Ratio: 0.5
IL: -5.72%
Calculation for $5,000 LP position:
With IL: $3,750 × 0.9428 = $3,535.50
IL Loss: -$214.50
+ Fee APR (30%): +$1,500
= Net: +$1,285.50
Note: Even in a bearish scenario, the 30% APR covers the IL loss. However, your total position value decreased due to ETH price decline.
Common Mistakes to Avoid
- Forgetting the square root: It's √(price_ratio), not just price_ratio
- Wrong price ratio: It's (new price / old price), not (old / new)
- Ignoring fee income: Always add the 30% APR to your LP returns
- Applying IL to non-LP strategies: Strategies 2, 3, 4, 5 have NO impermanent loss
- Confusing IL with total return: IL is just the rebalancing loss; total return includes fees and price changes
Pro Tip: When to Worry About IL
IL is manageable when:
- Price changes are moderate (±25%)
- Fee APR is high (30% in this case)
- You hold for a full year (more time to accumulate fees)
IL becomes problematic when:
- One token pumps >2x (IL exceeds -5.72%)
- Fee APR is low (e.g., 5% APR can't cover large IL)
- You withdraw early (less time to earn fees)
© Joerg Osterrieder 2025-2026. All rights reserved.