# Understanding Impermanent Loss in Defi
## TLDR
- Impermanent Loss (IL) is the opportunity cost of a liquidity provider (LP)
- It's the difference between the value of your deposited assets in the pool versus simply holding them.
- IL is paper loss unless the LP closes its position
## What's Impermanent Loss (IL)?
Impermanent Loss is **the opportunity cost experienced by a liquidity provider (LP)** when the value of their deposited assets in a liquidity pool changes compared to simply holding those assets.

IL = Value of holding the assets - Value of deposited assets in the liquidity pool

**It's "impermanent" because the loss is only realized (becomes permanent) when LP withdraw its liquidity from the pool.** If the prices of the assets return to the ratio they were when LP deposited, the impermanent loss disappears.

## Example Walk Through
> Interactive excel file: https://ab9jvcjkej.feishu.cn/sheets/L8M3snjLvhtANYtKZA4cXbGxn5g
### Initial deposit
You are the first LP, so you set the initial price.

- You deposit 100 ETH and 10,000 DAI
- At that moment, the implied pool price is:
- Price of ETH in DAI = 10,000/100 = 100 DAI/ETH
- The constant `k = 100 * 10,000 = 1,000,000`
### External Price Changes
- On CEX, ETH price goes up to 110
- Now there's a price discrepancy:
- Pool still thinks ETH = 100 DAI
- Market says ETH = 110 DAI
- Arbitrageurs will buy ETH from the pool (since it's cheaper there) until the pool price matches 110 DAI/ETH (minus gas & slippage).
### Arbitrage Trades Adjust the Pool
- After trades, the new reserves x′(ETH) and y′(DAI) must satisfy:
- `x' * y' = k = 1,000,000`
- The marginal price in the pool equals the external market price: `y' / x' = 110`
- So we solve:

    y' = 110 x'
    110 x' * x' = 1,000,000 => x' = 95.3
    y' = 110 * x' = 10,488.1

### Final pool state after arbitrage
- ETH: ≈ 95.3 ETH
- DAI: ≈ 10,488.1 DAI
### Value of LP position vs Holding original asset
- Value of LP position

    95.3 * 110 + 10,488.1 * 1 = 20,976

- Value of holding original asset

    100 * 110 + 10,000 * 1 = 21,000

- Impermanent loss
`20,976 - 21,000 = -24`

## Cause of IL
### Price volatility between token pair
- Core cause: IL arises when the relative price of the two tokens in a pool changes after user deposits.
- The greater the price divergence from the initial deposit ratio, the larger the IL.
### Use of constant product formula
- Core cause: Most AMMs uses this formula (xy = k), which forces rebalancing via arbitrage
- When external prices change, arbitrageurs trade against the pool to align its internal price with the market — **extracting value from LPs in the process**.
- This mechanical rebalancing **sells low and buys high** from the LP’s perspective, causing underperformance vs. holding.
### Lack of correlation between assets
- Pools with **uncorrelated or inversely correlated assets** suffer more IL.
- In contrast, **stablecoin pairs** have minimal IL because their prices stay near 1:1.
- Even **two volatile but highly correlated assets** (eg. ETH/wstETH) can reduce IL.
### Pool design & Fee structure
- Low-fee pools (eg. 0.05% on stable pairs) may not generate enough fee income to offset IL during volatility
- High-fee pools (eg. 1% on exotic pairs) can compensate for IL - but only if trading volume is sufficient

## Methods to Mitigate IL

| Strategy | How It Helps |
|--------------------------------------|------------------------------------------------------------------------------|
| Provide liquidity in stablecoin pairs | Minimal price divergence → near-zero IL |
| Use concentrated liquidity (eg. Uniswap v3) | Limit exposure to expected price range, reducing IL outside that range |
| Choose high-fee + high-volume pools | Trading fees can offset or exceed impermanent loss |
| Deposit correlated assets (e.g., stETH/ETH) | Lower relative volatility between tokens reduces IL |
| Hedge externally (advanced) | eg. short one asset to neutralize delta and lock in value |

## Reference
- What's IL by Finematics: https://www.youtube.com/watch?v=8XJ1MSTEuU0
- What is Impermanent Loss in Crypto? by Whiteboard crypto: https://www.youtube.com/watch?v=_m6Mowq3Ptk
- 6 Ways to Avoid Impermanent Loss by Whiteboard crypto: https://www.youtube.com/watch?v=oyriORaeJOw
- Impermanent Loss In Crypto by Milk Road: https://milkroad.com/guide/impermanent-loss/

## Discussion
Found an error? Have questions?
- Twitter: [@chloe_zhuX](https://x.com/Chloe_zhuX)
- Telegram: [@Chloe_zhu](https://t.me/chloe_zhu)
- GitHub: [@Chloezhu010](https://github.com/Chloezhu010)

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*Last updated: Nov 17th, 2025*
*Part of my #LearnInPublic Defi series*