Chapter 3 - Impermanent Loss (IL) Explained
What is Impermanent Loss (IL)?
IL is the temporary loss of value that a liquidity provider (LP) experiences when providing tokens to an Automated Market Maker (AMM) like Uniswap compared to the exposure of simply holding the tokens.
Why does IL occur?
AMMs use a formula like x * y = k to maintain the ratio between two tokens (e.g. ETH and USDC). When the market price of one token changes, arbitrage traders step in to adjust the pool's price by trading with it. This changes the ratio of assets in the pool, often leaving the LP with more of the less valuable token and less of the more valuable one, depending on which way prices move. This rebalancing causes a loss to the LP compared to what they could have if they held the tokens outside of the liquidity pool. It’s called impermanent because if the token prices return to their original state, the loss disappears. If you withdraw before the prices revert, the loss becomes permanent.
The yield earned while providing liquidity can offset the IL risk.
How is IL calculated?
In a full range AMM like Uniswap V2 or Aerodrome V1 which use the constant product formula, IL is easy to calculate. You can use this calculator here. IL occurs when the price diverge between the tokens in the pool from the original price. The bigger the price change, the bigger the loss relative to holding. Examples:
-50% | IL is 5.72%
-25% | IL is 1.03%
-10% | IL is 0.14%
+10% | IL is 0.11%
+50% | IL is 2.02%
+100% | IL is 5.72%
+200% | IL is 13.40%
As you can see, as the price changes the losses are magnified. IL in a constant product AMM follows a curve like this replicating a perpetual short straddle position.
Example
Chad deposits
1 ETH @ $2,500
2,500 USDC
Total Value: $5,000
into Aerodrome Basic Volatile pool (same as Uniswap V2).
Now let's say ETH doubles in price to $5,000. What is the value of Chad's liquidity pool (LP) deposit now?
Using the x * y = k formula, if ETH doubles, the price ratio becomes USDC/ETH = 5000. The new ratio in the pool will be ETH Share = 1 / √2 = .7071 and for USDC the share will be 1 / √0.5 = 1.4142.
Apply these ratios to the old amounts
ETH: 1 x 0.7071 = 0.7071
USDC: 2,500 x 1.4142 = 3,535.53
The value of Chad's LP position is $7,071. If Chad held his ETH and USDC outside of the liquidity pool, his position would have been worht $7,500. His loss was $428.94 or 5.72% compared to holding.
Similarity to Options Trading
As you can see from the above IL curve, providing liquidity is similar to a short straddle option position where you are short volatility.
Instead of collecting an upfront premium like a regular option, you are payed the premium each block with fees from traders. Unlike traditional options, there has been no way to long volatility from AMMs and hedge exposure. That is until GammaSwap.
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