Impermanent loss refers to the value "loss" that occurs when tokens' prices change after you had deposited your assets to a liquidity pool, compared with simply holding the assets in your wallet. It is the result of fluctuations in the underlying value of the assets being swapped, and happens whenever the relative prices of the tokens change. It is always negative.
When you provide liquidity to a concentrated liquidity pool, your gains and losses are amplified. Your capital efficiency and share of trading fees are higher, but so is your impermanent loss. The formula below can be used to calculate impermanent loss in a concentrated liquidity position.
Formula to calculate impermanent loss as a percentage change.
- L, liquidity of concentrated liquidity position
- p_a, p_b, the price range of concentrated liquidity position
- x, amount of asset X in the concentrated liquidity position
- y, amount of asset Y in the concentrated liquidity position
- k, price ratio, when there is a price movement to P’ = Pk where k > 0
- V_1, the value of the holding if kept in the pool (x, y move with price)
- V_held, the value of the holding if kept outside of the pool (x, y constant)
Consider a simple example where p_a/P = 1/n and P/p_b = 1/n. If the price range is roughly between 2*current price and 1/2*current price (the default ratio), the impermanent loss is nearly 4 times higher than with a CPMM model. If the current price moves beyond your chosen price range, the impermanent loss is even higher.
In the example below, we are using the same setup as above. With three sets of 1 ETH + 2,000 USDC, at ETH/USDC = 2,000, we will (1) provide liquidity to a Traditional AMM liquidity pool, (2) provide liquidity to a Concentrated Liquidity pool, and (3) HODL it in our wallet.
Comparison among LP value of traditional AMM liquidity position, LP value of Concentrated liquidity position, and value of HODL position
By comparing the two liquidity provision positions and the HODL position, we can find impermanent loss of the positions against ETH/USDC price movements. The gap between the purple and blue curves represents the impermanent loss of our liquidity position in the Traditional AMM liquidity pool. The gap between the purple and orange curves represents the impermanent loss of our liquidity position in the Concentrated Liquidity pool. The graph below is a visualization of impermanent loss of both our positions from another angle.
What the graph above shows is that a concentrated liquidity position has a greater value of potential impermanent loss than a traditional AMM liquidity position. The narrower the range of concentrated liquidity provided, the higher the potential impermanent loss ratio.
Please note that impermanent loss is not a real loss of your investment, instead, it is more like asset appreciation forgone compared to a HODL position. To compensate for this, protocols usually reward LPs with trading fees and yield farming rewards.
As defining an optimal price range of concentrated liquidity is a tricky business, we strongly suggest liquidity providers to consider the following parameters:
- 1.Potential impermanent loss in the selected price range
- 2.Whether expected trading fee income can cover impermanent loss along price movement
- 3.Fee-tiers of the selected price range
Liquidity providers should actively monitor whether the current price of the token has moved out of their selected price range. If and when that happens, only one of the tokens would remain in the position, and the entire position becomes inactive. As the token price continues to change, the impermanent loss associated with the position will also change accordingly. Therefore, a liquidity provider can either wait until the token price returns to his/her selected price range, or adjust the range according to the current price.
Crypto traders often hedge their risks using tools such as perpetual futures contracts and leverages. However, Uniswap v3, the first DEX to utilize the Concentrated Liquidity Market Maker model, did not offer any options for hedging.