What is Impermanent Loss?
Impermanent Loss refers to the temporary loss caused by market fluctuation when a Liquidity Provider (LP) injects liquidity to a certain liquidity pool. According to the "Constant Product Market Maker Formula" algorithm of AMM, when an LP removes liquidity during market fluctuation, the value of his withdrawal might be lower than the value of the assets he provided when injecting liquidity. This is what we called impermanent loss. However, with the revenues accumulation and price fluctuations, impermanent loss will gradually be wiped out.
Examples for Impermanent Loss
(1) Assuming that there are 900 CET and 900 USDT in the CET/USDT liquidity pool at the moment, and now the price of 1 CET = 1 USDT.
(2) Liquidity Provider(LP) Adam has added 100 CET and 100 USDT to the pool, thus there will be a total of 1,000 USDT and 1,000 CET. Adam now owns 10% of the assets in the pool, and the value of his assets is 200 USDT.
(3) Assuming that Trader Ben sold 100 CET and his order was executed in the CET/USDT liquidity pool.
According to the rules of CPMM (Constant Product Market Maker), the product of the quantities of the two assets is 1000 * 1000 = 1,000,000. Since Ben sold 100 CET to the pool, now there were 1,100 CET in the pool, and the total number of USDT is 1,000,000 / 1100 = 909.091 USDT.
So, how many USDT does Ben get for selling 100 CET? The answer is: 1000 - 909.091 = 90.909 USDT.
At this time, 1 CET = 0.826 USDT. At this time, the liquidity pool is imbalanced.
(4) Assuming that LP Adam is going to remove the liquidity at the above time, since he owns 10% of the total pool assets, in total he can remove 10% * 1,100 CET+ 10% * 909.091 USDT, that is, 110 CET and 90.9 USDT. The value of 110 CET + 90.9 USDT would be worth of 0.826 * 110 + 90.9 = 181.76 USDT.
(5) When adding liquidity, LP Adam owned a total value of 200 USDT. However, when removing liquidity, he only gets 181.76 USDT. So the impermanent loss for LP Adam is 18.24 USDT.
*To simplify the calculation, the trading fee is not considered during the process.
Impermanent Loss Estimation
Here’s a chart of estimated Impermanent Loss for your references:
Change after adding liquidity |
Impermanent Loss (Loss comparing adding liquidity with hodling) |
-60% |
9.65% |
-30% |
1.57% |
-10% |
0.14% |
0% |
0.00% |
10% |
0.11% |
30% |
0.85% |
60% |
2.70% |
100% |
5.72% |
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