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What is Impermanent Loss?

Impermanent Loss is the difference in asset value between holding assets in the wallet (HODL) and holding assets in the liquidity pool.

Impermanent Loss is most common in traditional pools where the liquidity provider (LP) must provide both assets in equal proportions and one of the assets is volatile in comparison to the other.

Impermanent Loss is exemplified by Uniswap’s DAI/ETH liquidity pool, where both tokens are represented in a 50:50 ratio:

  1. Stake in a pool of 1 ETH and 1,000 DAI.
  2. After a week, 1 ETH is equal to 2,000 DAI.
  3. If we had stored 1 ETH and 1000 DAI, the profit would be 50% (the value of 1000 DAI would not change, but the price of 1 ETH would increase to 2000 DAI).
  4. Staking tokens in the AMM pool on Uniswap yields less than 50% profit than simply storing assets.

Impermanent or unrealized losses are so named because they are not fixed until the liquidity tokens are withdrawn from the pool. In the preceding example, there are no impermanent losses if the price of ETH returns to the original 1,000 DAI and funds are withdrawn thereafter.

Uniswap, SushiSwap, and other similar AMMs use a simple formula:

x ∗ y = k

x is the number of tokens for asset A;

y is the number of tokens for asset B;

k is the so-called constant product of the pool — this value does not change.

Example of the Uniswap exchange DAI/ETH liquidity pool. Data: The Chain Bulletin.

The contract held tokens with an approximate value of $153.5 million — 29,116.6 WETH and 76.7 million DAI.

Using the formula above, we calculate the value of k for this pool at this time:

29 116,63 ∗ 76 737 921,22 ≈ 2,23 ∗ 10¹²

k changes only when users add or withdraw liquidity, or when transactions are charged a fee (for example, 0.3% in the case of Uniswap). These funds are added to the total liquidity in the pool.

Impermanent Loss in the classic pools

Example of Uniswap exchange DAI/ETH liquidity pool:

  1. When we stack 1 ETH and 100 DAI, the liquidity provider’s share is 10%.
  2. The pool contains 10 ETH and 1000 DAI.
  3. A week later 1 ETH trades for 200 DAI.
  4. There are no commissions in the pool.
  5. We calculate the non-permanent losses.

To determine the exact share in the pool (in each token), you can use Uniswap Analytics and SushiSwap Analytics platforms or third-party tools Croco Finance, Growing and APY.vision

Why should pool commissions be considered?

Commissions are an integral element of the economics of AMM-based platforms.

The higher the commission, the lower the non-permanent loss. When a certain amount of trading fees is reached, participation in the pool generates more profit than holding assets.

Let’s take the preceding example above and add a component in the form of commission:

  1. We steak in a pool of 1 ETH and 100 DAI;
  2. Our steak share is 10% (in a pool of 10 ETH and 1000 DAI);
  3. After a week, 1 ETH trades for 200 DAI;
  4. Commissions: 1 ETH and 100 DAI.

The non-permanent loss, excluding trading commissions, is 17.179 DAI. Because we have a 10% stake in the pool, we are entitled to 0.1 ETH and 10 DAI of the accumulated commissions. Given that ETH is currently trading at 200 DAI, 0.1 ETH is worth 20 DAI, and the total profit from commissions is 30 DAI. The total is thus $312,821 ($282,821 + $30).

Insert these new numbers into the formula — stackingUSD/storageUSD — 1:

312,821/300–1 ≈ 0,042 ≈ 4,2%

In this example, the non-permanent loss is -12,821 DAI (17,179–30). This is not a loss but a 4.2% gain because assets are held in the pool rather than held individually.

Does Impermanent Loss work in other pools?

Curve is a decentralized stabelcoin and tokenized bitcoin exchange based on an automated market maker mechanism. Its pools contain only assets that must have the same or comparable value: stabelcoins (USDC, DAI) or tokenized bitcoins (renBTC, wBTC). The risk of volatile losses in such pools is minimal.

Balancer provides token pools with arbitrary token ratios. For example, if a liquidity provider wants to supply a large number of specific tokens, it can select a pool in which those coins are weighted more heavily than others (the proportions can be 80/20 or even 98/2). In addition, this model minimizes non-permanent loss. The greater a token’s share of a pool, the smaller the difference in outcomes between holding a token and providing liquidity in that token.

Bancor version 2 pools automatically adjust token weights based on price oracle data. This allows you to reduce volatile losses even in pools containing volatile assets.

How to calculate Impermanent Loss easily?

Understanding Impermanent Loss is necessary for any user of AMM platforms. You can make your own IL calculations using the calculator at dailydefi.org (based on Uniswap formulas).

In general, regardless of price movements, AMM protocol users are always exposed to the risk of foregone costs. In comparison to custody, when asset prices rise, a participant’s position grows less; when prices fall, they lose more.

Trading commissions and income farming come to the rescue, helping to neutralize volatile losses so that participation in the AMM pool yields more profit than simply holding assets.

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