What is Impermanent Loss?

Impermanent loss (IL), in English ‘temporary loss’, is a phenomenon that has made its appearance with the advent of decentralized finance (DeFi). The ‘temporary loss’ is the result of an algorithmic rebalancing formula that AMM protocols use.

Simply put, the term ‘temporary loss’ is used to describe the difference in value between holding tokens in an AMM protocol on the one hand and holding those same tokens outside the protocol on the other. Only when prices return to exactly where they were when you entered the pool will there be no more loss. If the price does not return and you were to trade your tokens at that time, you would do so at a loss.

 

 

The video below explains ‘impermanent loss’ in detail.

How is impermanent loss calculated?

Because AMM rebalancing formulas prioritize a predetermined ratio, the value of your tokens may differ from the value of those same tokens outside the pool. To better understand how an impermanent loss works exactly, let’s look at an example:

In this example, the rebalancing volume will maintain the ratio of the two tokens 50/50 at all times.

1. We provide liquidity to a pool consisting of 50% ETH and 50% USDC.

The tokens we will add are 1 ETH and 1000 USDC.
At the time we add these tokens the prices are equal to;

1 ETH = $1000
1000 USDC = $1000

2. Due to extreme volatility, the price of Ethereum doubles
1 ETH = $2000

3. The rebalancing formula of the AMM protocol is going to balance the quantity of tokens. So that the value of ETH in the pool is equal to the value of USDC in the pool. Since the price of ETH has doubled, 0.5 ETH will equal the quantity of USDC.

1 ETH = $2000 → 0.5 ETH = $1000
1000 USDC = $1000

4. Because 0.5 ETH is sold to arbitrageurs to keep the quantity in proportion. Will the sale cause 500 USDC to be added to your USDC holdings.

0.5 ETH = $1000
1500 USDC = $1500
Total = $2500

5.
We now decide to withdraw our tokens from the protocol. Even though we have more USDC than at the beginning, our amount of Ethereum has decreased. So we would have had more if we had kept our tokens in our wallet.

1 ETH = $2000
1000 USDC = $1000
Total = $3000

As long as prices do not change due to volatility, no “impermanent loss” will occur. But if the price of a token rises, liquidity providers lose out compared to holders of the token outside the protocol.

In the following table we see how a price increase will result in the loss of the deployed token.

Price change Token Reduction token quantity %
1.25x 0.6% Loss
1.5x 2.0% Loss
1.75x 3.8% Loss
2x 5.7% Loss
3x 13.4% Loss
4x 20.0% verlies
5x 25.5% Loss

IL schematically represented

Tools

Simple calculator

With this calculator one can calculate how much ‘impermanent loss’ one is likely to incur before providing liquidity. The initial price of the tokens at the time you are going to provide liquidity and the expected price of the tokens are needed to calculate the ‘impermanent loss’.

Conclusion

Simply put, ‘impermanent loss’, is the loss that occurs when providing liquidity compared to just keeping the tokens in your wallet. This is the result of the rebalancing formulas that keeps the balance of the number of tokens in the pool in proportion.

This risk can be solved by using pools with other ratios such as; 80/10 – 95/5 so impermanent loss will not have such a big impact. Impermanent Loss can cause problems during periods of high volatility and so is important to understand when looking to provide liquidity.