What is Impermanent Loss?

DEFINITION

Liquidity Mining
It is a method used to obtain more cryptocurrency by staking cryptocurrency. It is a new trend in decentralized Finance (DeFi), which enables cryptocurrency investors to invest their encrypted assets and obtain higher returns, and anyone can participate in this ecosystem. In short, this means that you can get a reward by locking up your cryptocurrency.

Liquidity Pool
Each market that supports automatic market making (AMM) has a corresponding fund pool, which will provide the AMM with funds for automatic market making. During trading, the product of the number of assets in two coins in the fund pool of the market will remain unchanged. Users can become market makers by providing liquidity for the fund pool, so as to obtain the dividends gotten by the automatic market making exchange of the fund pool according to the proportion of the fund pool. When adding liquidity, you need to add assets in two coins at the same time in proportion. When redeeming, the liquidity assets will be converted into two coins in proportion and returned at the same time.

AMM
The automatic market making robot will determine the swap price according to the ratio of two kinds of tokens in the pool. When placing an order, the trader will trade directly according to the price determined by the system. Using an algorithmic robot to simulate trading behavior in the market and provide liquidity for the market is AMM automatic market making. The automatic market making of AMM on Gate.io calculates the buying and selling price according to the "constant product market maker model" (x * y = k), so as to provide continuous quotation for the market.

Impermanent Loss
It refers to the capital loss caused by the price difference in the change of digital assets after investors deposit digital assets into the automatic market maker liquidity pool. No matter the direction of the price change, it will produce impermanent loss. The greater the deviation, the greater the impermanent loss. This is a key problem for automatic market makers at present.

Forced Multi-token Exposure
As with impermanent losses, the forced multi-token exposure is a key challenge for automatic market makers today. The forced multi-token exposure refers to the fact that automatic market makers usually require liquidity providers to deposit two different tokens to ensure equal liquidity, which means that liquidity providers cannot maintain long-term risk exposure on one token and need to increase additional reserve assets, thus increasing the forced multi-token risk exposure.

Liquidity Mining and Impermanent Loss
In the third quarter of 2021, Gate.io launched liquidity mining products, which aims to activate the slightly deserted trading market and provide users with alternative investment options. With the strong support of the platform, Gate.io liquidity mining has a very high annualized rate of return. It is one of the best cryptocurrency products in the current bull market.

Now go to Gate.io Liquidity Mining →

To participate in liquidity mining, users can pledge their own tokens to provide token liquidity for the liquidity pool, and obtain the handling fee dividend from the automatic market making transaction of the fund pool according to the proportion of the fund pool. For the principle of liquidity mining and how to participate in liquidity mining, please refer to:

FAQ - Liquidity Mining
Gate.io Cryptopedia: How to Get Liquidity Mining Yields?
Science: What You Need to Know About Investments in Liquidity Mining Products
Science: From Market Maker to Liquidity Mining, How Important is Liquidity?

Determination of Price in Liquidity Pool

In the process of participating in liquidity mining, impermanent loss is one of the main risk types to be considered. When providing liquidity to the pool, users need to stake two different tokens. In the liquidity pool, the number of two tokens will be balanced according to a specific algorithm. In Gate.io liquidity mining, the number of two tokens is balanced according to the "constant product market maker model" (x * y = k). For any specific equilibrium point (A,B), the exchange ratio between the two tokens is p (x / y) = A / B, that is, the price is determined by the ratio of the two tokens in the liquidity pool and changes in real time with the change of the liquidity pool.

When other users trade with the liquidity pool, the proportion of the two assets in the liquidity pool will be changed. We take the ETH/USDT liquidity pool as an example. If a user trades with the liquidity pool and spends USDT to buy ETH, the number of ETH in the pool is bound to decrease and USDT is bound to increase. In order to keep the product of ETH and USDT constant in the liquidity pool all the time, the decrease of ETH must meet a certain relationship with the increase of USDT. According to the mathematical analysis, the relationship between the two is (the number of USDT increases) / (the number of ETH decreases) = (the immediate number of USDT in the pool) / (the immediate number of ETH in the pool), and the ratio between the number of USDT increases and the number of ETH decreases can also be regarded as the asset price in the liquidity pool.

Since there is no arbitrage opportunity in the effective market, the asset price in the liquidity pool is often close to the real price of the asset. Take the real ETH/USDT liquidity pool at a certain time as an example. At this time, the ETH quantity is 186.88 and the USDT quantity is 349,581. According to the formula, the USDT / ETH price in the liquidity pool should be 349,581 / 186.88 = 1,870.62, which is close to the market price of ETH at that time of $1872.87.

Calculation of Impermanent Loss

We already know that with the transactions between other users and the liquidity pool, the proportion of the two assets in the liquidity pool will be different from that when users first inject the two assets. However, when users retrieve assets, they retrieve them according to the changed asset proportion. Next, we will demonstrate by calculation why no matter which direction the price of digital assets changes, it will cause impermanent losses.

We take a simple GT/USDT capital pool as an example, and ignore the transaction fee.

1. Assuming that there are 9 GT and 900 USDTs in the GT/USDT capital pool, 1GT=100 USDTs and the total liquidity is 1800 USDs.
2. User Alice provides one GT and 100 USDTs for the GT/USDT fund pool, so there are 10 GTs and 1000 USDTs in the fund pool. The liquidity value held by user Alice is 200 USDs, accounting for 10%. At this time, the total liquidity of the pool is 2000 USDs.

The situation of GT price increase:

3. In the external market, the price of GT rose to 400 USDTs, when the trader Bob traded with the liquidity pool for arbitrage. Bob bought GT from the pool and put USDT into the capital pool until the price of GT in the pool also rose to 400 USDTs.
4. Although the quantity product of the two tokens in the fund pool remains unchanged, the ratio of GT to USDT in the pool has changed, GT decreases and USDT increases. Due to Bob's transaction, there are 5 GTs and 2000 USDTs in the pool. (i.e. 10GT*1000USDT=5GT*2000USDT)
5. At this time, user Alice decides to redeem all the funds. Her share accounts for 10%, so he can redeem 0.5 GT and 200 USDTs. The total value according to the market price is 0.5 * 400 + 200 = 400 USDs.
6. If user Alice chooses to hold 1GT and 100 USDTs all the time, the total value of the assets will reach 1 * 400 + 100 = 500 USDs. Instead, she can get higher revenue, which is the impermanent loss when the price rises, accounting for 20%.


The situation of GT price decrease:

3. In the external market, the price of GT fell to 25 USDTs, when the trader Bob traded with the liquidity pool for arbitrage. Bob sold GT to the pool and withdrew USDT from the fund pool until the price of GT in the pool also fell to 25 USDTs.
4. Although the quantity product of the two tokens in the fund pool remains unchanged, the ratio of GT to USDT in the pool has changed. GT increases and USDT decreases. Due to Bob's transaction, there are 20 GT and 500 USDTs in the pool. (that is, 10GT*1000USDT=20GT*500 USDT. At this time, the GT price in the liquidity pool is 500 / 20 = 25 USDTs, which is the same as that in the external market)
5. At this time, user Alice decides to redeem all the funds, and her share accounts for 10%, so she can redeem 2 GTs and 50 USDTs, with a total value of 2 * 25 + 50 = 100 USDs.
6. If user Alice chooses to hold 1GT and 100 USDTs all the time, the total value of the assets will reach 1 * 25 + 100 = 125 USDs. On the contrary, she can get higher revenue, which is the impermanent loss when the price falls, accounting for 20%.

According to the English definition of "impermanent loss", it actually refers to "temporary loss" or "non permanent loss". This is because the impermanent loss is not the loss that has been realized in the general sense, but the potential loss compared with the originally available income. No matter whether the asset price rises or falls, the impermanent loss will appear, but if the asset price returns to the original level before taking out the liquidity, the impermanent loss will disappear.

Frequently Asked Question (FAQ)

1. What is the scale of impermanent loss?
The following table can be obtained by calculating the proportion of impermanent loss with the change of price.


Draw the data in the table into a graph to get the relationship between the change of token price and impermanent loss.


When the change of token price is small, the scale of impermanent loss is generally small. Only when the token price falls by more than 60% or rises by more than 150%, the impermanent loss is likely to exceed 10%.


Taking the real GT/USDT liquidity pool as an example, the GT/USDT in the liquidity pool at a certain time is 6.85774:

Case 1: when GT/USDT rises to 9 (approximately 31%), the impermanent loss is only 0.92%.
Case 2: when GT/USDT rises to 12 (approximately 75%), the impermanent loss is only 3.79%.
Case 3: when GT/USDT falls to 5 (approximately 27%), the impermanent loss is only 1.23%.
Case 4: when GT/USDT falls to 3 (approximately 56%), the impermanent loss is only 7.98%

2. Once the impermanent loss occurs, can it not be recovered?
No, it isn't. Impermanent loss is only a temporary loss, which will be realized only when the liquidity is retrieved from the liquidity pool.

As long as the token price returns to the level when liquidity is put before liquidity is extracted, the impermanent loss will disappear.

3. Considering the impermanent loss, is it worth participating in liquidity mining?
It's generally worth it. When the token price changes little, the scale of impermanent loss is generally small, which is far lower than the handling fee income of liquidity mining.

Users can view the relationship between commission rate of return and impermanent loss on the liquidity mining page.





Author: Gate.io Observer: Edward.H
Disclaimer:
* This article represents only the views of the observers and does not constitute any investment suggestions.
*Gate.io reserves all rights to this article. Reposting of the article will be permitted provided Gate.io is referenced. In all other cases, legal action will be taken due to copyright infringement.

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