Have you ever provided liquidity to a liquidity pool just to realize that your coins is missing? In this article i will explain what impermament loss is and how it can affects liquidity providers profits.

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Impermament Loss

In essence, impermament loss is

• Temporary loss of funds occuring when providing liquidity

• It is often explained as the diferrence between holding an asset versus providing liquidity

• Usually observed in standard liquidity pools where the liquidity provider (LP) provides assets in a correct ratio; one of the assets is volatile in relation with the other

Example:

In UNISWAP DAI-ETH50/50 liquidity pool, if ETH goes up in value, the pool relies in arbitrageurs continually ensuring that the pool price reflects the real world price to maintain the same value of both tokens in the pool.

This basically leads to a situation where profit from the token that appreciated in value is taken away from the liquidity provider. At this point, if the liquidity provider decides to draw tgeir liquidity, the impermament loss becomes permanent.

Easiest Way to Understand Impermament Loss

Example:

A liquidity provider provides liquidity to a DAI-ETH5050 liquidity pool. To supply liquidity in a 50/50 pool, the liquidity probiders should provide an equal value of both tokens to the pool.

| price | supplied | value |

DAI $1 10000 $10000

ETH $500 20 $10000

So far so good, the value of the tokens is the same.

The price of ETH goes up in an external venue such as coinbase. Now, coinbases ETH price is $550, this is where other market participants called arbitrageurs come into play.

Arbitrageurs notices the price diferrence between coinbase and uniswap and sees that as an opportunity to make a profit.

Uniswap uses a constant product market maker to maintain correct ratio of tokens in the pool. So, as more ETH is bought in the pool, the higher the price of ETH becomes.

Arbitrageurs buys cheaper ETH in uniswap until there is no more price discrepancy between the two exchange.

Lets see how much ETH the arbitrageus needs to buy to make this happen.

By plugging the external price to a formula (x*y=k) that can be derived in a constant product market maker formula, we can see that the point the uniswap price will be $550 is when there are 10,488.09 DAI and 19.07 ETH in the pool.

So basically arbitrageurs need to buy 0.93 ETH in order to achieve equlibrium between uniswap and coinbase ETH price costing 488.09 DAI and achieving average price of 524.83 ETH/DAI.

Both ETH can be easily sold for DAI or any other USD based stablecoin on an external venue for $550.

Arbitrageurs just earned $25 less the fees.

Lets see how this liquidity affects the liquidity provider.

Before arbitrageurs,the liquidity providers had 10,000 DAI plus 20 ETH at the price of $500. The total assets is $20000.

After the arbitrageus, there is 10,488.09 DAI plus 19.07 ETH with a price of $550 each. The asset now reached $20,976.59.

If the liquid provider simply held the asset without providing liquidity, the Liquidity provider will end with 10000 DAI 20 ETH at the price of $550 each. The total asset now is $21,000.

The liquid provider will have 23.41 dollars more if they just held their asset and not provide liquidity. This $23.41 dollars is the liquidity provider's impermament loss.

Impermament loss is called impermament because the liquidity provider loss $23.41 only on the paper.

Of the liquidity provider doesn't withdraw their liquidity and the price of ETH goes back to 500 dollars, the impermament loss is cancelled back to zero.

On the other hand, if the liquidity provider decides to withdraw thwir liquidity, they would realize the oss of $23.41 permanent.

How can you take aways liquidity providers profit as the value of an asset increases in relation to the other?

Example: if the price of an asset goes up by 500%, the liquidity provider will experience 25% impermament loss

So if impermament loss can take away so much profit, what are the incentives of the liquidity provider to provide liquidity? To understand that, let's see how liquidity provider make money on their capital.

In the perfect world where there are no impermament loss, the liquidity provider would just be collecting moneys from the trading fees.

Example: in Uniswap, each trade that goes to liquidity pool pay as your 0.3% fee that is proportionally distributed to the liquidity providers of that pool.

This shows that liquidity providers still profit even with impermament loss under the condition that the impermament loss is smaller than the collected fees.

On top of that, majority of pools give incentives for liquidity providers by offering LP tokens. The value of additional tokens, sometimes can negate the loss by the impermament loss making providing liquidity highly profitable.

Providing Liquidity to other Pools aside from Uniswap

Example: curve pools holds assets with similar of the same value. This could be different stablecoins like USDC or DAI or different flavors of the same tokens such as SBTC, RENBTC and WBTC.

The risk of impermament loss is greatly minimised as there are no assets in the pool whose value is volatile in relation to the other.

All liquidity pool that holds stable assets usually attract more capital than a pool with no stable assets.

Another example: balancer offers pools that are arbitrary weight outside the standard 50/50 model. This means that for example, the liquidity providers wants to make higher exposure to a certain asset, they can participate in a pool where one token has much higher weight than the other such as 80/20, 98/2 pool. This can also reduce the imoact of impermament loss depending on the weight on the pool.

The higher the weight of token in the pool, the lesser the difference between holding the token and providing liquidity in that token becomes.

Example: bancor v2 pools adjusted their weight automatically based on external prices coming from price oracles.

This can mitigate impermament loss even with volatile assets with certain trade offs.