Concentrated Liquidity and Impermanent Loss

Chris M. Hiatt
3 min readDec 16, 2021

Summary: Price range pools concentrate liquidity inside that range and therefore increase capital efficiency, but that comes at the price of maximised impermanent loss outside that range.

Preliminary concepts:

(The following is optimised for people with at least a rudimentary understanding of those concepts; apologies to everyone else.)

The crucial aspects I want to bring forward are the following:

  • IL is not an absolute thing, it is defined as a difference to just holding the assets in your wallet. See the figure below.
  • When the price leaves the range of the pool in question, your provided liquidity will be converted 100% into the losing asset of the two. This is akin to being exposed to the maximally possible IL.
Comparison of different investment strategies. Given two assets called “base” and “other”, the x-axis shows the price of “other” denominated in “base”, while the y-axis shows the strategies’ respective portfolio’s value, measured in “base”: Value = balance_base + balance_other * Price

IL is computed as the difference in value between the strategies “hodl” and “pool”:

  • “hodl” just holds the assets in a given ratio — for simplicity’s sake, two assets, split 50:50 in value, no rebalancing later.
  • “pool” provides the same portfolio instead to a constant-product-AMM liquidity pool with those two tokens.

Since once the price crossed the range-boundary (in the example: above 2 and below 0.5) you’d only be exposed to the base-currency (former case) or the other one (the latter). In both cases the red lines describing both portfolios’ value are straightforward to draw.

An intuitive explanation is: IL happens because one of the defining differences of (most current) AMMs compared to traditional market makers is that the trader automatically adjusts the prices with their trade according to some given rule, whereas the latter adjusts the prices themselves. They need to be adjusted at all because if they were not, arbitrageurs would be having a field day: They would acquire the complete supply offered by the market maker at the wrong price, in order to resell it somewhere else at the correct quote. But by automatically correcting the price with each trade we put a limit to such opportunities.

The to-be-prevented, worst-case state however seems quite similar to the situation we are in while the price range is exited: Our assets consist entirely of the losing asset, we are unable to be arbitraged further, but that provides little solace.

The reason I take the time to point all that out is: Yes, technically range pools protect from IL, in the sense that the capital becomes inactive as long as the boundaries are crossed, and therefore is obviously not influenced anymore by price-movements. That however is achieved by pulling the (hypothetical) price-points of maximised IL — which are respectively at 0 and infinity — into the realm of reasonable numbers in the form of precisely the boundaries of the pool-defining price range.

We at MetaDEX.fi (formerly Mirqur.io) will still be offering range pools, as they allow far more sophisticated ways of providing liquidity to our more advanced users. Still, users need to be aware that this is not a tool of insurance but refinement, the latter of which tends to be an opposite of the former.

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