What the #$*&! Is Impermanent Loss, and Why Do I Care? Illuvium Edition - Part 1: Basics of Liquidity Pools & Impermanent Loss

What the #$*&! Is Impermanent Loss, and Why Do I Care? Illuvium Edition - Part 1: Basics of Liquidity Pools & Impermanent Loss

By Deraji | ILVFi | 30 Aug 2021

Welcome to my latest series on Illuvium!  This time, we’ll take on a more general challenge of explaining the topic of Impermanent Loss - that boogie monster that scares people away from the Sushi Liquidity Pool and it’s 600% APY (as of 8/29/2021).  In Part 1, we’ll examine the basics of DeFi, in Part 2 we start to understand the value of participating in liquidity pools, and finally in part 3, we’ll look at some examples and understand how IL can really impact your investment, and the value of staking rewards.  If you just want to skip to my conclusions and try out scenarios on your own, check out the latest version of my calculator and use the "Imperm Loss" tab to see how your investment may fare.

TL:DR - Impermanent Loss is better named Divergence Loss, and is a critical risk factor to consider before investing in liquidity pools like the ILV/ETH pool on Sushi.  The more the price of the two assets diverge, the greater your loss will be relative to just HODLing the assets.  Pool fees and staking rewards attempt to make up for this difference, though at high price divergence, you may lose money rather than just holding and not staking.  When you sell your Liquidity pool shares (SLP), you will receive less of the asset that appreciated more.  Use my calculator or other calculators online with your initial pooling price and your predicted final price to see the potential impact.

ILV - Only Two Directions on this Rocket Ship

Before we get into math and the complicated, confusing concept of Impermanent Loss (IL), let’s look at the possible outcomes for ILV.  If you only invest in the regular ILV staking pool, you essentially only care about the price of the token- either the project succeeds and the price goes up, or the project fails and the price goes down, potentially to zero.  That’s the crux of investing in crypto - there’s not a lot of middle ground yet.  If you’re in a blockchain project for long enough, either you pick the right horse and you get your lambo, or your dream crashes and burns into nothing.  Illuvium is no exception to this.  The price has run up 15x in just a couple months, and there is still no product to speak of.  While I’m long ILV, there is still a very real chance that the project fails, the ILV token crashes, and investors lose everything.  Cool.  

The other option in the cryptoverse is that this project takes off, achieving its goal of not just being the leader in the play-to-earn (P2E) space, but steals gamers (and their money) away from incumbents like EA and Activision Blizzard.  In that case, the fully decentralized organization of Illuvium distributes 100% of all revenue to staking token holders and rewrites the gaming industry.  It’s your call which is more likely and decide your own probability adjusted returns based on the likelihood for each of these scenarios.

Liquidity Pool Problems - the Third Option

The challenge with liquidity pools is that they introduce a third option, divergence.  While the ILV pool just cares if the project goes well or the project crashes, the liquidity pairs care about how the project performs COMPARED to a third entity.  In the case of the ILV liquidity pair, this entity is Ethereum.  Staking the liquidity pair requires acquiring equal dollar amounts of both ETH and ILV.  With this, you introduce a huge connection to Ethereum’s performance.  The three options for your investment performance now are

  • (1) the project bombs, and ILV crashes, you lose a lot of/all your money
  • (2) both ILV and ETH are incredibly successful and prices move together with their success
  • (3) ILV or ETH is much more successful than the other and the ratio of the two prices diverge 

This last scenario, where both projects are somewhat successful but one is more successful is the challenge of impermanent loss, or the better name, divergence loss (DL), as we’ll refer to it going forward.  The same issue exists if either project fails relative to the other, but that is more covered by scenario 1, a.k.a. you lose your money.  Here’s a handy spot for the disclaimer - this is for your education and not financial advice, but never invest more than you can afford to lose in a high risk project.

How liquidity pools work

It’s important that we ground ourselves in the basics of decentralized finance (DeFi) exchanges, and how they work, and why we care about divergence. (here's your chance to skip ahead if you know this stuff)  In traditional exchanges, an order book is used, where market makers set a price that they are willing to sell or buy an asset.  Market takers can see these orders, and determine if they want to become a match to a Maker, either by being willing to pay the price offered by the lowest priced seller (becoming a buyer), or accept the offer to sell to the highest priced buyer (being a seller).  Centralized exchanges operate on this one-on-one marketplace.  To make an instant transaction on a traditional exchange, you automatically just accept the price of these makers and you buy or sell the desired asset.  The difference between the highest buyer and the lowest seller is known as the spread.  The higher the liquidity in a centralized pool, the closer the spread, so buying and selling prices become very close together.

Key Idea - Centralized exchanges match makers and takers, and all orders are just one person paying another person for their asset.  The price of this exchange is set by the maker.

Decentralized Finance (DeFi) exchanges changed that model entirely.  Exchanges like Uniswap or Sushi created pools where you didn’t need to be matched to the market makers - the market was automatically made by math.  These exchanges use the Automated market making system to set a fixed ratio, or constant product formula for determining the price of an asset.  You can learn more about AMMs and the constant product model here.  

For our purposes, we’ll focus only on the ILV/ETH pair on Sushi.  In this exchange, liquidity providers have pooled equivalent dollar values of both assets, ILV and ETH, and created an automated liquidity market.  Now, anyone can come to Sushi.com and swap either their ETH for ILV, or ILV for ETH, and the trade will happen without needing to be paired to someone on the other side.  Those providing liquidity enabled this exchange to happen without their permission, and the ratio of the number of ETH and ILV in the pool sets the price to swap for the next token.  The greater the liquidity in the pool, the less likely a single order is to move the ratio significantly.  As of today (8/27/2021) there are over 194,000 ILV in the pool, paired with over 31,000 ETH, for a total pooled value of over $200 million dollars.  The average trade is around $11,000 (skewed by large trades), so individual trades only use a small portion of the liquidity.  

How AMM’s work is that the product of the two tokens is held constant (x * y = k), so to keep this formula in tact, the more of one asset that is purchased, the more expensive it becomes relative to the other.  This keeps someone from buying all of one side of the pool, as the more they buy, the more expensive it becomes.  

Key Idea - In DeFi liquidity pools, there is no maker or taker, and buyers swap automatically with the pool liquidity provided by other individuals.  The price is determined by the ratio of tokens in the pool.  A constant product formula (x * y = k) is applied to keep assets in balance.  For Sushi liquidity pairs, the assets are always 50/50 in value.  

The Binance Academy has a really good example of how impermanent loss works for the ETH/DAI pair, which also helps see how the constant product formula model works.  The ETH/ILV pair is a little more complicated as both assets can increase or decrease rather than one of them being a stablecoin.  To help understand the math for the ILV/ETH pair, let’s look at some examples.  Currently, ETH is at $3250 while ILV is at $520.  The ratio of the two if purchased today would be $3250/$520, or 6.25.  This is the ratio that someone adding liquidity to the pool cares about.  Suppose you decide to join the pool by adding liquidity, and to keep the math easy, you add 1 ETH and 6.25 ILV.  Your initial investment is $6500 (1x$3250 + 6.25x$3250, plus a bunch of ETH gas fees and three Metamask transaction approvals). 


You join a pool that already exists, and to keep life easy, we’ll say there are now 10 ETH and 62.5 ILV in the pool, meaning you own 10% of the pool.  You now will have an SLP token in your wallet that represents this share at the time of purchase.  The constant product model tells us the product for this pool is 10 ETH x 62.5 ILV = 625 (x * y = k).

Now, let’s say some time passes, no other liquidity is added, but after the Illuvium game play trailer (expected “soon”), the value of ILV jumps to $2,080, quadrupling, while ETH stays the same at $3250.  Due to the constant product model, there is now “cheap” ILV in the Sushi pool, and an investor known as an arbitrage trader sees this price discrepancy, and decides to remove the cheap ILV, swapping it with ETH.  For the new correct values of $2,080 for ILV and $3,250 for ETH, there needs to be 20 ETH and 31.25 ILV.  This keeps the constant product correct (20x31.25 = 625), and the pool is still a balanced 50/50 ratio of value (20 ETH x $3250 = $65000 = 31.25 ILV x $2080).  

What about your share of the pool?  You still own 10% of the pool, so if you were to trade your SLP token at this point, you would receive 3.125 ILV and 2 ETH.  The value of your stake would be worth $13,000 (3.125 ILV x $2080 + 2 ETH x $3250).  Awesome, you doubled your initial $6,500 investment!  

However, what if you never pooled your initial tokens at all?  You would have had 6.25 ILV now worth $13,000, plus 1 ETH worth $3250 for a total of $16,250.  This means by pooling and due to arbitrage trading, you lost $3,250 by participating in the liquidity pool, or your Divergence Loss  is 20% (Your loss divided by the HODL value of your tokens, $3,250/$16,250 = 20%).

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The ratio of ILV-to-ETH when you first joined was 6.25 (6.25 ILV per ETH).  When you exited the pool, the new ratio was 1.5625 (1.5625 ILV per 1 ETH, or $3250/$2080 = 1.5625).  


It’s really the ratio of your initial and final ratio that determines your divergence loss based on the following equation.



A key thing to note, this equation works either way, if ETH increase or ILV increases relative to each other.  No matter what, if you endure a 4x divergence in the ratio in your liquidity pool, your loss will be 20% relative to HODLing.

What’s in the name?

Impermanent Loss is a terrible and confusing name in my opinion.  Just like anything else in trading assets, all losses become very permanent as soon as you execute the sell transaction.  Divergence Loss is really a much better and somewhat more understandable name for the phenomenon, as it really refers to the loss incurred by two assets pooled in a liquidity pool diverging in their price ratio, COMPARED to the value of just HODLing the two assets.  That’s in.  Clearly, Impermanent loss makes perfect sense to describe that. <insert sarcasm here>


If your brain hasn’t exploded yet, you can continue over to part 2 where we’ll look at more examples, and understand why the heck anyone would risk this divergence loss thing.

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Crypto curious thinker, amateur economist, geriatric millennial gamer passionate about Illuvium. Happy to share my economic and financial assessment of this unique blockchain NFT Play-to-Earn project. patreon.com/ilvfi


ILVFI focuses on the upcoming P2E game, Illuvium, the first proposed AAA-quality video game based on blockchain technology and NFT ownership. We'll focus on both the game play, as well as the in-game and ILV governance token economics.

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