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Types of Loss: Impermanent Loss and Its Compatriots

Understanding various forms of loss and how they occur.

Written by

Ariana Fariab

Published on

December 29, 2023

Impermanent loss (IL) has been getting more attention lately as DeFi liquidity providers have begun seeing the permanent impact it can have on their returns. However, amid the consternation over losses, there also seems to be some confusion about what impermanent loss means and its distinction from other losses investors may face. This article breaks down different types of loss, with the aim of equipping LPs with the language to understand various forms of loss and how they occur.

At face value, losses appear straightforward. But often the same net result can have various root causes. For example, let’s pretend the price of ETH is $1k. You buy 1 ETH and hold it for two days. On day two, your ETH is worth $900, indicating a loss of $100. Why did this $100 loss occur? Of course, because the value of ETH dropped 10% relative to USD. This is basic capital loss (of course, the loss is only realized if you sell). Now, how about instead of holding your ETH, you decide to day trade it. Three days after your original purchase, the price of ETH is back to $1k. However, you made some bad trades and now only have 0.9 ETH, netting you a $100 loss on your principal. In this case, trading resulted in a loss of ETH, not capital loss. In these examples, the net result of the two strategies is the same, but the causes of the loss differ. Of course, it’s also possible for both of these types of loss to occur simultaneously, creating a compounded effect. These forms of loss will be obvious to most, but they lay a good foundation for thinking about different modes of loss.

Opportunity Cost and Loss vs. a Benchmark

More abstract ways of viewing loss could include opportunity cost and “loss” versus a chosen benchmark. What I’ll call “opportunity cost loss” is when a chosen strategy or asset underperforms alternatives of roughly equivalent or less risk. For example, if you decide to buy ETH instead of SOL and a month later ETH is up 15% and SOL is up 40%, the opportunity cost of not having bought SOL is a 25% return on capital. Other examples could include yield farming or borrow/lend strategies vs. HODLing. Any case where HODLing would have produced better returns can also be thought of as “loss vs. HODLing” (still a form of opportunity cost).

“Loss” versus a benchmark is essentially a subset of opportunity cost. It occurs when a strategy or asset underperforms the chosen benchmark. A common example of this is in traditional finance, the S&P 500 is often used as a benchmark for hedge fund or individual asset performance. If a fund underperforms SPY, its limited partners may view this as a loss versus an industry standard benchmark.

Impermanent Loss

Impermanent loss is a form of opportunity cost that’s the product of price divergence and adverse selection. It occurs when LPs provide liquidity to a pool and, upon withdrawal, the value of their retrieved assets is less than if they had held the original assets themselves (“loss vs. HODLing”).

Here’s how IL occurs:

IL occurs in CPMM-based liquidity pools due to the way the XYK constant product formula prices tokens. This is best explained via an example.

Let’s say you’re an LP in a dual-asset ETH<>USDC pool. This pool requires that token pairs be added and removed in a 1:1 price ratio, so you deposit 1 ETH and 1,000 USDC. At the time of deposit, the total dollar value of your provision is $2k. The pool now contains 10 ETH and 10,000 USDC. You own a 10% share of this pool.

Asset prices within CPMM DEX pools don’t automatically adjust with external market prices. Instead, they’re determined by the formula x*y = k, which moves exchange prices according to token ratios while maintaining liquidity as a constant product. In our example pool, x represents the quantity of ETH, y represents the quantity of USDC, and k is the constant product from which token prices are derived. This tells us that this pool must maintain a constant product of 100,000 (10 ETH * 10,000 USDC = 100,000).

Continuing our example, let’s say the external market price of ETH rises to $4k. Pool prices won’t adjust to reflect this without trading activity, so there’s an arbitrage opportunity. Arbitrageurs rush in and buy the underpriced ETH until it realigns with external markets. This results in a pool of 5 ETH and 20,000 USDC. At this point, you decide to withdraw your liquidity. Your 10% share now entitles you to .5 ETH and 2,000 USDC–a total dollar value of $4k. That’s double your $2k deposit–pretty good, right? But remember, this gain came solely from a price change in ETH (we haven’t gotten to fees yet). What if you had simply held your original 1 ETH and 1,000 USDC instead of depositing it into the pool? You would now have $5k instead of $4k. That’s a 20% impermanent loss.

It’s important to understand that IL arises from any divergence in asset prices–in either direction–between deposit and withdrawal. If ETH had risen to $4k and then dropped back down to $1k by the time you withdrew your liquidity, the loss wouldn’t have been realized (like how capital loss isn’t realized until you sell). That’s where the “impermanent” in impermanent loss comes from. However, seeing as crypto prices are constantly changing, the likelihood of this “impermanence” is low. Divergence loss is a better name, as the loss that is realized stems from price divergence. This system is obviously problematic as it exacerbates losses and eats into gains–quite counterproductive to profit-seeking.

Keep in mind that the above calculation neglects the trading fees LPs earn for providing capital to the pool (the whole point of LPing). In theory, if those yields are high enough they can offset IL, ideally making LPs profitable despite it. In practice, this is tough to accomplish. To use an example, if the price of an underlying asset moved 40% in the month’s time between when an LP deposited and withdrew their liquidity, they would need to have been earning a consistent 20.14% APY just to break even on IL. For context, Uniswap V3’s current median APY is 18.44%. Plus, no matter how high yields from fees are, if there’s impermanent loss, a portion of those yields will always be eaten away by it–which is still counterintuitive to maximizing returns.

Note that impermanent loss is a product of CPMMs specifically and not all DEXs. It can be circumvented with alternative AMM models, such as Clipper’s FMM.

Let’s Talk About Loss

As we can see, loss has many different forms and root causes, despite similar net results. It’s important for investors and LPs to consider the causes of each type of loss to determine if losses can be mitigated or avoided, as well as the soundness of different strategies and protocols. In the case of liquidity pools that produce impermanent loss, does this cost support a sustainable yield-generation strategy?

Probably not.

Written by

Ariana Fariab

Published on

December 29, 2023

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