AMMs, DEXS and Impermanent Loss

As Decentralized Finance (DeFi) has experienced a continued boom in the past six months, we have seen a rise in decentralized exchanges (DEX), the largest of which being UniSwap, SushiSwap, and PancakeSwap. These DEX’s rely on automated market marking (AMM) technology, which uses an algorithm and game theory to create a working exchange-- “DEX.” AMM’s utilize liquidity pools to generate liquidity for specific pairs; this technology relies on arbitragers to govern the price, which introduces impermanent loss (IL), something that users will incur when providing liquidity to these protocols.

Before we jump into IL, last week’s installment of Cryptonomics covered Decentralized Exchanges in-depth. I highly suggest touching upon the subject to better understand Impermant Loss, especially for those who do not know how DEX’s operate.

What is Impermanent Loss (IL)

Impermanent loss is a loss of funds that a user will incur when they provide liquidity. The name impermanent stems from the fact that the loss is temporary and can be recovered if asset prices return to their original state, which often does not happen. This loss is calculated based on your deposited assets’ worth at the time of deposit versus each asset’s current value.

Liquidity providers must provide their assets in 1:1 ratio, 50/50 CAKE/BNB, for example. The AMM then uses this liquidity to facilitate transactions and arbitragers will ensure that the price reflects the “true” price among all exchanges. AMM technology relies on this arbitrage to maintain the correct price; on the other side of the arbitrage are the liquidity providers, selling or buying at a premium. This is most visible in high volatility pairs with low correlation as there is continuously an arbitrage opportunity that users will take advantage of. Impermanent loss is pertinent in traditional liquidity pools due to the arbitrage opportunity the AMM technology relies on.

IL example

So let’s use a BNB/CAKE pool, for example. Lets assume that BNB = $40 and CAKE = $0.50

Currently, if a user wants to provide liquidity 2BNB($80) worth of CAKE/BNB they would deposit 1 BNB and 80 CAKE as liquidity pools require a 1:1 ratio of assets.

This also means that one BNB is equivalent to 80 CAKE at the deposit time, resulting in a total deposit of $80. There is not only one user in this liquidity pool; for example, lets assume 1 BNB and 80 CAKE results in 1% of the total pool share, meaning the pool contains 100 BNB and 8000 CAKE. So what happens when the price changes?

Let’s say the price of CAKE begins rising on the Binance exchange to $1 per CAKE token; users will take advantage of this arbitrage opportunity buying CAKE from the AMM and selling it on Binance, causing liquidity providers IL through taking advantage of the temporary price discrepancy. The best way to understand this is that the CAKE ratio is changing in the pool; instead of the collection consisting of 100 BNB and 8000 CAKE, it now consists of 150 BNB and 4000 CAKE, as the ratio must remain 1:1. So what happened to our initial users share?

The user’s share is now 1.5 BNB and 40 CAKE, which equates to $100, but if this user held each asset individually, they would instead have $120. This is the impermanent loss in action, as arbitragers begin to buy CAKE with BNB, the pool shifts’ ratio, allowing the arbitragers to profit off the liquidity providers.

This same scenario will play out when the price of an asset decreases. As arbitragers take advantage of the price discrepancy, the liquidity providers will have more of the “weaker” token to balance the pool ratio.

Impermanent Loss Overview

Impermanent loss is bound to occur in all liquidity provision scenarios. The most common way of realizing the loss is through comparing the value of LPing vs. Holding each asset individually (HODLing). As previously mentioned, impermanent loss affects users equally whether the price goes up or down.

The following graph has been developed to display the effects of IL:

This graph shows IL based on price change without accounting LP incentives. The chart displays the following data:

a 1.25x price change results in a 0.6% loss relative to HODL
a 1.50x price change results in a 2.0% loss relative to HODL
a 1.75x price change results in a 3.8% loss relative to HODL
a 2x price change results in a 5.7% loss relative to HODL
a 3x price change results in a 13.4% loss relative to HODL
a 4x price change results in a 20.0% loss relative to HODL
a 5x price change results in a 25.5% loss relative to HODL

Overall, these figures are essential to keep in mind as they give liquidity providers an idea of how much they should be compensated while providing liquidity. If a user knows they will receive more in rewards than lost in IL, it is most likely a no-brainer to provide liquidity.

Why Provide Liquidity?

From a glance, it seems like it makes no sense for users to provide liquidity to AMM’s, but there is more. Impermanent loss has been factored in by these DEX’s, so they give liquidity providers incentives to combat this risk. Typical AMM’s allocate a .3% trading fee to liquidity providers, which allows LP’s to profit based on the transaction volume.

On top of this, most AMM’s offer additional rewards to liquidity providers by providing users with governance tokens. LP’s are heavily incentivized to provide liquidity between the transaction fees and governance rewards, making it worthwhile for specific pairs.

Correlation In a Bull Market

Typically the best assets to pair together are ones that have a high correlation and are not volatile. While it is hard to find un-volatile assets in the crypto-space, it is much easier to find correlated assets. This rings especially true in the bull market phase as crypto markets are highly auto-correlated. 

Auto-correlation refers to the delayed correlation or copy, meaning cryptocurrencies will typically behave very similarly over time.

This brings us into an undiscussed power of liquidity providing. As price fluctuates and one asset outperforms another, you end up selling the more expensive asset for the "lagging" one. This acts as a portfolio that rebalances profits into the underperforming token. This rebalancing can be extremely powerful, considering how heavily correlated crypto assets are. If and when the other token “catches up”, it will have allowed the user to maximize the gains as the user caught both of the assets rallies.

We have a Dive Into DeFi article which specifically outlines these aspects of liquidity provision. 

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Stay SAFU

Overall, IL is a crucial concept that all liquidity providers must understand. It is inevitable and will be present in all liquidity pools, besides stablecoin pools with perfect correlation. IL is not a reason to avoid LPing; it is just a cost that comes with earning the additional rewards.

The key is weighing the opportunity costs of HODLing assets individually vs. LPing them to earn extra rewards at the expense of impermanent loss. If the liquidity rewards outweigh the IL potential, then why would a user not participate in liquidity provision? With every investment, that is the most challenging part, recognizing and understanding the most optimal investment.

I hope this article helps beginner and experienced users better understand the underlying risk of providing liquidity and impermanent loss. It isn’t a reason not to provide liquidity, but merely an investment aspect, which users will incur in nearly all LP situations.

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