Impermanent Loss in Decentralized Finance

Instead of relying on an active market of buyers and sellers and an order book, AMM-based exchanges trade your assets against pools of tokens supplied by liquidity providers. The make-up of these pools of tokens — known as liquidity pools — is regulated by a constant algorithmic formula, which balances the ratio of tokens within the pool. This process of automated market making (AMM) allows decentralized exchanges, or DEXs, to function without intermediaries, which ensures trades are always available and never reliant on a third party.

The model results in a unique instance of asset depreciation known as impermanent loss, or divergence loss. Impermanent loss refers to when the value of the tokens inside of a liquidity pool diverges from the value of the same tokens outside of the pool. As AMM formulas prioritize a ratio balance, your asset value can differ from its value outside of the liquidity pool. If you were to trade your tokens out of the liquidity pool, it would be at a loss.

To mitigate impermanent loss and incentivize liquidity providers, decentralized finance AMMs use a stakeholder model that pays liquidity providers a percentage of all trading fees and rewards users with platform-specific tokens that can become highly valuable assets in their own right. To explain how impermanent loss works, we will examine Uniswap, a decentralized exchange protocol on the Ethereum blockchain. In Uniswap’s liquidity pools, token pairs must maintain equal total values. This balance of equal values is managed by the formula: x* y = k.

x * y = k

This formula maintains that the total value of one token in a Uniswap liquidity pool must always equal the total value of the other token in the pool. Maintaining the equal value relationship between the token pair is the basis of the automated pricing mechanism.

For example, a Uniswap pool might be made of 50% ether (ETH) and 50% DAI. When a trader comes to Uniswap to trade ETH for DAI, the quantity of ETH in the pool decreases while the quantity of DAI increases. In response to this change in quantity balance, the constant formula on Uniswap increases the price of ETH relative to DAI so the value of the pool’s ETH — once again — equals the value of the pool’s DAI.

Mathematical Example

Let’s take a look at the numbers: For simplicity, we will assume you are the only liquidity provider in a Uniswap pool made of 50% ETH and 50% DAI, and you supply 10 ETH and 1000 DAI to the pool. A liquidity pool with one provider does not present a realistic scenario, but provides a good example to understand how impermanent loss hypothetically functions.

Let’s say, hypothetically, when you enter the liquidity pool, ETH is worth $100 USD:

• The price of 1 ETH = 100 DAI

• The pool consists of 10 ETH and 1000 DAI

Then, the price of ETH doubles to $200:

• The price of 1 ETH = 200 DAI

• Arbitrageurs from outside of Uniswap come in and buy all the ETH in your pool until the price reaches 200 DAI and matches external exchanges

• Based on the x * y = k formula, the liquidity pool will now consist of:

• • 7.071 ETH and 1414.21 DAI 

  • • At the new ETH price of $200, the total value of your holdings in the liquidity pool would be:

    • • $1414.21 + $1414.21 = $2828.42 

    • If you just held on to your original 10 ETH and 1000 DAI, the total value of your holdings outside of the liquidity pool would now be:

    • • $2000 + $1000 = $3000 

    • Your impermanent loss is:

    • • $3000 – $2828.43 = $171.57

Only in the rare instance that prices return to exactly where they were when you entered the pool will impermanent loss be totally erased. The greater the divergence between assets in the pool, the greater the impermanent loss. In this scenario, if the price of ETH went down instead of up, you would have still experienced a similar magnitude of impermanent loss. In decentralized finance AMM liquidity pools made up of similarly behaving assets like Curve, impermanent loss is greatly reduced since the divergence of relative prices in the pool is limited.

In practice, if you were to go to Uniswap to become a liquidity provider, your experience would be less extreme than our hypothetical example above. You would not be the sole liquidity provider, but would instead be one of thousands providing various amounts of ETH and DAI to the liquidity pool at different times. Though the magnitude of the impermanent loss could still be similar to our example, calculating the exact value of the loss becomes exponentially more complex as you have to factor in thousands of other liquidity providers independently and asynchronously interacting with your liquidity pool.

Automated Market Maker Rewards

To mitigate impermanent loss within the decentralized finance ecosystem and incentivize users to supply tokens to liquidity pools, AMM platforms pay trading fees to liquidity pools and providers, and often distribute platform tokens to users. On Uniswap, liquidity providers earn a 0.3% fee every time a trade occurs. For liquidity providers, more trading and more volatility means more money. With enough trading volume on the platform, liquidity providers can accumulate fees to negate the occurrence of impermanent loss.

Recently, AMMs have begun establishing reward systems for liquidity providers via project-based tokens. For example, if you provide tokens to a designated Uniswap liquidity pool distributing token rewards, you can earn UNI tokens on Uniswap. Providing tokens to the right Balancer or Curve pools would earn you BAL or CRV tokens. These tokens can be used elsewhere in the decentralized finance ecosystem and traded on exchanges. The accumulation of fees and the value of reward tokens can not only offset impermanent loss, but make being a liquidity provider profitable.

However, becoming a profitable AMM liquidity provider largely depends on timing and circumstance. If you provide tokens to the right liquidity pool in a time of high trading activity, you can accumulate a considerable amount of fees.