How to Calculate Impermanent Loss in DeFi

Impermanent loss is a phenomenon encountered by individuals providing liquidity to decentralized finance (DeFi) protocols, particularly within automated market maker (AMM) liquidity pools. It represents a potential divergence in value compared to simply holding the underlying assets outside the pool.

Understanding Impermanent Loss

Impermanent loss occurs when the price ratio of assets within a liquidity pool changes from the ratio at the time of the initial deposit. This difference arises because automated market makers maintain a constant product formula, X multiplied by Y equals K, where X and Y are the quantities of the two tokens in the pool, and K is a constant. When external market prices of these tokens fluctuate, arbitragers interact with the pool to bring its internal prices in line with the broader market. This rebalancing act means liquidity providers end up with a different proportion of the two assets than they initially deposited.

The “loss” is not necessarily an absolute reduction in the dollar value of the investment, but rather an opportunity cost. It signifies that the value of the assets held within the liquidity pool has become less than the value those same assets would have if they had been held directly in a wallet instead. This divergence becomes more pronounced as the price difference between the pooled assets widens. For instance, if one asset significantly increases or decreases in price relative to the other, the impermanent loss grows.

The term “impermanent” indicates that this loss is only realized if the liquidity provider withdraws their assets from the pool before the asset prices return to their original deposit ratio. If prices revert, the impermanent loss diminishes or even disappears. However, if the price divergence persists or increases, and the liquidity provider decides to exit the pool, the impermanent loss becomes a realized difference in the value of their holdings compared to a simple buy-and-hold strategy.

Key Inputs for Calculation

Calculating impermanent loss requires gathering specific data points from both the time of the initial deposit and the current moment. The initial prices of both assets at the exact time they were added to the liquidity pool are necessary. These historical prices establish the baseline ratio against which future changes will be measured. Similarly, the current prices of both assets are needed to determine the present price ratio and the current value of the pooled assets.

The initial quantity of each asset deposited into the pool is also a fundamental input. This allows for a clear understanding of the original investment and provides the basis for comparing the value of pooled assets to simply holding them. For example, if a user deposited 1 Ether and 2,000 USDC, these quantities form the starting point for the calculation.

These inputs allow for a direct comparison between the value of assets held within the liquidity pool and the value of those same assets if they had never been pooled. Without accurate initial and current price data, and precise quantities, quantifying the divergence is impossible.

Step-by-Step Calculation

To calculate impermanent loss, one must first determine the change in the price ratio between the two assets since the initial deposit. A common approach involves comparing the value of the assets if simply held against their value when provided as liquidity in a constant product market maker pool. For instance, assume an initial deposit of 10 ETH and 20,000 USDC into a pool where ETH is priced at 2,000 USDC. The initial total value of this holding would be 10 ETH $2,000 + 20,000 USDC = $40,000.

Now, consider a scenario where the price of ETH increases to 4,000 USDC, while USDC remains stable at $1. If these assets were simply held, their value would be 10 ETH $4,000 + 20,000 USDC = $60,000. Within the liquidity pool, the constant product formula (xy=k) ensures that the product of the quantities of the two tokens remains constant. Since the initial K was 10 ETH 20,000 USDC = 200,000, new quantities of ETH and USDC in the pool must satisfy this product.

At the new price of 4,000 USDC per ETH, the pool would rebalance. The ratio of assets in the pool would adjust to reflect the new external price. Specifically, if the price of ETH is now 4,000 USDC, then for every 1 ETH, there are 4,000 USDC in the pool’s ratio. Solving for x and y where xy = 200,000 and y/x = 4000 (or y = 4000x), we find x (ETH) is approximately 7.071 and y (USDC) is approximately 28,284.

The current value of the pooled assets would then be 7.071 ETH $4,000 + 28,284 USDC = $28,284 + $28,284 = $56,568. Comparing this to the $60,000 value if the assets were simply held, the impermanent loss is $60,000 – $56,568 = $3,432. This represents the financial difference between the two strategies. The loss can also be expressed as a percentage of the held value, in this case, $3,432 / $60,000 = 5.72%.

Interpreting Calculation Outcomes

The calculated impermanent loss value provides insight into the financial performance of providing liquidity compared to a static holding strategy. When expressed as a percentage, it directly quantifies the proportional difference in value. A positive percentage indicates that holding the assets would have yielded a higher value than providing them to the liquidity pool. Conversely, a zero or negative percentage would imply no impermanent loss, or even a gain relative to holding, which can happen if asset prices revert to their initial ratio.