CLAMM Series 5: Impermanent Loss of a Tick

CLAMM Series 5: Impermanent Loss of a Tick

Let’s Cover Impermanent Loss of a Ticks

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In the last discussion, we explored tick composition in CLAMMs, with the main takeaways being:

  1. Spot Price > Tick: Position is 100% in $ETH.
  2. Spot Price < Tick: Position is 100% in $USDC.
  3. Spot Price within Tick: Position is a mix of $ETH and $USDC.

Building on this, we now dive into impermanent loss (IL)—the difference in value of holdings when providing liquidity compared to holding assets directly.

Understanding Impermanent Loss

If you deposit 1 $ETH into a CLAMM tick, it will be either 1 $ETH or $USDC equal to the tick price (e.g., $1,750 for the $1,750 tick). While holding 1 $ETH retains its exact value, LP positions can fluctuate with market price, resulting in IL.

Impermanent Loss at the Tick Level

Consider an LP with 1 $ETH deposited in the $1,750 tick. This LP is willing to hold either 1 $ETH or $1,750 in $USDC in exchange for trading fees. Let’s examine IL as the price of $ETH changes:

  1. If Spot Price < $1,750: Suppose the price falls to $1,600. The position remains fully in $ETH, retaining the 1 $ETH initially deposited, but now worth $1,600. There is no IL in terms of $ETH quantity.
  2. If Spot Price > $1,750: Suppose the price rises to $1,900. The position is now fully in $USDC, holding $1,750. Since $ETH is now worth $1,900, this position is equivalent to only 0.92 $ETH, resulting in an IL of 0.08 $ETH.

Impermanent Loss Calculation

The LP’s position changes as the spot price fluctuates:

  • At $1,600: Composition is 100% $ETH, holding 1 $ETH, equal to the starting amount but worth less in USD.
  • At $1,900: Composition is 100% $USDC, holding $1,750. In $ETH terms, this is 0.92 $ETH, leading to an IL of 0.08 $ETH.

Summary

Impermanent loss arises from the rebalancing of an LP’s position as the spot price shifts:

  1. When $ETH < Tick price, holdings remain in $ETH, with no IL.
  2. When $ETH > Tick price, holdings are in $USDC, with IL in terms of $ETH.
  3. IL represents the difference between the value held in the tick versus holding $ETH directly.

In the next lesson, we’ll delve further into CLAMMs, exploring how impermanent loss ties into broader strategies within decentralised finance.

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