How Does the Constant Product Formula (X Y = K) Relate to Impermanent Loss?
The constant product formula, x y = k, dictates the relationship between the quantities of the two tokens (x and y) in the pool, where k is a constant. When the external price of one token changes, arbitrageurs trade with the pool to maintain the price equilibrium.
To keep k constant, a change in x must be accompanied by a proportional, inverse change in y. This forced rebalancing to maintain the invariant k is precisely what causes the liquidity provider's asset value to diverge from the HODL value, resulting in impermanent loss.
Glossar
Concentrated Liquidity
Allocation ⎊ ⎊ Concentrated liquidity represents a departure from traditional automated market maker models by enabling liquidity providers to specify precise price ranges where their capital will be deployed, fundamentally altering capital efficiency.
Constant Product Formula
Formula ⎊ The Constant Product Formula, a cornerstone of Automated Market Makers (AMMs) like Uniswap, dictates the relationship between the reserves of two tokens within a liquidity pool.
Liquidity Depth
Resilience ⎊ Liquidity depth, within cryptocurrency and derivatives markets, signifies the capacity of an order book to absorb substantial orders without experiencing disproportionate price movements; it’s a critical measure of market health and operational robustness.
Constant Product
Invariant ⎊ The core principle dictates that the product of the quantities of the two assets in a liquidity pool remains constant, represented mathematically as $x cdot y = k$, where $x$ and $y$ are the reserves of the two tokens.