How Can Path-Dependent Volatility, as Opposed to Simple Price Change, Affect the Actual Realized Impermanent Loss?

Simple price change calculations for impermanent loss only consider the start and end prices. However, path-dependent volatility ▴ the journey the price takes between two points ▴ can significantly impact realized loss.

High volatility along the path generates more trading fees for the liquidity provider. Therefore, a volatile path that ends at the original price ratio could result in a net gain for the LP, while a smooth path to a new price might result in a loss not fully covered by fees.

The actual outcome depends on the fees accrued versus the divergence loss.