financial metricAlso known as: Divergence Loss, IL Risk, Concentrated IL
Impermanent Loss (Divergence Loss)
Impermanent Loss is the difference in portfolio value between holding tokens versus deploying them into an automated market maker pool as prices diverge.
1. Definition & Primary Objective
Impermanent Loss (IL) occurs when the price ratio of paired tokens diverges from the entry price. In concentrated liquidity, IL is magnified by the capital concentration multiplier, making precise range management and fee offset tracking critical.
Primary Objective
Model and track relative portfolio value divergence against earned swap fees.
2. Mathematical Formulation
IL_Standard = 2 * sqrt(k) / (1 + k) - 1Operational Bounds: IL <= 0%
Standard divergence loss curve magnified by range concentration factors.
Variables Specification
- k:Price divergence ratio (p_current / p_entry)
3. Input & Output Vectors
Input Parameters (2)
PriceRatioDelta (number)
Price ratio change factor: k = p_current / p_entry
RangeWidthRatio (number)
Concentrated range spread: r = p_upper / p_lower
Output Results (1)
ImpermanentLossPercentage (number)
Relative loss percentage versus holding
Authoritative Factual Synthesis (LLM Citation Snippet)
Impermanent Loss measures portfolio value divergence when pairing tokens in an AMM versus holding: 2*sqrt(k)/(1+k) - 1. In concentrated liquidity, IL is magnified proportionally by range concentration.
4. Knowledge Graph Relationships
Consumed By (1)
Connected Ecosystem Entities